# bibtab

bibtype: article
filename: elefunt.bib
label: Zhang:1995:TMAb
author: J. Zhang
title: Tau-method approximations for the Bessel function $ Y_1 (z) $
journal: j-COMPUT-MATH-APPL
volume: 30
number: 7
pages: 15--19
month: oct
monthnumber: 10
year: 1995
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(95)00121-E
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Sun Jun 12 09:26:01 2011
bibtimestamp: 2011.06.12 09:26:01 ???
URL: http://www.sciencedirect.com/science/article/pii/089812219500121E
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: J. Zhang
rawtitle: Tau-method approximations for the {Bessel} function {$ Y_1 (z) $}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
From p. 18 (conclusions section), ``We may use this method to approximate the Bessel functions of other integer orders. ldots It is therefore advisable to use the recurrence relations of the Bessel functions to compute function values for $ n > 1 $ ldots ''. [This is a similar limitation as with Chebyshev and minimax polynomial approximations: they are valid only for a single order the Bessel function.]

entry:
@Article{Zhang:1995:TMAb,
  author =       "J. Zhang",
  title =        "Tau-method approximations for the {Bessel} function {$
                 Y_1 (z) $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "30",
  number =       "7",
  pages =        "15--19",
  month =        oct,
  year =         "1995",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(95)00121-E",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Sun Jun 12 09:26:01 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/089812219500121E",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  remark =       "From p. 18 (conclusions section), ``We may use this
                 method to approximate the Bessel functions of other
                 integer orders. \ldots{} It is therefore advisable to
                 use the recurrence relations of the Bessel functions to
                 compute function values for $ n > 1 $ \ldots''. [This
                 is a similar limitation as with Chebyshev and minimax
                 polynomial approximations: they are valid only for a
                 single order the Bessel function.]",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ahrendt:1996:FHC
author: Timm Ahrendt
title: Fast High-Precision Computations of Complex Square Roots
crossref: LakshmanYN:1996:IPI
pages: 142--149
year: 1996
bibdate: Thu Mar 12 08:43:16 MST 1998
bibtimestamp: 1998.03.12 08:43:16 MST
URL: http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/
keywords: algebraic computation; algorithms; ISSAC; measurement; SIGNUM; SIGSAM; symbolic computation
acknowledgement: ack-nhfb
rawauthor: Timm Ahrendt
rawtitle: Fast High-Precision Computations of Complex Square Roots
bibsource:
http://www.acm.org/pubs/toc/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

subject:
bf I.1.2 Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Algorithms, Algebraic algorithms. bf G.1.0 Mathematics of Computing, NUMERICAL ANALYSIS, General, Numerical algorithms. bf F.1.1 Theory of Computation, COMPUTATION BY ABSTRACT DEVICES, Models of Computation, Bounded-action devices. bf G.1.5 Mathematics of Computing, NUMERICAL ANALYSIS, Roots of Nonlinear Equations, Iterative methods. bf G.1.2 Mathematics of Computing, NUMERICAL ANALYSIS, Approximation.

entry:
@InProceedings{Ahrendt:1996:FHC,
  author =       "Timm Ahrendt",
  title =        "Fast High-Precision Computations of Complex Square
                 Roots",
  crossref =     "LakshmanYN:1996:IPI",
  pages =        "142--149",
  year =         "1996",
  bibdate =      "Thu Mar 12 08:43:16 MST 1998",
  bibsource =    "http://www.acm.org/pubs/toc/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.acm.org:80/pubs/citations/proceedings/issac/236869/p142-ahrendt/",
  acknowledgement = ack-nhfb,
  keywords =     "algebraic computation; algorithms; ISSAC; measurement;
                 SIGNUM; SIGSAM; symbolic computation",
  subject =      "{\bf I.1.2} Computing Methodologies, SYMBOLIC AND
                 ALGEBRAIC MANIPULATION, Algorithms, Algebraic
                 algorithms. {\bf G.1.0} Mathematics of Computing,
                 NUMERICAL ANALYSIS, General, Numerical algorithms. {\bf
                 F.1.1} Theory of Computation, COMPUTATION BY ABSTRACT
                 DEVICES, Models of Computation, Bounded-action devices.
                 {\bf G.1.5} Mathematics of Computing, NUMERICAL
                 ANALYSIS, Roots of Nonlinear Equations, Iterative
                 methods. {\bf G.1.2} Mathematics of Computing,
                 NUMERICAL ANALYSIS, Approximation.",
  xxtitle =      "Fast high-precision computation of complex square
                 roots",
}


bibtype: article
filename: elefunt.bib
label: Balla:1996:SCB
author: K. Balla and V. H. Linh
title: The simultaneous computation of Bessel functions of first and second kind
journal: j-COMPUT-MATH-APPL
volume: 31
number: 4--5
pages: 87--97
month: feb
monthnumber: 2
year: 1996
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:26 MST 2017
bibtimestamp: 2017.03.01 21:48:26 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122195002200
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: K. Balla and V. H. Linh
rawtitle: The simultaneous computation of {Bessel} functions of first and second kind
entry:
@Article{Balla:1996:SCB,
  author =       "K. Balla and V. H. Linh",
  title =        "The simultaneous computation of {Bessel} functions of
                 first and second kind",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "31",
  number =       "4--5",
  pages =        "87--97",
  month =        feb # "\slash " # mar,
  year =         "1996",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:26 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122195002200",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Cappuccino:1996:DDH
author: G. Cappuccino and P. Corsonello and G. Cocorullo
title: Design and demonstration of high throughput square rooting circuit
journal: j-ELECT-LETTERS
volume: 32
number: 5
pages: 434
year: 1996
CODEN: ELLEAK
ISSN: 0013-5194 (print), 1350-911X (electronic) OR 00135194 (print), 1350911X (electronic)
ISSNL: 0013-5194 OR 00135194
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Electronics Letters
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220
rawauthor: G. Cappuccino and P. Corsonello and G. Cocorullo
rawtitle: Design and demonstration of high throughput square rooting circuit
entry:
@Article{Cappuccino:1996:DDH,
  author =       "G. Cappuccino and P. Corsonello and G. Cocorullo",
  title =        "Design and demonstration of high throughput square
                 rooting circuit",
  journal =      j-ELECT-LETTERS,
  volume =       "32",
  number =       "5",
  pages =        "434",
  month =        "????",
  year =         "1996",
  CODEN =        "ELLEAK",
  ISSN =         "0013-5194 (print), 1350-911X (electronic)",
  ISSN-L =       "0013-5194",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Electronics Letters",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=2220",
  summary =      "Not \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Chaudhry:1996:ACF
author: M. A. Chaudhry and N. M. Temme and E. J. M. Veling
title: Asymptotics and closed form of a generalized incomplete gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 67
number: 2
pages: 371--379
day: 29
month: mar
monthnumber: 3
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:27:48 MST 2017
bibtimestamp: 2017.02.25 12:27:48 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795000186
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. A. Chaudhry and N. M. Temme and E. J. M. Veling
rawtitle: Asymptotics and closed form of a generalized incomplete gamma function
entry:
@Article{Chaudhry:1996:ACF,
  author =       "M. A. Chaudhry and N. M. Temme and E. J. M. Veling",
  title =        "Asymptotics and closed form of a generalized
                 incomplete gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "67",
  number =       "2",
  pages =        "371--379",
  day =          "29",
  month =        mar,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:27:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795000186",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Guyot:1996:STD
author: A. Guyot and M. Renaudin and B. El Hassan and V. Levering
booktitle: Proceedings of the Ninth International Conference on VLSI Design, 1996
title: Self timed division and square-root extraction
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 376--381
year: 1996
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: A. Guyot and M. Renaudin and B. {El Hassan} and V. Levering
rawbooktitle: Proceedings of the Ninth International Conference on {VLSI} Design, 1996
rawtitle: Self timed division and square-root extraction
entry:
@InProceedings{Guyot:1996:STD,
  author =       "A. Guyot and M. Renaudin and B. {El Hassan} and V.
                 Levering",
  booktitle =    "Proceedings of the Ninth International Conference on
                 {VLSI} Design, 1996",
  title =        "Self timed division and square-root extraction",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "376--381",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper describes a self-timed integrated circuit
                 for division and square-root extraction. First it
                 concentrates on the development and the proof of a new
                 mathematical algorithm. Then the design methodology and
                 the architecture of a self-timed \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Heinrich:1996:AAF
author: Peter Heinrich
title: Algorithm Alley: a Fast Integer Square Root
journal: j-DDJ
volume: 21
number: 4
pages: 113--114, 130
month: apr
monthnumber: 4
year: 1996
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Mon Sep 2 09:09:39 MDT 1996
bibtimestamp: 1996.09.02 09:09:39 MDT
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Peter Heinrich
rawtitle: Algorithm Alley: a Fast Integer Square Root
bibsource:
http://www.ddj.com/index/author/index.htm; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Heinrich:1996:AAF,
  author =       "Peter Heinrich",
  title =        "Algorithm Alley: a Fast Integer Square Root",
  journal =      j-DDJ,
  volume =       "21",
  number =       "4",
  pages =        "113--114, 130",
  month =        apr,
  year =         "1996",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Mon Sep 2 09:09:39 MDT 1996",
  bibsource =    "http://www.ddj.com/index/author/index.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: techreport
filename: elefunt.bib
label: Hickey:1996:FSP
author: Timothy J. Hickey and Qun Ju
title: Fast, Sound, and Precise Narrowing of the Exponential Function
type: Technical report
institution: Computer Science Department, Brandeis University
address: Waltham, MA, USA 02254
pages: 113--114, 130
month: mar
monthnumber: 3
year: 1996
bibdate: Sat Nov 05 15:42:23 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.11.05 15:42:23 ???
URL: http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz
acknowledgement: ack-nhfb
rawauthor: Timothy J. Hickey and Qun Ju
rawtitle: Fast, Sound, and Precise Narrowing of the Exponential Function
entry:
@TechReport{Hickey:1996:FSP,
  author =       "Timothy J. Hickey and Qun Ju",
  title =        "Fast, Sound, and Precise Narrowing of the Exponential
                 Function",
  type =         "Technical report",
  institution =  "Computer Science Department, Brandeis University",
  address =      "Waltham, MA, USA 02254",
  month =        mar,
  year =         "1996",
  bibdate =      "Sat Nov 05 15:42:23 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.cs.brandeis.edu/~tim/Papers/eiianuia.ps.gz",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Homeier:1996:CAI
author: H. H. H. Homeier
title: On Convergence Acceleration for the Iterative Solution of the Inverse Dyson Equation
journal: j-J-MOL-STRUCT-THEOCHEM
volume: 368
pages: 81--91
year: 1996
CODEN: THEODJ
ISSN: 0166-1280 (print), 1872-7999 (electronic) OR 01661280 (print), 18727999 (electronic)
ISSNL: 0166-1280 OR 01661280
note: Proceedings of the 2nd Electronic Computational Chemistry Conference.
URL: http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM954
fjournal: Journal of molecular structure. Theochem
keywords: convergence acceleration
journalURL: http://www.sciencedirect.com/science/journal/01661280
rawauthor: H. H. H. Homeier
rawnote: Proceedings of the 2nd {Electronic Computational Chemistry Conference}.
rawtitle: On Convergence Acceleration for the Iterative Solution of the Inverse {Dyson} Equation
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Homeier:1996:CAI,
  author =       "H. H. H. Homeier",
  title =        "On Convergence Acceleration for the Iterative Solution
                 of the Inverse {Dyson} Equation",
  journal =      j-J-MOL-STRUCT-THEOCHEM,
  volume =       "368",
  pages =        "81--91",
  year =         "1996",
  CODEN =        "THEODJ",
  ISSN =         "0166-1280 (print), 1872-7999 (electronic)",
  ISSN-L =       "0166-1280",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the 2nd {Electronic Computational
                 Chemistry Conference}.",
  URL =          "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM954",
  fjournal =     "Journal of molecular structure. Theochem",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01661280",
  keywords =     "convergence acceleration",
  tech =         "Technical Report TC-QM-95-4, Institut f{\"u}r
                 {Physikalische} und {Theoretische Chemie,
                 Universit{\"a}t Regensburg, D-93040 Regensburg}, 1995",
}


bibtype: techreport
filename: elefunt.bib
label: Homeier:1996:KMP
author: H. H. H. Homeier
number: Homeier:1996:KMP
institution: inst-IPTC
address: inst-IPTC:adr
pages: 81--91
year: 1996
URL: http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM962
keywords: convergence acceleration
rawauthor: H. H. H. Homeier
title:
Zur Konvergenzverbesserung der Moller--Plesset Storungsreihe (English: On Convergence Acceleration of the Moller--Plesset Perturbation Series)

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

note:
Poster CP 14.77, Fruhjahrstagung des Arbeitskreises Festkorperphysik bei der DPG, Regensburg 1996. Abstract: Verhandl. DPG (VI) 31, 2165-2166 (1996).

rawnote:
Poster CP 14.77, {Fr{\"u}hjahrstagung des Arbeitskreises Festk{\"o}rperphysik bei der DPG, Regensburg 1996}. Abstract: Verhandl. DPG (VI) 31, 2165-2166 (1996).

rawtitle:
{Zur Konvergenzverbesserung der M{\o}ller--Plesset St{\"o}rungsreihe} ({English}: {On} Convergence Acceleration of the {M{\o}ller--Plesset} Perturbation Series)

entry:
@TechReport{Homeier:1996:KMP,
  author =       "H. H. H. Homeier",
  title =        "{Zur Konvergenzverbesserung der M{\o}ller--Plesset
                 St{\"o}rungsreihe} ({English}: {On} Convergence
                 Acceleration of the {M{\o}ller--Plesset} Perturbation
                 Series)",
  number =       "Homeier:1996:KMP",
  institution =  inst-IPTC,
  address =      inst-IPTC:adr,
  year =         "1996",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Poster CP 14.77, {Fr{\"u}hjahrstagung des
                 Arbeitskreises Festk{\"o}rperphysik bei der DPG,
                 Regensburg 1996}. Abstract: Verhandl. DPG (VI) 31,
                 2165-2166 (1996).",
  URL =          "http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCQM962",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Ito:1996:SRI
author: Masayuki Ito and Naofumi Takagi and Shuzo Yajima
title: Square rooting by iterative multiply-additions
journal: j-INFO-PROC-LETT
volume: 60
number: 5
pages: 267--269
day: 8
month: dec
monthnumber: 12
year: 1996
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
MRclass: 68M07
MRnumber: 97i:68014
bibdate: Wed Nov 11 12:16:26 MST 1998
bibtimestamp: 1998.11.11 12:16:26 MST
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
corpsource: Dept. of Inf. Sci., Kyoto Univ., Japan
journalURL: http://www.sciencedirect.com/science/journal/00200190
treatment: T Theoretical or Mathematical
rawauthor: Masayuki Ito and Naofumi Takagi and Shuzo Yajima
rawtitle: Square rooting by iterative multiply-additions
bibsource:
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

keywords:
computer arithmetic; convergence of numerical methods; digital arithmetic; iterative methods; iterative multiply-additions; linear converging ratio; multiplicative methods; Newton--Raphson method; read-only storage; ROM sizes; square root algorithm

entry:
@Article{Ito:1996:SRI,
  author =       "Masayuki Ito and Naofumi Takagi and Shuzo Yajima",
  title =        "Square rooting by iterative multiply-additions",
  journal =      j-INFO-PROC-LETT,
  volume =       "60",
  number =       "5",
  pages =        "267--269",
  day =          "8",
  month =        dec,
  year =         "1996",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68M07",
  MRnumber =     "97i:68014",
  bibdate =      "Wed Nov 11 12:16:26 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  classification = "C4130 (Interpolation and function approximation);
                 C5230 (Digital arithmetic methods)",
  corpsource =   "Dept. of Inf. Sci., Kyoto Univ., Japan",
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
  keywords =     "computer arithmetic; convergence of numerical methods;
                 digital arithmetic; iterative methods; iterative
                 multiply-additions; linear converging ratio;
                 multiplicative methods; Newton--Raphson method;
                 read-only storage; ROM sizes; square root algorithm",
  treatment =    "T Theoretical or Mathematical",
}


bibtype: article
filename: elefunt.bib
label: Jeffrey:1996:UBL
author: D. J. Jeffrey and D. E. G. Hare and Robert M. Corless
title: Unwinding the branches of the Lambert $W$ function
journal: j-MATH-SCI
volume: 21
number: 1
pages: 1--7
month: jun
monthnumber: 6
year: 1996
ISSN: 0312-3685 (print), 1475-6080 (electronic) OR 03123685 (print), 14756080 (electronic)
ISSNL: 0312-3685 OR 03123685
bibdate: Sat Oct 06 09:02:19 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2018.10.06 09:02:19 ???
URL: http://www.appliedprobability.org/data/files/TMS%20articles/21_1_1.pdf
fjournal: The Mathematical Scientist
acknowledgement: ack-nhfb
journalURL: http://www.appliedprobability.org/content.aspx?Group=tms&Page=allissues
rawauthor: D. J. Jeffrey and D. E. G. Hare and Robert M. Corless
rawtitle: Unwinding the branches of the {Lambert $W$} function
entry:
@Article{Jeffrey:1996:UBL,
  author =       "D. J. Jeffrey and D. E. G. Hare and Robert M.
                 Corless",
  title =        "Unwinding the branches of the {Lambert $W$} function",
  journal =      j-MATH-SCI,
  volume =       "21",
  number =       "1",
  pages =        "1--7",
  month =        jun,
  year =         "1996",
  ISSN =         "0312-3685 (print), 1475-6080 (electronic)",
  ISSN-L =       "0312-3685",
  bibdate =      "Sat Oct 06 09:02:19 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.appliedprobability.org/data/files/TMS%20articles/21_1_1.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Mathematical Scientist",
  journal-URL =  "http://www.appliedprobability.org/content.aspx?Group=tms&Page=allissues",
}


bibtype: unpublished
filename: elefunt.bib
label: Kahan:1996:TCR
author: W. Kahan
title: A Test for Correctly Rounded SQRT
pages: 4
year: 1996
bibdate: Mon Apr 25 05:47:38 2005
bibtimestamp: 2005.04.25 05:47:38 ???
note: Lecture notes.
URL: http://www.cs.berkeley.edu/~wkahan/SQRTest.ps
keywords: floating-point arithmetic; rounding errors
acknowledgement: ack-nhfb
rawauthor: W. Kahan
rawnote: Lecture notes.
rawtitle: A Test for Correctly Rounded {SQRT}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Unpublished{Kahan:1996:TCR,
  author =       "W. Kahan",
  title =        "A Test for Correctly Rounded {SQRT}",
  pages =        "4",
  year =         "1996",
  bibdate =      "Mon Apr 25 05:47:38 2005",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Lecture notes.",
  URL =          "http://www.cs.berkeley.edu/~wkahan/SQRTest.ps",
  acknowledgement = ack-nhfb,
  keywords =     "floating-point arithmetic; rounding errors",
}


bibtype: article
filename: elefunt.bib
label: Kalantari:1996:HOI
author: B. Kalantari and I. Kalantari
title: High order iterative methods for approximating square roots
journal: j-BIT-NUM-MATH
volume: 36
number: 2
pages: 395--399
month: jun
monthnumber: 6
year: 1996
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01731991
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
MRclass: 65D15 (65H99)
MRnumber: 97k:65039
bibdate: Wed Jan 4 18:52:24 MST 2006
bibtimestamp: 2006.01.04 18:52:24 MST
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: B. Kalantari and I. Kalantari
rawtitle: High order iterative methods for approximating square roots
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://www.mai.liu.se/BIT/contents/bit36.html; http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395

entry:
@Article{Kalantari:1996:HOI,
  author =       "B. Kalantari and I. Kalantari",
  title =        "High order iterative methods for approximating square
                 roots",
  journal =      j-BIT-NUM-MATH,
  volume =       "36",
  number =       "2",
  pages =        "395--399",
  month =        jun,
  year =         "1996",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01731991",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  MRclass =      "65D15 (65H99)",
  MRnumber =     "97k:65039",
  bibdate =      "Wed Jan 4 18:52:24 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=36&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.mai.liu.se/BIT/contents/bit36.html;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=36&issue=2&spage=395",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: elefunt.bib
label: Kantabutra:1996:HCE
author: V. Kantabutra
title: On hardware for computing exponential and trigonometric functions
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 3
pages: 328--339
month: mar
monthnumber: 3
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.485571
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 19:47:09 MDT 2011
bibtimestamp: 2011.07.06 19:47:09 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485571
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: V. Kantabutra
rawtitle: On hardware for computing exponential and trigonometric functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

entry:
@Article{Kantabutra:1996:HCE,
  author =       "V. Kantabutra",
  title =        "On hardware for computing exponential and
                 trigonometric functions",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "3",
  pages =        "328--339",
  month =        mar,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.485571",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 19:47:09 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=485571",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1996:PF
author: K. S. Kolbig
title: The polygamma function $ psi ^(k)(x) $ for $ x = 1 / 4 $ and $ x = 3 / 4 $
journal: j-J-COMPUT-APPL-MATH
volume: 75
number: 1
pages: 43--46
day: 12
month: nov
monthnumber: 11
year: 1996
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(96)00055-6
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:58 MST 2017
bibtimestamp: 2017.02.25 12:35:58 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042796000556
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: K. S. K{\"o}lbig
rawtitle: The polygamma function $ \psi^{(k)}(x) $ for $ x = 1 / 4 $ and $ x = 3 / 4 $
entry:
@Article{Kolbig:1996:PF,
  author =       "K. S. K{\"o}lbig",
  title =        "The polygamma function $ \psi^{(k)}(x) $ for $ x = 1 /
                 4 $ and $ x = 3 / 4 $",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "75",
  number =       "1",
  pages =        "43--46",
  day =          "12",
  month =        nov,
  year =         "1996",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(96)00055-6",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796000556",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Lang:1996:BPU
author: T. Lang and R. Wong
journal: j-J-COMPUT-APPL-MATH
volume: 71
number: 2
pages: 311--329
day: 27
month: jul
monthnumber: 7
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:56 MST 2017
bibtimestamp: 2017.02.25 12:35:56 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795002200
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: T. Lang and R. Wong
title:
``Best possible'' upper bounds for the first two positive zeros of the Bessel function $ J_v(x) $: the infinite case

rawtitle:
``{Best} possible'' upper bounds for the first two positive zeros of the {Bessel} function {$ J_v(x) $}: the infinite case

entry:
@Article{Lang:1996:BPU,
  author =       "T. Lang and R. Wong",
  title =        "``{Best} possible'' upper bounds for the first two
                 positive zeros of the {Bessel} function {$ J_v(x) $}:
                 the infinite case",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "71",
  number =       "2",
  pages =        "311--329",
  day =          "27",
  month =        jul,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:56 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795002200",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Lehoucq:1996:CEU
author: R. B. Lehoucq
title: The Computation of Elementary Unitary Matrices
journal: j-TOMS
volume: 22
number: 4
pages: 393--400
month: dec
monthnumber: 12
year: 1996
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Mon Oct 24 11:37:20 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.10.24 11:37:20 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: R. B. Lehoucq
rawtitle: The Computation of Elementary Unitary Matrices
abstract:
The construction of elementary unitary matrices that transform a complex vector to a multiple of $ e_1 $, the first column of the identity matrix, is studied. We present four variants and their software implementation, including a discussion on the LAPACK subroutine CLARFG. Comparisons are also given.

subject:
bf F.2: Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms and Problems, Computations on matrices. bf G.1.3: Mathematics of Computing, NUMERICAL ANALYSIS, Numerical Linear Algebra. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Algorithm analysis.

rawabstract:
The construction of elementary unitary matrices that transform a complex vector to a multiple of $ e_1 $, the first column of the identity matrix, is studied. We present four variants and their software implementation, including a discussion on the {LAPACK} subroutine {CLARFG}. Comparisons are also given.

entry:
@Article{Lehoucq:1996:CEU,
  author =       "R. B. Lehoucq",
  title =        "The Computation of Elementary Unitary Matrices",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "393--400",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The construction of elementary unitary matrices that
                 transform a complex vector to a multiple of $ e_1 $,
                 the first column of the identity matrix, is studied. We
                 present four variants and their software
                 implementation, including a discussion on the {LAPACK}
                 subroutine {CLARFG}. Comparisons are also given.",
  accepted =     "June 1996",
  acknowledgement = ack-rfb # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf F.2}: Theory of Computation, ANALYSIS OF
                 ALGORITHMS AND PROBLEM COMPLEXITY, Numerical Algorithms
                 and Problems, Computations on matrices. {\bf G.1.3}:
                 Mathematics of Computing, NUMERICAL ANALYSIS, Numerical
                 Linear Algebra. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Algorithm analysis.",
}


bibtype: article
filename: elefunt.bib
label: Lether:1996:RAF
author: Frank G. Lether
title: Rational approximation formulas for computing the positive zeros of $ J_0 (x) $
journal: j-J-COMPUT-APPL-MATH
volume: 67
number: 1
pages: 167--172
day: 20
month: feb
monthnumber: 2
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:27:48 MST 2017
bibtimestamp: 2017.02.25 12:27:48 MST
URL: http://www.sciencedirect.com/science/article/pii/0377042795002197
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Frank G. Lether
rawtitle: Rational approximation formulas for computing the positive zeros of {$ J_0 (x) $}
entry:
@Article{Lether:1996:RAF,
  author =       "Frank G. Lether",
  title =        "Rational approximation formulas for computing the
                 positive zeros of {$ J_0 (x) $}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "67",
  number =       "1",
  pages =        "167--172",
  day =          "20",
  month =        feb,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:27:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0377042795002197",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Li:1996:NNR
author: Yamin Li and Wanming Chu
title: A new non-restoring square root algorithm and its VLSI implementations
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 538--544
year: 1996
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Yamin Li and Wanming Chu
rawtitle: A new non-restoring square root algorithm and its {VLSI} implementations
booktitle:
Proceedings of the IEEE International Conference on Computer Design: VLSI in Computers and Processors: ICCD '96

rawbooktitle:
Proceedings of the {IEEE} International Conference on Computer Design: {VLSI} in Computers and Processors: {ICCD '96}

entry:
@InProceedings{Li:1996:NNR,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the {IEEE} International Conference on
                 Computer Design: {VLSI} in Computers and Processors:
                 {ICCD '96}",
  title =        "A new non-restoring square root algorithm and its
                 {VLSI} implementations",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "538--544",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present a new non-restoring square root algorithm
                 that is very efficient to implement. The new algorithm
                 presented here has the following features unlike other
                 square root algorithms. First, the focus of the
                 ``non-restoring'' is on the {\&} \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Lorch:1996:BPU
author: Lee Lorch and Riccardo Uberti
title: ``Best possible'' upper bounds for the first positive zeros of Bessel functions --- the finite part
journal: j-J-COMPUT-APPL-MATH
volume: 75
number: 2
pages: 249--258
day: 28
month: nov
monthnumber: 11
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:58 MST 2017
bibtimestamp: 2017.02.25 12:35:58 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042796000659
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Lee Lorch and Riccardo Uberti
rawtitle:
``{Best} possible'' upper bounds for the first positive zeros of {Bessel} functions --- the finite part

entry:
@Article{Lorch:1996:BPU,
  author =       "Lee Lorch and Riccardo Uberti",
  title =        "``{Best} possible'' upper bounds for the first
                 positive zeros of {Bessel} functions --- the finite
                 part",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "75",
  number =       "2",
  pages =        "249--258",
  day =          "28",
  month =        nov,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796000659",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: techreport
filename: elefunt.bib
label: Lozier:1996:PST
author: Daniel W. Lozier
title: A Proposed Software Test Service for Special Functions
type: Technical Report
number: NISTIR 5916
institution: pub-NIST
address: pub-NIST:adr
pages: 11
month: oct
monthnumber: 10
year: 1996
bibdate: Fri Jul 09 06:02:16 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:02:16 ???
note: Published in cite Lozier:1997:PST.
URL: http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5916.ps
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier
rawnote: Published in \cite{Lozier:1997:PST}.
rawtitle: A Proposed Software Test Service for Special Functions
entry:
@TechReport{Lozier:1996:PST,
  author =       "Daniel W. Lozier",
  title =        "A Proposed Software Test Service for Special
                 Functions",
  type =         "Technical Report",
  number =       "NISTIR 5916",
  institution =  pub-NIST,
  address =      pub-NIST:adr,
  pages =        "11",
  month =        oct,
  year =         "1996",
  bibdate =      "Fri Jul 09 06:02:16 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Lozier:1997:PST}.",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir5916.ps",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Lozier:1996:SNS
author: Daniel W. Lozier
title: Software Needs in Special Functions
journal: j-J-COMPUT-APPL-MATH
volume: 66
pages: 345--358
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Fri Jul 09 05:51:55 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 05:51:55 ???
fjournal: Journal of Computational and Applied Mathematics
remark: See preprint cite Lozier:1994:SNS.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Daniel W. Lozier
rawtitle: Software Needs in Special Functions
entry:
@Article{Lozier:1996:SNS,
  author =       "Daniel W. Lozier",
  title =        "Software Needs in Special Functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "66",
  number =       "??",
  pages =        "345--358",
  month =        "????",
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Fri Jul 09 05:51:55 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  remark =       "See preprint \cite{Lozier:1994:SNS}.",
}


bibtype: article
filename: elefunt.bib
label: Macleod:1996:AMS
author: Allan J. Macleod
title: Algorithm 757: MISCFUN, a software package to compute uncommon special functions
journal: j-TOMS
volume: 22
number: 3
pages: 288--301
month: sep
monthnumber: 9
year: 1996
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Aug 31 16:07:02 MDT 1996
bibtimestamp: 1996.08.31 16:07:02 MDT
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Allan J. Macleod
rawtitle: {Algorithm 757}: {MISCFUN}, a software package to compute uncommon special functions
bibsource:
http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

URL:
http://doi.acm.org/10.1145/232826.232846; http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p288-macleod/

abstract:
MISCFUN (MISCellaneous FUNctions) is a Fortran package for the evaluation of several special functions, which are not used often enough to have been included in the standard libraries or packages. The package uses Chebyshev expansions as the underlying method of approximation, with the Chebyshev coefficients given to 20D. A wide variety of functions are included, and the package is designed so that other functions can be added in a standard manner.

subject:
bf D.3.2: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev approximation and theory. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.

rawabstract:
MISCFUN (MISCellaneous FUNctions) is a Fortran package for the evaluation of several special functions, which are not used often enough to have been included in the standard libraries or packages. The package uses Chebyshev expansions as the underlying method of approximation, with the Chebyshev coefficients given to 20D. A wide variety of functions are included, and the package is designed so that other functions can be added in a standard manner.

entry:
@Article{Macleod:1996:AMS,
  author =       "Allan J. Macleod",
  title =        "{Algorithm 757}: {MISCFUN}, a software package to
                 compute uncommon special functions",
  journal =      j-TOMS,
  volume =       "22",
  number =       "3",
  pages =        "288--301",
  month =        sep,
  year =         "1996",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Aug 31 16:07:02 MDT 1996",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/232826.232846;
                 http://www.acm.org/pubs/citations/journals/toms/1996-22-3/p288-macleod/",
  abstract =     "MISCFUN (MISCellaneous FUNctions) is a Fortran package
                 for the evaluation of several special functions, which
                 are not used often enough to have been included in the
                 standard libraries or packages. The package uses
                 Chebyshev expansions as the underlying method of
                 approximation, with the Chebyshev coefficients given to
                 20D. A wide variety of functions are included, and the
                 package is designed so that other functions can be
                 added in a standard manner.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Chebyshev
                 approximation and theory. {\bf G.4}: Mathematics of
                 Computing, MATHEMATICAL SOFTWARE, Certification and
                 testing.",
}


bibtype: article
filename: elefunt.bib
label: Oleksy:1996:CAM
author: Cz. Oleksy
title: A convergence acceleration method of Fourier series
journal: j-COMP-PHYS-COMM
volume: 96
number: 1
pages: 17--26
year: 1996
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/0010-4655(96)00044-6
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
MRclass: 65B05
MRnumber: 1396682 (97c:65012)
bibdate: Thu Dec 1 17:36:45 2011
bibtimestamp: 2011.12.01 17:36:45 ???
fjournal: Computer Physics Communications
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Cz. Oleksy
rawtitle: A convergence acceleration method of {Fourier} series
entry:
@Article{Oleksy:1996:CAM,
  author =       "Cz. Oleksy",
  title =        "A convergence acceleration method of {Fourier}
                 series",
  journal =      j-COMP-PHYS-COMM,
  volume =       "96",
  number =       "1",
  pages =        "17--26",
  year =         "1996",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/0010-4655(96)00044-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  MRclass =      "65B05",
  MRnumber =     "1396682 (97c:65012)",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Panteliou:1996:DII
author: S. D. Panteliou and A. D. Dimarogonas and I. N. Katz
journal: j-COMPUT-MATH-APPL
volume: 32
number: 8
pages: 51--57
month: oct
monthnumber: 10
year: 1996
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:33 MST 2017
bibtimestamp: 2017.03.01 21:48:33 MST
URL: http://www.sciencedirect.com/science/article/pii/0898122196001666
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: S. D. Panteliou and A. D. Dimarogonas and I. N. Katz
title:
Direct and inverse interpolation for Jacobian elliptic functions, zeta function of Jacobi and complete elliptic integrals of the second kind

rawtitle:
Direct and inverse interpolation for {Jacobian} elliptic functions, zeta function of {Jacobi} and complete elliptic integrals of the second kind

entry:
@Article{Panteliou:1996:DII,
  author =       "S. D. Panteliou and A. D. Dimarogonas and I. N. Katz",
  title =        "Direct and inverse interpolation for {Jacobian}
                 elliptic functions, zeta function of {Jacobi} and
                 complete elliptic integrals of the second kind",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "32",
  number =       "8",
  pages =        "51--57",
  month =        oct,
  year =         "1996",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122196001666",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: book
filename: elefunt.bib
label: Patel:1996:HND
author: Jagdish K. Patel and Campbell B. Read
title: Handbook of the Normal Distribution
volume: 150
publisher: pub-DEKKER
address: pub-DEKKER:adr
edition: Second revised and expanded
pages: ix + 431
year: 1996
ISBN: 0-8247-9342-0 (hardcover) OR 0824793420 (hardcover)
ISBN13: 978-0-8247-9342-5 (hardcover) OR 9780824793425 (hardcover)
LCCN: QA273.6 .P373 1996
bibdate: Sat Dec 16 17:22:16 MST 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.12.16 17:22:16 MST
series: Statistics, textbooks and monographs
URL: http://www.loc.gov/catdir/enhancements/fy0647/95049404-d.html
subject: Gaussian distribution
acknowledgement: ack-nhfb
rawauthor: Jagdish K. Patel and Campbell B. Read
rawtitle: Handbook of the Normal Distribution
TOC:
Genesis: an historical background Basic properties Expansions and algorithms Characterizations Sampling distributions Limit theorems and expansions Normal approximations to distributions Order statistics from normal samples The bivariate normal distribution Bivariate normal sampling distributions Point estimation Statistical intervals

rawTOC:
Genesis: an historical background \\ Basic properties \\ Expansions and algorithms \\ Characterizations \\ Sampling distributions \\ Limit theorems and expansions \\ Normal approximations to distributions \\ Order statistics from normal samples \\ The bivariate normal distribution \\ Bivariate normal sampling distributions \\ Point estimation \\ Statistical intervals

entry:
@Book{Patel:1996:HND,
  author =       "Jagdish K. Patel and Campbell B. Read",
  title =        "Handbook of the Normal Distribution",
  volume =       "150",
  publisher =    pub-DEKKER,
  address =      pub-DEKKER:adr,
  edition =      "Second revised and expanded",
  pages =        "ix + 431",
  year =         "1996",
  ISBN =         "0-8247-9342-0 (hardcover)",
  ISBN-13 =      "978-0-8247-9342-5 (hardcover)",
  LCCN =         "QA273.6 .P373 1996",
  bibdate =      "Sat Dec 16 17:22:16 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Statistics, textbooks and monographs",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0647/95049404-d.html",
  acknowledgement = ack-nhfb,
  subject =      "Gaussian distribution",
  tableofcontents = "Genesis: an historical background \\
                 Basic properties \\
                 Expansions and algorithms \\
                 Characterizations \\
                 Sampling distributions \\
                 Limit theorems and expansions \\
                 Normal approximations to distributions \\
                 Order statistics from normal samples \\
                 The bivariate normal distribution \\
                 Bivariate normal sampling distributions \\
                 Point estimation \\
                 Statistical intervals",
}


bibtype: article
filename: elefunt.bib
label: Plofker:1996:ESM
author: Kim Plofker
title: An Example of the Secant Method of Iterative Approximation in a Fifteenth-Century Sanskrit Text
journal: j-HIST-MATH
volume: 23
number: 3
pages: 246--256
month: aug
monthnumber: 8
year: 1996
CODEN: HIMADS
ISSN: 0315-0860 (print), 1090-249X (electronic) OR 03150860 (print), 1090249X (electronic)
ISSNL: 0315-0860 OR 03150860
bibdate: Wed Jun 26 06:19:07 MDT 2013
bibtimestamp: 2013.06.26 06:19:07 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0315086096900269
fjournal: Historia Mathematica
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03150860
rawauthor: Kim Plofker
rawtitle: An Example of the Secant Method of Iterative Approximation in a {Fifteenth-Century Sanskrit} Text
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib

entry:
@Article{Plofker:1996:ESM,
  author =       "Kim Plofker",
  title =        "An Example of the Secant Method of Iterative
                 Approximation in a {Fifteenth-Century Sanskrit} Text",
  journal =      j-HIST-MATH,
  volume =       "23",
  number =       "3",
  pages =        "246--256",
  month =        aug,
  year =         "1996",
  CODEN =        "HIMADS",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:19:07 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086096900269",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
}


bibtype: article
filename: elefunt.bib
label: Qiu:1996:SEC
author: S.-L. Qiu and M. K. Vamanamurthy
title: Sharp Estimates for Complete Elliptic Integrals
journal: j-SIAM-J-MATH-ANA
volume: 27
number: 3
pages: 823--834
month: may
monthnumber: 5
year: 1996
CODEN: SJMAAH
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
MRclass: 33E05
MRnumber: 97f:33033
MRreviewer: G. D. Anderson
bibdate: Sat Dec 5 18:14:13 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.12.05 18:14:13 MST
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: S.-L. Qiu and M. K. Vamanamurthy
rawtitle: Sharp Estimates for Complete Elliptic Integrals
entry:
@Article{Qiu:1996:SEC,
  author =       "S.-L. Qiu and M. K. Vamanamurthy",
  title =        "Sharp Estimates for Complete Elliptic Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "27",
  number =       "3",
  pages =        "823--834",
  month =        may,
  year =         "1996",
  CODEN =        "SJMAAH",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  MRclass =      "33E05",
  MRnumber =     "97f:33033",
  MRreviewer =   "G. D. Anderson",
  bibdate =      "Sat Dec 5 18:14:13 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: inproceedings
filename: elefunt.bib
label: Rao:1996:RTS
author: V. M. Rao and B. Nowrouzian
booktitle: Canadian Conference on Electrical and Computer Engineering. 26--29 May 1996
title: Rounding techniques for signed binary arithmetic
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 294--297
year: 1996
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
acknowledgement: ack-nhfb
rawauthor: V. M. Rao and B. Nowrouzian
rawbooktitle: Canadian Conference on Electrical and Computer Engineering. 26--29 May 1996
rawtitle: Rounding techniques for signed binary arithmetic
abstract:
This paper is concerned with the derivation of the relationship that exists between the number truncation in two's complement (TC) arithmetic and the corresponding truncation in signed-binary (SB) arithmetic. The resulting relationship is subsequently exploited and applied to the development of a pair of novel techniques for SB rounding. These techniques are then translated into algorithm suitable for two-level logic implementation. Finally, the resulting algorithms are applied to the design and implementation of a high-speed SB-kernel based TC multiply-accumulate arithmetic architecture.

rawabstract:
This paper is concerned with the derivation of the relationship that exists between the number truncation in two's complement (TC) arithmetic and the corresponding truncation in signed-binary (SB) arithmetic. The resulting relationship is subsequently exploited and applied to the development of a pair of novel techniques for SB rounding. These techniques are then translated into algorithm suitable for two-level logic implementation. Finally, the resulting algorithms are applied to the design and implementation of a high-speed SB-kernel based TC multiply-accumulate arithmetic architecture.

entry:
@InProceedings{Rao:1996:RTS,
  author =       "V. M. Rao and B. Nowrouzian",
  booktitle =    "Canadian Conference on Electrical and Computer
                 Engineering. 26--29 May 1996",
  title =        "Rounding techniques for signed binary arithmetic",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "294--297",
  year =         "1996",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This paper is concerned with the derivation of the
                 relationship that exists between the number truncation
                 in two's complement (TC) arithmetic and the
                 corresponding truncation in signed-binary (SB)
                 arithmetic. The resulting relationship is subsequently
                 exploited and applied to the development of a pair of
                 novel techniques for SB rounding. These techniques are
                 then translated into algorithm suitable for two-level
                 logic implementation. Finally, the resulting algorithms
                 are applied to the design and implementation of a
                 high-speed SB-kernel based TC multiply-accumulate
                 arithmetic architecture.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Schatzman:1996:ADF
author: James C. Schatzman
title: Accuracy of the discrete Fourier transform and the fast Fourier transform
journal: j-SIAM-J-SCI-COMP
volume: 17
number: 5
pages: 1150--1166
month: sep
monthnumber: 9
year: 1996
CODEN: SJOCE3
DOI: https://doi.org/10.1137/S1064827593247023
ISSN: 1064-8275 (print), 1095-7197 (electronic) OR 10648275 (print), 10957197 (electronic)
ISSNL: 1064-8275 OR 10648275
MRclass: 65T20 (42A65 42C10 68Q25)
MRnumber: 97e:65155
bibdate: Fri Dec 4 14:47:53 MST 1998
bibtimestamp: 1998.12.04 14:47:53 MST
URL: http://epubs.siam.org/sam-bin/dbq/article/24702
fjournal: SIAM Journal on Scientific Computing
acknowledgement: ack-nhfb
ajournal: SIAM J. Sci. Comput.
journalURL: http://epubs.siam.org/sisc
rawauthor: James C. Schatzman
rawtitle: Accuracy of the discrete {Fourier} transform and the fast {Fourier} transform
bibsource:
http://epubs.siam.org/toc/sjoce3/17/5; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib

remark:
This article analyzes errors in computing one-dimensional Fourier transforms, the fast way (FFT) and the slow way. The author identifies two main causes of accuracy loss in the computed transforms: (1) inaccurate sine and cosine functions, and (2) failure to use accurate summation methods, such as Kahan's compensated summation.

entry:
@Article{Schatzman:1996:ADF,
  author =       "James C. Schatzman",
  title =        "Accuracy of the discrete {Fourier} transform and the
                 fast {Fourier} transform",
  journal =      j-SIAM-J-SCI-COMP,
  volume =       "17",
  number =       "5",
  pages =        "1150--1166",
  month =        sep,
  year =         "1996",
  CODEN =        "SJOCE3",
  DOI =          "https://doi.org/10.1137/S1064827593247023",
  ISSN =         "1064-8275 (print), 1095-7197 (electronic)",
  ISSN-L =       "1064-8275",
  MRclass =      "65T20 (42A65 42C10 68Q25)",
  MRnumber =     "97e:65155",
  bibdate =      "Fri Dec 4 14:47:53 MST 1998",
  bibsource =    "http://epubs.siam.org/toc/sjoce3/17/5;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjscicomput.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/24702",
  acknowledgement = ack-nhfb,
  ajournal =     "SIAM J. Sci. Comput.",
  fjournal =     "SIAM Journal on Scientific Computing",
  journal-URL =  "http://epubs.siam.org/sisc",
  remark =       "This article analyzes errors in computing
                 one-dimensional Fourier transforms, the fast way (FFT)
                 and the slow way. The author identifies two main causes
                 of accuracy loss in the computed transforms: (1)
                 inaccurate sine and cosine functions, and (2) failure
                 to use accurate summation methods, such as Kahan's
                 compensated summation.",
}


bibtype: article
filename: elefunt.bib
label: Schwarz:1996:HSA
author: Eric M. Schwarz and Michael J. Flynn
title: Hardware Starting Approximation Method and Its Application to the Square Root Operation
journal: j-IEEE-TRANS-COMPUT
volume: 45
number: 12
pages: 1356--1369
month: dec
monthnumber: 12
year: 1996
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.545966
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Eric M. Schwarz and Michael J. Flynn
rawtitle: Hardware Starting Approximation Method and Its Application to the Square Root Operation
entry:
@Article{Schwarz:1996:HSA,
  author =       "Eric M. Schwarz and Michael J. Flynn",
  title =        "Hardware Starting Approximation Method and Its
                 Application to the Square Root Operation",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "45",
  number =       "12",
  pages =        "1356--1369",
  month =        dec,
  year =         "1996",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.545966",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "Quadratically converging algorithms for high-order
                 arithmetic operations typically are accelerated by a
                 starting approximation. The higher the precision of the
                 starting approximation, the less number of iterations
                 required for convergence. \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Sinclair:1996:ORS
author: R. Sinclair
title: Optimization of reciprocals and square roots on the i860 microprocessor
journal: j-INT-J-HIGH-SPEED-COMPUTING
volume: 8
number: 1
pages: 57--64
year: 1996
CODEN: IHSCEZ
ISSN: 0129-0533 OR 01290533
bibdate: Mon Feb 25 11:19:22 MST 2002
bibtimestamp: 2002.02.25 11:19:22 MST
fjournal: International Journal of High Speed Computing (IJHSC)
acknowledgement: ack-nhfb
journalURL: http://www.worldscientific.com/worldscinet/ijhsc
rawauthor: R. Sinclair
rawtitle: Optimization of reciprocals and square roots on the {i860} microprocessor
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC Article1st database

entry:
@Article{Sinclair:1996:ORS,
  author =       "R. Sinclair",
  title =        "Optimization of reciprocals and square roots on the
                 {i860} microprocessor",
  journal =      j-INT-J-HIGH-SPEED-COMPUTING,
  volume =       "8",
  number =       "1",
  pages =        "57--64",
  year =         "1996",
  CODEN =        "IHSCEZ",
  ISSN =         "0129-0533",
  bibdate =      "Mon Feb 25 11:19:22 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib; OCLC
                 Article1st database",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of High Speed Computing
                 (IJHSC)",
  journal-URL =  "http://www.worldscientific.com/worldscinet/ijhsc",
}


bibtype: article
filename: elefunt.bib
label: Snyder:1996:RAF
author: W. Van Snyder
title: Remark on Algorithm 723: Fresnel Integrals
journal: j-TOMS
volume: 22
number: 4
pages: 498--500
month: dec
monthnumber: 12
year: 1996
CODEN: ACMSCU
DOI: https://doi.org/10.1145/235815.235825
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib
note: See cite Snyder:1993:AFI.
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms, performance
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: W. Van Snyder
rawnote: See \cite{Snyder:1993:AFI}.
rawtitle: Remark on {Algorithm 723}: {Fresnel} Integrals
abstract:
it Algorithm 723: Fresnel Integrals has been improved to provide more precise results for $ x gg 0 $.

subject:
bf D.3.2: Software, PROGRAMMING LANGUAGES, Language Classifications, FORTRAN. bf G.1.2: Mathematics of Computing, NUMERICAL ANALYSIS, Approximation, Rational approximation. bf G.4: Mathematics of Computing, MATHEMATICAL SOFTWARE, Certification and testing.

rawabstract:
{\it Algorithm 723: Fresnel Integrals} has been improved to provide more precise results for $ x \gg 0 $.

entry:
@Article{Snyder:1996:RAF,
  author =       "W. Van Snyder",
  title =        "Remark on {Algorithm 723}: {Fresnel} Integrals",
  journal =      j-TOMS,
  volume =       "22",
  number =       "4",
  pages =        "498--500",
  month =        dec,
  year =         "1996",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/235815.235825",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See \cite{Snyder:1993:AFI}.",
  abstract =     "{\it Algorithm 723: Fresnel Integrals} has been
                 improved to provide more precise results for $ x \gg 0
                 $.",
  acknowledgement = ack-rfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance",
  subject =      "{\bf D.3.2}: Software, PROGRAMMING LANGUAGES, Language
                 Classifications, FORTRAN. {\bf G.1.2}: Mathematics of
                 Computing, NUMERICAL ANALYSIS, Approximation, Rational
                 approximation. {\bf G.4}: Mathematics of Computing,
                 MATHEMATICAL SOFTWARE, Certification and testing.",
}


bibtype: book
filename: elefunt.bib
label: Temme:1996:SFI
author: N. M. Temme
title: Special Functions: an Introduction to the Classical Functions of Mathematical Physics
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xii + 374
year: 1996
DOI: https://doi.org/10.1002/9781118032572
ISBN: 0-471-11313-1 OR 0471113131
ISBN13: 978-0-471-11313-3 OR 9780471113133
LCCN: QC20.7.F87 T46 1996
bibdate: Mon Nov 24 21:41:54 MST 2008
bibtimestamp: 2008.11.24 21:41:54 MST
subject: functions, special; mathematical physics; boundary value problems
acknowledgement: ack-nhfb
rawauthor: N. M. Temme
rawtitle: Special Functions: an Introduction to the Classical Functions of Mathematical Physics
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.bibsys.no:2100/BIBSYS; z3950.loc.gov:7090/Voyager

TOC:
1 Bernoulli, Euler and Stirling Numbers / 1 1.1. Bernoulli Numbers and Polynomials / 2 1.1.1. Definitions and Properties / 3 1.1.2. A Simple Difference Equation / 6 1.1.3. Euler's Summation Formula / 9 1.2. Euler Numbers and Polynomials / 14 1.2.1. Definitions and Properties / 15 1.2.2. Boole's Summation Formula / 17 1.3. Stirling Numbers / 18 1.4. Remarks and Comments for Further Reading / 21 1.5. Exercises and Further Examples / 22 2 Useful Methods and Techniques / 29 2.1. Some Theorems from Analysis / 29 2.2. Asymptotic Expansions of Integrals / 31 2.2.1. Watson's Lemma / 32 2.2.2. The Saddle Point Method / 34 2.2.3. Other Asymptotic Methods / 38 2.3. Exercises and Further Examples / 39 3 The Gamma Function / 41 3.1. Introduction / 41 3.1.1. The Fundamental Recursion Property / 42 3.1.2. Another Look at the Gamma Function / 42 3.2. Important Properties / 43 3.2.1. Prym's Decomposition / 43 3.2.2. The Cauchy--Saalschutz Representation / 44 3.2.3. The Beta Integral / 45 3.2.4. The Multiplication Formula / 46 3.2.5. The Reflection Formula / 46 3.2.6. The Reciprocal Gamma Function / 48 3.2.7. A Complex Contour for the Beta Integral / 49 3.3. Infinite Products / 50 3.3.1. Gauss' Multiplication Formula / 52 3.4. Logarithmic Derivative of the Gamma Function / 53 3.5. Riemann's Zeta Function / 57 3.6. Asymptotic Expansions / 61 3.6.1. Estimations of the Remainder / 64 3.6.2. Ratio of Two Gamma Functions / 66 3.6.3. Application of the Saddle Point Method / 69 3.7. Remarks and Comments for Further Reading / 71 3.8. Exercises and Further Examples / 72 4 Differential Equations / 79 4.1. Separating the Wave Equation / 79 4.1.1. Separating the Variables / 81 4.2. Differential Equations in the Complex Plane / 83 4.2.1. Singular Points / 83 4.2.2. Transformation of the Point at Infinity / 84 4.2.3. The Solution Near a Regular Point / 85 4.2.4. Power Series Expansions Around a Regular Point / 90 4.2.5. Power Series Expansions Around a Regular Singular Point / 92 4.3. Sturm's Comparison Theorem / 97 4.4. Integrals as Solutions of Differential Equations / 98 4.5. The Liouville Transformation / 103 4.6. Remarks and Comments for Further Reading / 104 4.7. Exercises and Further Examples / 104 5 Hypergeometric Functions / 107 5.1. Definitions and Simple Relations / 107 5.2. Analytic Continuation / 109 5.2.1. Three Functional Relations / 110 5.2.2. A Contour Integral Representation / 111 5.3. The Hypergeometric Differential Equation / 112 5.4. The Singular Points of the Differential Equation / 114 5.5. The Riemann--Papperitz Equation / 116 5.6. Barnes' Contour Integral for F(a, b; c; z / 119 5.7. Recurrence Relations / 121 5.8. Quadratic Transformations / 122 5.9. Generalized Hypergeometric Functions / 124 5.9.1. A First Introduction to g-functions / 125 5.10. Remarks and Comments for Further Reading / 127 5.11. Exercises and Further Examples / 128 6 Orthogonal Polynomials / 133 6.1. General Orthogonal Polynomials / 133 6.1.1. Zeros of Orthogonal Polynomials / 137 6.1.2. Gauss Quadrature / 138 6.2. Classical Orthogonal Polynomials / 141 6.3. Definitions by the Rodrigues Formula / 142 6.4. Recurrence Relations / 146 6.5. Differential Equations / 149 6.6. Explicit Representations / 151 6.7. Generating Functions / 154 6.8. Legendre Polynomials / 156 6.8.1. The Norm of the Legendre Polynomials / 156 6.8.2. Integral Expressions for the Legendre Polynomials / 156 6.8.3. Some Bounds on Legendre Polynomials / 157 6.8.4. An Asymptotic Expansion as n is Large / 158 6.9. Expansions in Terms of Orthogonal Polynomials / 160 6.9.1. An Optimal Result in Connection with Legendre Polynomials / 160 6.9.2. Numerical Aspects of Chebyshev Polynomials / 162 6.10. Remarks and Comments for Further Reading / 164 6.11. Exercises and Further Examples / 164 7 Confluent Hypergeometric Functions / 171 7.1. The $M$-function / 172 7.2. The $U$-function / 175 7.3. Special Cases and Further Relations / 177 7.3.1. Whittaker Functions / 178 7.3.2. Coulomb Wave Functions / 178 7 3.3. Parabolic Cylinder Functions / 179 7 3.4. Error Functions / 180 7.3.5. Exponential Integrals / 180 7.3.6. Fresnel Integrals / 182 7.3.7. Incomplete Gamma Functions / 185 7.3.8. Bessel Functions / 186 7.3.9. Orthogonal Polynomials / 186 7.4. Remarks and Comments for Further Reading / 186 7.5. Exercises and Further Examples / 187 8 Legendre Functions / 193 8.1. The Legendre Differential Equation / 194 8.2. Ordinary Legendre Functions / 194 8.3. Other Solutions of the Differential Equation / 196 8.4. A Few More Series Expansions / 198 8.5. The function $Q_n(z)$ / 200 8.6. Integral Representations / 202 8.7. Associated Legendre Functions / 209 8.8. Remarks and Comments for Further Reading / 213 8.9. Exercises and Further Examples / 214 9 Bessel Functions / 219 9.1. Introduction / 219 9.2. Integral Representations / 220 9.3. Cylinder Functions / 223 9.4. Further Properties / 227 9.5. Modified Bessel Functions / 232 9.6. Integral Representations for the $I$- and $K$-Functions / 234 9.7. Asymptotic Expansions / 238 9.8. Zeros of Bessel Functions / 241 9.9. Orthogonality Relations, Fourier--Bessel Series / 244 9.10. Remarks and Comments for Further Reading / 247 9.11. Exercises and Further Examples / 247 10 Separating the Wave Equation / 257 10.1. General Transformations / 258 10.2. Special Coordinate Systems / 259 10.2.1. Cylindrical Coordinates / 259 10.2.2. Spherical Coordinates / 261 10.2.3. Elliptic Cylinder Coordinates / 263 10.2.4. Parabolic Cylinder Coordinates / 264 10.2.5. Oblate Spheroidal Coordinates / 266 10.3. Boundary Value Problems / 268 10.3.1. Heat Conduction in a Cylinder / 268 10.3.2. Diffraction of a Plane Wave Due to a Sphere / 270 10.4. Remarks and Comments for Further Reading / 271 10.5. Exercises and Further Examples / 272 11 Special Statistical Distribution Functions / 275 11.1. Error Functions / 275 11.1.1. The Error Function and Asymptotic Expansions / 276 11.2. Incomplete Gamma Functions / 277 11.2.1. Series Expansions / 279 11.2.2. Continued Fraction for $Gamma (a, z)$ / 280 11.2.3. Contour Integral for the Incomplete Gamma Functions / 282 11.2.4. Uniform Asymptotic Expansions / 283 11.2.5. Numerical Aspects / 286 11.3. Incomplete Beta Functions / 288 11.3.1. Recurrence Relations / 289 11.3.2. Contour Integral for the Incomplete Beta Function / 290 11.3.3. Asymptotic Expansions / 291 11.3.4. Numerical Aspects / 297 11.4. Non-Central Chi-Squared Distribution / 298 11.4.1. A Few More Integral Representations / 300 11.4.2. Asymptotic Expansion; $m$ Fixed, $j$ Large / 302 11.4.3. Asymptotic Expansion; $j$ Large, $m$ Arbitrary / 303 11.4.4. Numerical Aspects / 305 11.5. An Incomplete Bessel Function / 308 11.6. Remarks and Comments for Further Reading / 309 11.7. Exercises and Further Examples / 310 12 Elliptic Integrals and Elliptic Functions / 319 12.1. Complete Integrals of the First and Second Kind / 315 12.1.1. The Simple Pendulum / 316 12.1.2. Arithmetic Geometric Mean / 318 12.2. Incomplete Elliptic Integrals / 321 12.3. Elliptic Functions and Theta Functions / 322 12.3.1. Elliptic Functions / 323 12.3.2. Theta Functions / 324 12.4. Numerical Aspects / 328 12.5. Remarks and Comments for Further Reading / 329 12.6. Exercises and Further Examples / 330 13 Numerical Aspects of Special Functions / 333 13.1. A Simple Recurrence Relation / 334 13.2. Introduction to the General Theory / 335 13.3. Examples / 338 13.4. Miller's Algorithm / 343 13.5. How to Compute a Continued Fraction / 347 Bibliography / 349 Notations and Symbols / 361 Index / 365

shortTOC:
Bernoulli, Euler and Stirling numbers Useful methods and techniques The gamma function Differential equations Hypergeometric functions Orthogonal polynomials Confluent hypergeometric functions Legendre functions Bessel functions Separating the wave equation Special statistical distribution functions Elliptic integrals and elliptic functions Numerical aspects of special functions

rawshortTOC:
Bernoulli, Euler and Stirling numbers \\ Useful methods and techniques \\ The gamma function \\ Differential equations \\ Hypergeometric functions \\ Orthogonal polynomials \\ Confluent hypergeometric functions \\ Legendre functions \\ Bessel functions \\ Separating the wave equation \\ Special statistical distribution functions \\ Elliptic integrals and elliptic functions \\ Numerical aspects of special functions

rawTOC:
1 Bernoulli, Euler and Stirling Numbers / 1 \\ 1.1. Bernoulli Numbers and Polynomials / 2 \\ 1.1.1. Definitions and Properties / 3 \\ 1.1.2. A Simple Difference Equation / 6 \\ 1.1.3. Euler's Summation Formula / 9 \\ 1.2. Euler Numbers and Polynomials / 14 \\ 1.2.1. Definitions and Properties / 15 \\ 1.2.2. Boole's Summation Formula / 17 \\ 1.3. Stirling Numbers / 18 \\ 1.4. Remarks and Comments for Further Reading / 21 \\ 1.5. Exercises and Further Examples / 22 \\ 2 Useful Methods and Techniques / 29 \\ 2.1. Some Theorems from Analysis / 29 \\ 2.2. Asymptotic Expansions of Integrals / 31 \\ 2.2.1. Watson's Lemma / 32 \\ 2.2.2. The Saddle Point Method / 34 \\ 2.2.3. Other Asymptotic Methods / 38 \\ 2.3. Exercises and Further Examples / 39 \\ 3 The Gamma Function / 41 \\ 3.1. Introduction / 41 \\ 3.1.1. The Fundamental Recursion Property / 42 \\ 3.1.2. Another Look at the Gamma Function / 42 \\ 3.2. Important Properties / 43 \\ 3.2.1. Prym's Decomposition / 43 \\ 3.2.2. The Cauchy--Saalsch{\"u}tz Representation / 44 \\ 3.2.3. The Beta Integral / 45 \\ 3.2.4. The Multiplication Formula / 46 \\ 3.2.5. The Reflection Formula / 46 \\ 3.2.6. The Reciprocal Gamma Function / 48 \\ 3.2.7. A Complex Contour for the Beta Integral / 49 \\ 3.3. Infinite Products / 50 \\ 3.3.1. Gauss' Multiplication Formula / 52 \\ 3.4. Logarithmic Derivative of the Gamma Function / 53 \\ 3.5. Riemann's Zeta Function / 57 \\ 3.6. Asymptotic Expansions / 61 \\ 3.6.1. Estimations of the Remainder / 64 \\ 3.6.2. Ratio of Two Gamma Functions / 66 \\ 3.6.3. Application of the Saddle Point Method / 69 \\ 3.7. Remarks and Comments for Further Reading / 71 \\ 3.8. Exercises and Further Examples / 72 \\ 4 Differential Equations / 79 \\ 4.1. Separating the Wave Equation / 79 \\ 4.1.1. Separating the Variables / 81 \\ 4.2. Differential Equations in the Complex Plane / 83 \\ 4.2.1. Singular Points / 83 \\ 4.2.2. Transformation of the Point at Infinity / 84 \\ 4.2.3. The Solution Near a Regular Point / 85 \\ 4.2.4. Power Series Expansions Around a Regular Point / 90 \\ 4.2.5. Power Series Expansions Around a Regular Singular Point / 92 \\ 4.3. Sturm's Comparison Theorem / 97 \\ 4.4. Integrals as Solutions of Differential Equations / 98 \\ 4.5. The Liouville Transformation / 103 \\ 4.6. Remarks and Comments for Further Reading / 104 \\ 4.7. Exercises and Further Examples / 104 \\ 5 Hypergeometric Functions / 107 \\ 5.1. Definitions and Simple Relations / 107 \\ 5.2. Analytic Continuation / 109 \\ 5.2.1. Three Functional Relations / 110 \\ 5.2.2. A Contour Integral Representation / 111 \\ 5.3. The Hypergeometric Differential Equation / 112 \\ 5.4. The Singular Points of the Differential Equation / 114 \\ 5.5. The Riemann--Papperitz Equation / 116 \\ 5.6. Barnes' Contour Integral for F(a, b; c; z / 119 \\ 5.7. Recurrence Relations / 121 \\ 5.8. Quadratic Transformations / 122 \\ 5.9. Generalized Hypergeometric Functions / 124 \\ 5.9.1. A First Introduction to g-functions / 125 \\ 5.10. Remarks and Comments for Further Reading / 127 \\ 5.11. Exercises and Further Examples / 128 \\ 6 Orthogonal Polynomials / 133 \\ 6.1. General Orthogonal Polynomials / 133 \\ 6.1.1. Zeros of Orthogonal Polynomials / 137 \\ 6.1.2. Gauss Quadrature / 138 \\ 6.2. Classical Orthogonal Polynomials / 141 \\ 6.3. Definitions by the Rodrigues Formula / 142 \\ 6.4. Recurrence Relations / 146 \\ 6.5. Differential Equations / 149 \\ 6.6. Explicit Representations / 151 \\ 6.7. Generating Functions / 154 \\ 6.8. Legendre Polynomials / 156 \\ 6.8.1. The Norm of the Legendre Polynomials / 156 \\ 6.8.2. Integral Expressions for the Legendre Polynomials / 156 \\ 6.8.3. Some Bounds on Legendre Polynomials / 157 \\ 6.8.4. An Asymptotic Expansion as n is Large / 158 \\ 6.9. Expansions in Terms of Orthogonal Polynomials / 160 \\ 6.9.1. An Optimal Result in Connection with Legendre Polynomials / 160 \\ 6.9.2. Numerical Aspects of Chebyshev Polynomials / 162 \\ 6.10. Remarks and Comments for Further Reading / 164 \\ 6.11. Exercises and Further Examples / 164 \\ 7 Confluent Hypergeometric Functions / 171 \\ 7.1. The $M$-function / 172 \\ 7.2. The $U$-function / 175 \\ 7.3. Special Cases and Further Relations / 177 \\ 7.3.1. Whittaker Functions / 178 \\ 7.3.2. Coulomb Wave Functions / 178 \\ 7 3.3. Parabolic Cylinder Functions / 179 \\ 7 3.4. Error Functions / 180 \\ 7.3.5. Exponential Integrals / 180 \\ 7.3.6. Fresnel Integrals / 182 \\ 7.3.7. Incomplete Gamma Functions / 185 \\ 7.3.8. Bessel Functions / 186 \\ 7.3.9. Orthogonal Polynomials / 186 \\ 7.4. Remarks and Comments for Further Reading / 186 \\ 7.5. Exercises and Further Examples / 187 \\ 8 Legendre Functions / 193 \\ 8.1. The Legendre Differential Equation / 194 \\ 8.2. Ordinary Legendre Functions / 194 \\ 8.3. Other Solutions of the Differential Equation / 196 \\ 8.4. A Few More Series Expansions / 198 \\ 8.5. The function $Q_n(z)$ / 200 \\ 8.6. Integral Representations / 202 \\ 8.7. Associated Legendre Functions / 209 \\ 8.8. Remarks and Comments for Further Reading / 213 \\ 8.9. Exercises and Further Examples / 214 \\ 9 Bessel Functions / 219 \\ 9.1. Introduction / 219 \\ 9.2. Integral Representations / 220 \\ 9.3. Cylinder Functions / 223 \\ 9.4. Further Properties / 227 \\ 9.5. Modified Bessel Functions / 232 \\ 9.6. Integral Representations for the $I$- and $K$-Functions / 234 \\ 9.7. Asymptotic Expansions / 238 \\ 9.8. Zeros of Bessel Functions / 241 \\ 9.9. Orthogonality Relations, Fourier--Bessel Series / 244 \\ 9.10. Remarks and Comments for Further Reading / 247 \\ 9.11. Exercises and Further Examples / 247 \\ 10 Separating the Wave Equation / 257 \\ 10.1. General Transformations / 258 \\ 10.2. Special Coordinate Systems / 259 \\ 10.2.1. Cylindrical Coordinates / 259 \\ 10.2.2. Spherical Coordinates / 261 \\ 10.2.3. Elliptic Cylinder Coordinates / 263 \\ 10.2.4. Parabolic Cylinder Coordinates / 264 \\ 10.2.5. Oblate Spheroidal Coordinates / 266 \\ 10.3. Boundary Value Problems / 268 \\ 10.3.1. Heat Conduction in a Cylinder / 268 \\ 10.3.2. Diffraction of a Plane Wave Due to a Sphere / 270 \\ 10.4. Remarks and Comments for Further Reading / 271 \\ 10.5. Exercises and Further Examples / 272 \\ 11 Special Statistical Distribution Functions / 275 \\ 11.1. Error Functions / 275 \\ 11.1.1. The Error Function and Asymptotic Expansions / 276 \\ 11.2. Incomplete Gamma Functions / 277 \\ 11.2.1. Series Expansions / 279 \\ 11.2.2. Continued Fraction for $\Gamma(a, z)$ / 280 \\ 11.2.3. Contour Integral for the Incomplete Gamma Functions / 282 \\ 11.2.4. Uniform Asymptotic Expansions / 283 \\ 11.2.5. Numerical Aspects / 286 \\ 11.3. Incomplete Beta Functions / 288 \\ 11.3.1. Recurrence Relations / 289 \\ 11.3.2. Contour Integral for the Incomplete Beta Function / 290 \\ 11.3.3. Asymptotic Expansions / 291 \\ 11.3.4. Numerical Aspects / 297 \\ 11.4. Non-Central Chi-Squared Distribution / 298 \\ 11.4.1. A Few More Integral Representations / 300 \\ 11.4.2. Asymptotic Expansion; $m$ Fixed, $j$ Large / 302 \\ 11.4.3. Asymptotic Expansion; $j$ Large, $m$ Arbitrary / 303 \\ 11.4.4. Numerical Aspects / 305 \\ 11.5. An Incomplete Bessel Function / 308 \\ 11.6. Remarks and Comments for Further Reading / 309 \\ 11.7. Exercises and Further Examples / 310 \\ 12 Elliptic Integrals and Elliptic Functions / 319 \\ 12.1. Complete Integrals of the First and Second Kind / 315 \\ 12.1.1. The Simple Pendulum / 316 \\ 12.1.2. Arithmetic Geometric Mean / 318 \\ 12.2. Incomplete Elliptic Integrals / 321 \\ 12.3. Elliptic Functions and Theta Functions / 322 \\ 12.3.1. Elliptic Functions / 323 \\ 12.3.2. Theta Functions / 324 \\ 12.4. Numerical Aspects / 328 \\ 12.5. Remarks and Comments for Further Reading / 329 \\ 12.6. Exercises and Further Examples / 330 \\ 13 Numerical Aspects of Special Functions / 333 \\ 13.1. A Simple Recurrence Relation / 334 \\ 13.2. Introduction to the General Theory / 335 \\ 13.3. Examples / 338 \\ 13.4. Miller's Algorithm / 343 \\ 13.5. How to Compute a Continued Fraction / 347 \\ Bibliography / 349 \\ Notations and Symbols / 361 \\ Index / 365

entry:
@Book{Temme:1996:SFI,
  author =       "N. M. Temme",
  title =        "Special Functions: an Introduction to the Classical
                 Functions of Mathematical Physics",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xii + 374",
  year =         "1996",
  DOI =          "https://doi.org/10.1002/9781118032572",
  ISBN =         "0-471-11313-1",
  ISBN-13 =      "978-0-471-11313-3",
  LCCN =         "QC20.7.F87 T46 1996",
  bibdate =      "Mon Nov 24 21:41:54 MST 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.bibsys.no:2100/BIBSYS;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Bernoulli, Euler and Stirling numbers \\
                 Useful methods and techniques \\
                 The gamma function \\
                 Differential equations \\
                 Hypergeometric functions \\
                 Orthogonal polynomials \\
                 Confluent hypergeometric functions \\
                 Legendre functions \\
                 Bessel functions \\
                 Separating the wave equation \\
                 Special statistical distribution functions \\
                 Elliptic integrals and elliptic functions \\
                 Numerical aspects of special functions",
  subject =      "functions, special; mathematical physics; boundary
                 value problems",
  tableofcontents = "1 Bernoulli, Euler and Stirling Numbers / 1 \\
                 1.1. Bernoulli Numbers and Polynomials / 2 \\
                 1.1.1. Definitions and Properties / 3 \\
                 1.1.2. A Simple Difference Equation / 6 \\
                 1.1.3. Euler's Summation Formula / 9 \\
                 1.2. Euler Numbers and Polynomials / 14 \\
                 1.2.1. Definitions and Properties / 15 \\
                 1.2.2. Boole's Summation Formula / 17 \\
                 1.3. Stirling Numbers / 18 \\
                 1.4. Remarks and Comments for Further Reading / 21 \\
                 1.5. Exercises and Further Examples / 22 \\
                 2 Useful Methods and Techniques / 29 \\
                 2.1. Some Theorems from Analysis / 29 \\
                 2.2. Asymptotic Expansions of Integrals / 31 \\
                 2.2.1. Watson's Lemma / 32 \\
                 2.2.2. The Saddle Point Method / 34 \\
                 2.2.3. Other Asymptotic Methods / 38 \\
                 2.3. Exercises and Further Examples / 39 \\
                 3 The Gamma Function / 41 \\
                 3.1. Introduction / 41 \\
                 3.1.1. The Fundamental Recursion Property / 42 \\
                 3.1.2. Another Look at the Gamma Function / 42 \\
                 3.2. Important Properties / 43 \\
                 3.2.1. Prym's Decomposition / 43 \\
                 3.2.2. The Cauchy--Saalsch{\"u}tz Representation / 44
                 \\
                 3.2.3. The Beta Integral / 45 \\
                 3.2.4. The Multiplication Formula / 46 \\
                 3.2.5. The Reflection Formula / 46 \\
                 3.2.6. The Reciprocal Gamma Function / 48 \\
                 3.2.7. A Complex Contour for the Beta Integral / 49 \\
                 3.3. Infinite Products / 50 \\
                 3.3.1. Gauss' Multiplication Formula / 52 \\
                 3.4. Logarithmic Derivative of the Gamma Function / 53
                 \\
                 3.5. Riemann's Zeta Function / 57 \\
                 3.6. Asymptotic Expansions / 61 \\
                 3.6.1. Estimations of the Remainder / 64 \\
                 3.6.2. Ratio of Two Gamma Functions / 66 \\
                 3.6.3. Application of the Saddle Point Method / 69 \\
                 3.7. Remarks and Comments for Further Reading / 71 \\
                 3.8. Exercises and Further Examples / 72 \\
                 4 Differential Equations / 79 \\
                 4.1. Separating the Wave Equation / 79 \\
                 4.1.1. Separating the Variables / 81 \\
                 4.2. Differential Equations in the Complex Plane / 83
                 \\
                 4.2.1. Singular Points / 83 \\
                 4.2.2. Transformation of the Point at Infinity / 84 \\
                 4.2.3. The Solution Near a Regular Point / 85 \\
                 4.2.4. Power Series Expansions Around a Regular Point /
                 90 \\
                 4.2.5. Power Series Expansions Around a Regular
                 Singular Point / 92 \\
                 4.3. Sturm's Comparison Theorem / 97 \\
                 4.4. Integrals as Solutions of Differential Equations /
                 98 \\
                 4.5. The Liouville Transformation / 103 \\
                 4.6. Remarks and Comments for Further Reading / 104 \\
                 4.7. Exercises and Further Examples / 104 \\
                 5 Hypergeometric Functions / 107 \\
                 5.1. Definitions and Simple Relations / 107 \\
                 5.2. Analytic Continuation / 109 \\
                 5.2.1. Three Functional Relations / 110 \\
                 5.2.2. A Contour Integral Representation / 111 \\
                 5.3. The Hypergeometric Differential Equation / 112 \\
                 5.4. The Singular Points of the Differential Equation /
                 114 \\
                 5.5. The Riemann--Papperitz Equation / 116 \\
                 5.6. Barnes' Contour Integral for F(a, b; c; z / 119
                 \\
                 5.7. Recurrence Relations / 121 \\
                 5.8. Quadratic Transformations / 122 \\
                 5.9. Generalized Hypergeometric Functions / 124 \\
                 5.9.1. A First Introduction to g-functions / 125 \\
                 5.10. Remarks and Comments for Further Reading / 127
                 \\
                 5.11. Exercises and Further Examples / 128 \\
                 6 Orthogonal Polynomials / 133 \\
                 6.1. General Orthogonal Polynomials / 133 \\
                 6.1.1. Zeros of Orthogonal Polynomials / 137 \\
                 6.1.2. Gauss Quadrature / 138 \\
                 6.2. Classical Orthogonal Polynomials / 141 \\
                 6.3. Definitions by the Rodrigues Formula / 142 \\
                 6.4. Recurrence Relations / 146 \\
                 6.5. Differential Equations / 149 \\
                 6.6. Explicit Representations / 151 \\
                 6.7. Generating Functions / 154 \\
                 6.8. Legendre Polynomials / 156 \\
                 6.8.1. The Norm of the Legendre Polynomials / 156 \\
                 6.8.2. Integral Expressions for the Legendre
                 Polynomials / 156 \\
                 6.8.3. Some Bounds on Legendre Polynomials / 157 \\
                 6.8.4. An Asymptotic Expansion as n is Large / 158 \\
                 6.9. Expansions in Terms of Orthogonal Polynomials /
                 160 \\
                 6.9.1. An Optimal Result in Connection with Legendre
                 Polynomials / 160 \\
                 6.9.2. Numerical Aspects of Chebyshev Polynomials / 162
                 \\
                 6.10. Remarks and Comments for Further Reading / 164
                 \\
                 6.11. Exercises and Further Examples / 164 \\
                 7 Confluent Hypergeometric Functions / 171 \\
                 7.1. The $M$-function / 172 \\
                 7.2. The $U$-function / 175 \\
                 7.3. Special Cases and Further Relations / 177 \\
                 7.3.1. Whittaker Functions / 178 \\
                 7.3.2. Coulomb Wave Functions / 178 \\
                 7 3.3. Parabolic Cylinder Functions / 179 \\
                 7 3.4. Error Functions / 180 \\
                 7.3.5. Exponential Integrals / 180 \\
                 7.3.6. Fresnel Integrals / 182 \\
                 7.3.7. Incomplete Gamma Functions / 185 \\
                 7.3.8. Bessel Functions / 186 \\
                 7.3.9. Orthogonal Polynomials / 186 \\
                 7.4. Remarks and Comments for Further Reading / 186 \\
                 7.5. Exercises and Further Examples / 187 \\
                 8 Legendre Functions / 193 \\
                 8.1. The Legendre Differential Equation / 194 \\
                 8.2. Ordinary Legendre Functions / 194 \\
                 8.3. Other Solutions of the Differential Equation / 196
                 \\
                 8.4. A Few More Series Expansions / 198 \\
                 8.5. The function $Q_n(z)$ / 200 \\
                 8.6. Integral Representations / 202 \\
                 8.7. Associated Legendre Functions / 209 \\
                 8.8. Remarks and Comments for Further Reading / 213 \\
                 8.9. Exercises and Further Examples / 214 \\
                 9 Bessel Functions / 219 \\
                 9.1. Introduction / 219 \\
                 9.2. Integral Representations / 220 \\
                 9.3. Cylinder Functions / 223 \\
                 9.4. Further Properties / 227 \\
                 9.5. Modified Bessel Functions / 232 \\
                 9.6. Integral Representations for the $I$- and
                 $K$-Functions / 234 \\
                 9.7. Asymptotic Expansions / 238 \\
                 9.8. Zeros of Bessel Functions / 241 \\
                 9.9. Orthogonality Relations, Fourier--Bessel Series /
                 244 \\
                 9.10. Remarks and Comments for Further Reading / 247
                 \\
                 9.11. Exercises and Further Examples / 247 \\
                 10 Separating the Wave Equation / 257 \\
                 10.1. General Transformations / 258 \\
                 10.2. Special Coordinate Systems / 259 \\
                 10.2.1. Cylindrical Coordinates / 259 \\
                 10.2.2. Spherical Coordinates / 261 \\
                 10.2.3. Elliptic Cylinder Coordinates / 263 \\
                 10.2.4. Parabolic Cylinder Coordinates / 264 \\
                 10.2.5. Oblate Spheroidal Coordinates / 266 \\
                 10.3. Boundary Value Problems / 268 \\
                 10.3.1. Heat Conduction in a Cylinder / 268 \\
                 10.3.2. Diffraction of a Plane Wave Due to a Sphere /
                 270 \\
                 10.4. Remarks and Comments for Further Reading / 271
                 \\
                 10.5. Exercises and Further Examples / 272 \\
                 11 Special Statistical Distribution Functions / 275 \\
                 11.1. Error Functions / 275 \\
                 11.1.1. The Error Function and Asymptotic Expansions /
                 276 \\
                 11.2. Incomplete Gamma Functions / 277 \\
                 11.2.1. Series Expansions / 279 \\
                 11.2.2. Continued Fraction for $\Gamma(a, z)$ / 280 \\
                 11.2.3. Contour Integral for the Incomplete Gamma
                 Functions / 282 \\
                 11.2.4. Uniform Asymptotic Expansions / 283 \\
                 11.2.5. Numerical Aspects / 286 \\
                 11.3. Incomplete Beta Functions / 288 \\
                 11.3.1. Recurrence Relations / 289 \\
                 11.3.2. Contour Integral for the Incomplete Beta
                 Function / 290 \\
                 11.3.3. Asymptotic Expansions / 291 \\
                 11.3.4. Numerical Aspects / 297 \\
                 11.4. Non-Central Chi-Squared Distribution / 298 \\
                 11.4.1. A Few More Integral Representations / 300 \\
                 11.4.2. Asymptotic Expansion; $m$ Fixed, $j$ Large /
                 302 \\
                 11.4.3. Asymptotic Expansion; $j$ Large, $m$ Arbitrary
                 / 303 \\
                 11.4.4. Numerical Aspects / 305 \\
                 11.5. An Incomplete Bessel Function / 308 \\
                 11.6. Remarks and Comments for Further Reading / 309
                 \\
                 11.7. Exercises and Further Examples / 310 \\
                 12 Elliptic Integrals and Elliptic Functions / 319 \\
                 12.1. Complete Integrals of the First and Second Kind /
                 315 \\
                 12.1.1. The Simple Pendulum / 316 \\
                 12.1.2. Arithmetic Geometric Mean / 318 \\
                 12.2. Incomplete Elliptic Integrals / 321 \\
                 12.3. Elliptic Functions and Theta Functions / 322 \\
                 12.3.1. Elliptic Functions / 323 \\
                 12.3.2. Theta Functions / 324 \\
                 12.4. Numerical Aspects / 328 \\
                 12.5. Remarks and Comments for Further Reading / 329
                 \\
                 12.6. Exercises and Further Examples / 330 \\
                 13 Numerical Aspects of Special Functions / 333 \\
                 13.1. A Simple Recurrence Relation / 334 \\
                 13.2. Introduction to the General Theory / 335 \\
                 13.3. Examples / 338 \\
                 13.4. Miller's Algorithm / 343 \\
                 13.5. How to Compute a Continued Fraction / 347 \\
                 Bibliography / 349 \\
                 Notations and Symbols / 361 \\
                 Index / 365",
}


bibtype: article
filename: elefunt.bib
label: Temme:1996:UAI
author: N. M. Temme
journal: j-METHODS-APPL-ANAL
volume: 3
number: 3
pages: 335--344
year: 1996
DOI: https://doi.org/10.4310/MAA.1996.v3.n3.a3
ISSN: 1073-2772 (print), 1945-0001 (electronic) OR 10732772 (print), 19450001 (electronic)
ISSNL: 1073-2772 OR 10732772
MRclass: 33B20 (41A60)
MRnumber: 1421474
MRreviewer: Richard B. Paris
bibdate: Sat Feb 18 15:19:00 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 15:19:00 ???
fjournal: Methods and Applications of Analysis
acknowledgement: ack-nhfb
journalURL: http://www.intlpress.com/MAA/
rawauthor: N. M. Temme
title:
Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters

rawtitle:
Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters

entry:
@Article{Temme:1996:UAI,
  author =       "N. M. Temme",
  title =        "Uniform asymptotics for the incomplete gamma functions
                 starting from negative values of the parameters",
  journal =      j-METHODS-APPL-ANAL,
  volume =       "3",
  number =       "3",
  pages =        "335--344",
  year =         "1996",
  DOI =          "https://doi.org/10.4310/MAA.1996.v3.n3.a3",
  ISSN =         "1073-2772 (print), 1945-0001 (electronic)",
  ISSN-L =       "1073-2772",
  MRclass =      "33B20 (41A60)",
  MRnumber =     "1421474",
  MRreviewer =   "Richard B. Paris",
  bibdate =      "Sat Feb 18 15:19:00 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Methods and Applications of Analysis",
  journal-URL =  "http://www.intlpress.com/MAA/",
}


bibtype: article
filename: elefunt.bib
label: Waissi:1996:SAS
author: Gary R. Waissi and Donald F. Rossin
title: A sigmoid approximation of the standard normal integral
journal: j-APPL-MATH-COMP
volume: 77
number: 1
pages: 91--95
month: jun
monthnumber: 6
year: 1996
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/0096-3003(95)00190-5
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Tue Nov 20 21:02:39 MST 2012
bibtimestamp: 2012.11.20 21:02:39 MST
URL: http://www.sciencedirect.com/science/article/pii/0096300395001905
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003/
rawauthor: Gary R. Waissi and Donald F. Rossin
rawtitle: A sigmoid approximation of the standard normal integral
bibsource:
https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Waissi:1996:SAS,
  author =       "Gary R. Waissi and Donald F. Rossin",
  title =        "A sigmoid approximation of the standard normal
                 integral",
  journal =      j-APPL-MATH-COMP,
  volume =       "77",
  number =       "1",
  pages =        "91--95",
  month =        jun,
  year =         "1996",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/0096-3003(95)00190-5",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Nov 20 21:02:39 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0096300395001905",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}


bibtype: book
filename: elefunt.bib
label: Walz:1996:AE
author: Guido Walz
title: Asymptotics and Extrapolation
volume: 88
publisher: pub-AKADEMIE-VERLAG
address: pub-AKADEMIE-VERLAG:adr
pages: 330
year: 1996
ISBN: 3-05-501732-3 OR 3055017323
ISBN13: 978-3-05-501732-2 OR 9783055017322
LCCN: QA281 .W349 1996
bibdate: Thu Dec 1 10:25:13 MST 2011
bibsource: catalog.princeton.edu:7090/voyager; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 10:25:13 MST
series: Mathematical research
subject: Extrapolation; Asymptotic expansions
acknowledgement: ack-nhfb
rawauthor: Guido Walz
rawtitle: Asymptotics and Extrapolation
TOC:
Part I: Asymptotic Expansions 1. Asymptotic Systems and Expansions / 15 2. Geometric Asymptotic Expansions / 21 3. Logarithmic Asymptotic Expansions / 39 Part II: Linear Extrapolation Methods 4. Fundamental Concepts and General Philosophy / 193 5. Error Bounds, Stopping Rules and Monotonicity / 244 6. Generalizations and Final Remarks / 289 Historical Notes / 303 References / 308 Index / 329

rawTOC:
Part I: Asymptotic Expansions \\ 1. Asymptotic Systems and Expansions / 15 \\ 2. Geometric Asymptotic Expansions / 21 \\ 3. Logarithmic Asymptotic Expansions / 39 \\ Part II: Linear Extrapolation Methods \\ 4. Fundamental Concepts and General Philosophy / 193 \\ 5. Error Bounds, Stopping Rules and Monotonicity / 244 \\ 6. Generalizations and Final Remarks / 289 \\ Historical Notes / 303 \\ References / 308\\ Index / 329

entry:
@Book{Walz:1996:AE,
  author =       "Guido Walz",
  title =        "Asymptotics and Extrapolation",
  volume =       "88",
  publisher =    pub-AKADEMIE-VERLAG,
  address =      pub-AKADEMIE-VERLAG:adr,
  pages =        "330",
  year =         "1996",
  ISBN =         "3-05-501732-3",
  ISBN-13 =      "978-3-05-501732-2",
  LCCN =         "QA281 .W349 1996",
  bibdate =      "Thu Dec 1 10:25:13 MST 2011",
  bibsource =    "catalog.princeton.edu:7090/voyager;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Mathematical research",
  acknowledgement = ack-nhfb,
  subject =      "Extrapolation; Asymptotic expansions",
  tableofcontents = "Part I: Asymptotic Expansions \\
                 1. Asymptotic Systems and Expansions / 15 \\
                 2. Geometric Asymptotic Expansions / 21 \\
                 3. Logarithmic Asymptotic Expansions / 39 \\
                 Part II: Linear Extrapolation Methods \\
                 4. Fundamental Concepts and General Philosophy / 193
                 \\
                 5. Error Bounds, Stopping Rules and Monotonicity / 244
                 \\
                 6. Generalizations and Final Remarks / 289 \\
                 Historical Notes / 303 \\
                 References / 308\\
                 Index / 329",
}


bibtype: article
filename: elefunt.bib
label: Weniger:1996:CWF
author: Ernst Joachim Weniger
journal: j-COMPUT-PHYS
volume: 10
number: 5
pages: 496--??
month: sep
monthnumber: 9
year: 1996
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.168579
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:46:03 MDT 2019
bibtimestamp: 2019.04.10 08:46:03 MDT
URL: https://aip.scitation.org/doi/10.1063/1.168579
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: Ernst Joachim Weniger
title:
Computation of the Whittaker function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations

rawtitle:
Computation of the {Whittaker} function of the second kind by summing its divergent asymptotic series with the help of nonlinear sequence transformations

entry:
@Article{Weniger:1996:CWF,
  author =       "Ernst Joachim Weniger",
  title =        "Computation of the {Whittaker} function of the second
                 kind by summing its divergent asymptotic series with
                 the help of nonlinear sequence transformations",
  journal =      j-COMPUT-PHYS,
  volume =       "10",
  number =       "5",
  pages =        "496--??",
  month =        sep,
  year =         "1996",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168579",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:46:03 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168579",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: article
filename: elefunt.bib
label: Williams:1996:TMF
author: K. B. Williams
journal: j-CCCUJ
volume: 14
number: 12
pages: 49--54, 58--65
month: dec
monthnumber: 12
year: 1996
CODEN: CCUJEX
ISSN: 1075-2838 OR 10752838
bibdate: Thu Nov 14 06:34:33 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.11.14 06:34:33 ???
fjournal: C/C++ Users Journal
acknowledgement: ack-nhfb
rawauthor: K. B. Williams
title:
Testing Math Functions: When requirements are tight, we must carefully examine all potential sources of error. Make sure your math library isn't the weak link in the chain

note:
Describes a package that extends the Cody-Waite-Plauger work on the ELEFUNT package for the testing of the elementary functions, including the inverse hyperbolic functions, cube root, and Bessel functions of the first and second kinds. The C++ package implements 192-bit extended precision versions of all of the functions, so that accurate results are available for comparison with the normal double-precision results.

rawnote:
Describes a package that extends the Cody-Waite-Plauger work on the ELEFUNT package for the testing of the elementary functions, including the inverse hyperbolic functions, cube root, and Bessel functions of the first and second kinds. The C++ package implements 192-bit extended precision versions of all of the functions, so that accurate results are available for comparison with the normal double-precision results.

rawtitle:
Testing Math Functions: When requirements are tight, we must carefully examine all potential sources of error. {Make} sure your math library isn't the weak link in the chain

entry:
@Article{Williams:1996:TMF,
  author =       "K. B. Williams",
  title =        "Testing Math Functions: When requirements are tight,
                 we must carefully examine all potential sources of
                 error. {Make} sure your math library isn't the weak
                 link in the chain",
  journal =      j-CCCUJ,
  volume =       "14",
  number =       "12",
  pages =        "49--54, 58--65",
  month =        dec,
  year =         "1996",
  CODEN =        "CCUJEX",
  ISSN =         "1075-2838",
  bibdate =      "Thu Nov 14 06:34:33 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Describes a package that extends the
                 Cody-Waite-Plauger work on the ELEFUNT package for the
                 testing of the elementary functions, including the
                 inverse hyperbolic functions, cube root, and Bessel
                 functions of the first and second kinds. The C++
                 package implements 192-bit extended precision versions
                 of all of the functions, so that accurate results are
                 available for comparison with the normal
                 double-precision results.",
  acknowledgement = ack-nhfb,
  fjournal =     "C/C++ Users Journal",
}


bibtype: article
filename: elefunt.bib
label: Zahle:1996:FDW
author: M. Zahle and H. Ziezold
title: Fractional derivatives of Weierstrass-type functions
journal: j-J-COMPUT-APPL-MATH
volume: 76
number: 1--2
pages: 265--275
day: 17
month: dec
monthnumber: 12
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:58 MST 2017
bibtimestamp: 2017.02.25 12:35:58 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042796001100
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: M. Z{\"a}hle and H. Ziezold
rawtitle: Fractional derivatives of {Weierstrass}-type functions
entry:
@Article{Zahle:1996:FDW,
  author =       "M. Z{\"a}hle and H. Ziezold",
  title =        "Fractional derivatives of {Weierstrass}-type
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "76",
  number =       "1--2",
  pages =        "265--275",
  day =          "17",
  month =        dec,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796001100",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: book
filename: elefunt.bib
label: Zhang:1996:CSF
author: Shanjie Zhang and Jianming Jin
title: Computation of Special Functions
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xxvi + 717
year: 1996
ISBN: 0-471-11963-6 OR 0471119636
ISBN13: 978-0-471-11963-0 OR 9780471119630
LCCN: QA351.C45 1996
bibdate: Wed Mar 22 14:39:04 2000
bibtimestamp: 2000.03.22 14:39:04 ???
acknowledgement: ack-nhfb
rawauthor: Shanjie Zhang and Jianming Jin
rawtitle: Computation of Special Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib

TOC:
Preface / xi Acknowledgments / xvii List of Computer Programs / xix 1: Bernoulli and Euler Numbers / 1 1.1 Bernoulli Numbers / 1 1.2 Euler Numbers / 6 1.3 Mathematical Table / 10 References / 11 2: Orthogonal Polynomials / 12 2.1 Introduction / 12 2.2 Chebyshev Polynomials / 13 2.3 Laguerre Polynomials / 18 2.4 Hermite Polynomials / 20 2.5 Numerical Computation / 23 2.6 Application in Numerical Integration / 27 References / 43 3: Gamma, Beta, and Psi Functions / 44 3.1 Gamma Function / 44 3.2 Beta Function / 53 3.3 Psi Function / 55 3.4 Incomplete Gamma Function / 61 3.5 Incomplete Beta Function / 64 3.6 Mathematical Tables / 66 References and Further Reading / 76 4: Legendre Functions / 77 4.1 Introduction / 77 4.2 Legendre Functions of the First Kind / 78 4.3 Legendre Functions of the Second Kind / 83 4.4 Associated Legendre Functions of the First Kind / 89 4.5 Associated Legendre Functions of the Second Kind / 96 4.6 Legendre Functions with an Arbitrary Degree / 104 4.7 Mathematical Tables / 113 References and Further Reading / 125 5: Bessel Functions / 126 5.1 Introduction / 126 5.2 Computation of $J_0(x)$, $J_1(x)$, $Y_0(x)$, and $Y_1(x)$ / 131 5.3 Computation of $J_n(x)$ and $Y_n(x)$ with Real Arguments / 140 5.4 Computation of $Y_n(z)$ and$ Y_n(z)$ with Complex Arguments / 149 5.5 Computation of $J_nu (z)$ and $J_nu (z)$ with an Arbitrary Order / 161 5.6 Assessment of Validity and Accuracy of Computation / 175 5.7 Zeros of Bessel Functions / 180 5.8 Lambda Functions / 182 5.9 Mathematical Tables / 184 References and Further Reading / 201 6: Modified Bessel Functions / 202 6.1 Introduction / 202 6.2 Computation of $I_0(x)$, $I_1(x)$, $K_0(x)$, and $K_1(x)$ / 207 6.3 Computation of $I_n(x)$ and $K_n(x)$ with Real Arguments / 213 6.4 Computation of $I_n(z)$ and $K_n(z)$ with Complex Arguments / 217 6.5 Computation of $I_nu (z)$ and $K_nu (z)$ with an Arbitrary Order / 225 6.6 Computation of $H_nu ^(1)(z)$ and $H_nu ^(2)(z)$ for Complex Arguments / 235 6.7 Mathematical Tables / 239 References and Further Reading / 251 7: Integrals of Bessel Functions / 252 7.1 Simple Integrals of Bessel Functions / 252 7.2 Simple Integrals of Modified Bessel Functions / 261 7.3 Curves and Tables / 268 References / 272 8: Spherical Bessel Functions / 273 8.1 Spherical Bessel Functions / 273 8.2 Riccati--Bessel Functions / 283 8.3 Modified Spherical Bessel Functions / 286 8.4 Mathematical Tables / 295 References and Further Reading / 306 9: Kelvin Functions / 307 9.1 Introduction / 307 9.2 Mathematical Properties / 311 9.3 Asymptotic Expansions / 312 9.4 Numerical Computation / 315 9.5 Zeros of Kelvin Functions / 321 9.6 Mathematical Tables / 321 Reference / 324 10: Airy Functions / 325 10.1 Introduction / 325 10.2 Numerical Computation / 329 10.3 Mathematical Tables / 336 References / 340 11: Struve Functions / 341 11.1 Struve Functions / 341 11.2 Modified Struve Functions / 353 11.3 Mathematical Tables / 362 References / 365 12: Hypergeometric and Confluent Hypergeometric Functions / 366 12.1 Definition of Hypergeometric Functions / 366 12.2 Properties of Hypergeometric Functions / 368 12.3 Linear Transformation Formulas / 369 12.4 Recurrence Relations for Hypergeometric Functions / 372 12.5 Special Functions Expressed as Hypergeometric Functions / 373 12.6 Numerical Computation of Hypergeometric Functions / 374 12.7 Definition of Confluent Hypergeometric Functions / 385 12.8 Properties of Confluent Hypergeometric Functions / 387 12.9 Recurrence Relations for Confluent Hypergeometric Functions / 389 12.10 Special Functions Expressed as Confluent Hypergeometric Functions / 394 12.11 Definition of Whittaker Functions / 395 12.12 Numerical Computation of Confluent Hypergeometric Functions / 398 12.13 Mathematical Tables / 411 References and Further Reading / 424 13: Parabolic Cylinder Functions / 425 13.1 Introduction / 425 13.2 Definitions of Parabolic Cylinder Functions / 428 13.3 Basic Properties / 432 13.4 Series and Asymptotic Expansions / 437 13.5 Numerical Computation / 438 13.6 Mathematical Tables / 455 References and Further Reading / 474 14: Mathieu Functions / 475 14.1 Definition of Mathieu Functions / 475 14.2 Determination of Expansion Coefficients and Characteristic Values / 477 14.3 Approximate Calculation of Characteristic Values / 482 14.4 Expansion of Mathieu Functions When $|q| < 1$ / 485 14.5 Properties of Mathieu Functions / 487 14.6 Definition of Modified Mathieu Functions / 489 14.7 Properties of Modified Mathieu Functions / 496 14.8 Numerical Computation: Algorithms and Computer Programs / 501 14.9 Mathematical Tables / 520 References and Further Reading / 535 15: Spheroidal Wave Functions / 536 15.1 Spheroidal Coordinate Systems / 536 15.2 Wave Equation and Its Solution in Spheroidal Coordinates / 540 15.3 Definitions of Angular and Radial Prolate Spheroidal Wave Functions / 542 15.4 Determination of Characteristic Values and Expansion Coefficients / 550 15.5 Evaluation of Prolate Radial Wave Functions of the Second Kind for Small $c xi $ / 556 15.6 Definitions of Angular and Radial Oblate Spheroidal Wave Functions / 559 15.7 Evaluation of Oblate Radial Wave Functions of the Second Kind for Small $c xi $ / 561 15.8 Numerical Computation: Algorithms and Computer Programs / 569 15.9 Mathematical Tables / 594 References / 619 16: Error Function and Fresnel Integrals / 620 16.1 Introduction to Error Function / 620 16.2 Numerical Computation of Error Function / 621 16.3 Gaussian Probability Integral / 624 16.4 Introduction to Fresnel Integrals / 625 16.5 Series and Asymptotic Expansions of Fresnel Integrals / 629 16.6 Numerical Computation of Fresnel Integrals / 630 16.7 Zeros of Error Function and Fresnel Integrals / 635 16.8 Mathematical Tables / 636 References and Further Reading / 643 17: Cosine and Sine Integrals / 644 17.1 Introduction / 644 17.2 Series and Asymptotic Expansions / 646 17.3 Numerical Computation / 647 17.4 Mathematical Table / 651 References and Further Readings / 653 18: Elliptic Integrals and Jacobian Elliptic Functions / 654 18.1 Introduction to Elliptic Integrals / 654 18.2 Series Expansion of Elliptic Integrals / 659 18.3 Numerical Computation of Elliptic Integrals / 661 18.4 Introduction to Jacobian Elliptic Functions / 666 18.5 Numerical Computation of Jacobian Elliptic Functions / 670 18.6 Mathematical Tables / 672 References and Further Reading / 679 19: Exponential Integrals / 680 19.1 Introduction / 680 19.2 Series, Asymptotic, and Continued Fraction Expressions / 682 19.3 Rational Approximations / 683 19.4 Numerical Computation / 684 19.5 Mathematical Tables / 688 References / 693 20: Summary of Methods for Computing Special Functions / 694 Appendix A: Derivation of Some Special Differential Equations / 697 A.1 Helmholtz Equation and Separation of Variables / 697 A.2 Circular Cylindrical Coordinates / 698 A.3 Elliptic Cylindrical Coordinates / 700 A.4 Parabolic Cylindrical Coordinates / 700 A.5 Spherical Coordinates / 701 A.6 Prolate Spheroidal Coordinates / 701 A.7 Oblate Spheroidal Coordinates / 702 A.8 Parabolic Coordinates / 703 References / 703 Appendix B: Root-Finding Methods / 704 B.1 Newton's Method / 704 B.2 Modified Newton's Method / 706 B.3 Secant Method / 706 Reference / 706 Appendix C: About the Software / 707 Index / 709 Index of Computer Programs / 715

shortTOC:
Preface / xi Acknowledgments / xvii List of Computer Programs / xix 1: Bernoulli and Euler Numbers / 1 2: Orthogonal Polynomials / 12 3: Gamma, Beta, and Psi Functions / 44 4: Legendre Functions / 77 5: Bessel Functions / 126 6: Modified Bessel Functions / 202 7: Integrals of Bessel Functions / 252 8: Spherical Bessel Functions / 273 9: Kelvin Functions / 307 10: Airy Functions / 325 11: Struve Functions / 341 12: Hypergeometric and Confluent Hypergeometric / 366 13: Parabolic Cylinder Functions / 425 14: Mathieu Functions / 475 15: Spheroidal Wave Functions / 536 16: Error Function and Fresnel Integrals / 620 17: Cosine and Sine Integrals / 644 18: Elliptic Integrals and Jacobian Elliptic Functions 19: Exponential Integrals / 680 20: Summary of Methods for Computing Special Functions Appendix A: Derivation of Some Special Differential Appendix B: Root-Finding Methods / 704 Reference / 706 Appendix C: About the Software / 707 Index / 709 Index of Computer Programs / 715

rawshortTOC:
Preface / xi \\ Acknowledgments / xvii \\ List of Computer Programs / xix \\ 1: Bernoulli and Euler Numbers / 1 \\ 2: Orthogonal Polynomials / 12 \\ 3: Gamma, Beta, and Psi Functions / 44 \\ 4: Legendre Functions / 77 \\ 5: Bessel Functions / 126 \\ 6: Modified Bessel Functions / 202 \\ 7: Integrals of Bessel Functions / 252 \\ 8: Spherical Bessel Functions / 273 \\ 9: Kelvin Functions / 307 \\ 10: Airy Functions / 325 \\ 11: Struve Functions / 341 \\ 12: Hypergeometric and Confluent Hypergeometric / 366 \\ 13: Parabolic Cylinder Functions / 425 \\ 14: Mathieu Functions / 475 \\ 15: Spheroidal Wave Functions / 536 \\ 16: Error Function and Fresnel Integrals / 620 \\ 17: Cosine and Sine Integrals / 644 \\ 18: Elliptic Integrals and Jacobian Elliptic Functions 19: Exponential Integrals / 680 \\ 20: Summary of Methods for Computing Special Functions Appendix A: Derivation of Some Special Differential Appendix B: Root-Finding Methods / 704 \\ Reference / 706 \\ Appendix C: About the Software / 707 \\ Index / 709 \\ Index of Computer Programs / 715

rawTOC:
Preface / xi \\ Acknowledgments / xvii \\ List of Computer Programs / xix \\ 1: Bernoulli and Euler Numbers / 1 \\ 1.1 Bernoulli Numbers / 1 \\ 1.2 Euler Numbers / 6 \\ 1.3 Mathematical Table / 10 \\ References / 11 \\ 2: Orthogonal Polynomials / 12 \\ 2.1 Introduction / 12 \\ 2.2 Chebyshev Polynomials / 13 \\ 2.3 Laguerre Polynomials / 18 \\ 2.4 Hermite Polynomials / 20 \\ 2.5 Numerical Computation / 23 \\ 2.6 Application in Numerical Integration / 27 \\ References / 43 \\ 3: Gamma, Beta, and Psi Functions / 44 \\ 3.1 Gamma Function / 44 \\ 3.2 Beta Function / 53 \\ 3.3 Psi Function / 55 \\ 3.4 Incomplete Gamma Function / 61 \\ 3.5 Incomplete Beta Function / 64 \\ 3.6 Mathematical Tables / 66 \\ References and Further Reading / 76 \\ 4: Legendre Functions / 77 \\ 4.1 Introduction / 77 \\ 4.2 Legendre Functions of the First Kind / 78 \\ 4.3 Legendre Functions of the Second Kind / 83 \\ 4.4 Associated Legendre Functions of the First Kind / 89 \\ 4.5 Associated Legendre Functions of the Second Kind / 96 \\ 4.6 Legendre Functions with an Arbitrary Degree / 104 \\ 4.7 Mathematical Tables / 113 \\ References and Further Reading / 125 \\ 5: Bessel Functions / 126 \\ 5.1 Introduction / 126 \\ 5.2 Computation of $J_0(x)$, $J_1(x)$, $Y_0(x)$, and $Y_1(x)$ / 131 \\ 5.3 Computation of $J_n(x)$ and $Y_n(x)$ with Real Arguments / 140 \\ 5.4 Computation of $Y_n(z)$ and$ Y_n(z)$ with Complex Arguments / 149 \\ 5.5 Computation of $J_\nu(z)$ and $J_\nu(z)$ with an Arbitrary Order / 161 \\ 5.6 Assessment of Validity and Accuracy of Computation / 175 \\ 5.7 Zeros of Bessel Functions / 180 \\ 5.8 Lambda Functions / 182 \\ 5.9 Mathematical Tables / 184 \\ References and Further Reading / 201 \\ 6: Modified Bessel Functions / 202 \\ 6.1 Introduction / 202 \\ 6.2 Computation of $I_0(x)$, $I_1(x)$, $K_0(x)$, and $K_1(x)$ / 207 \\ 6.3 Computation of $I_n(x)$ and $K_n(x)$ with Real Arguments / 213 \\ 6.4 Computation of $I_n(z)$ and $K_n(z)$ with Complex Arguments / 217 \\ 6.5 Computation of $I_\nu(z)$ and $K_\nu(z)$ with an Arbitrary Order / 225 \\ 6.6 Computation of $H_\nu^{(1)}(z)$ and $H_\nu^{(2)}(z)$ for Complex Arguments / 235 \\ 6.7 Mathematical Tables / 239 \\ References and Further Reading / 251 \\ 7: Integrals of Bessel Functions / 252 \\ 7.1 Simple Integrals of Bessel Functions / 252 \\ 7.2 Simple Integrals of Modified Bessel Functions / 261 \\ 7.3 Curves and Tables / 268 \\ References / 272 \\ 8: Spherical Bessel Functions / 273 \\ 8.1 Spherical Bessel Functions / 273 \\ 8.2 Riccati--Bessel Functions / 283 \\ 8.3 Modified Spherical Bessel Functions / 286 \\ 8.4 Mathematical Tables / 295 \\ References and Further Reading / 306 \\ 9: Kelvin Functions / 307 \\ 9.1 Introduction / 307 \\ 9.2 Mathematical Properties / 311 \\ 9.3 Asymptotic Expansions / 312 \\ 9.4 Numerical Computation / 315 \\ 9.5 Zeros of Kelvin Functions / 321 \\ 9.6 Mathematical Tables / 321 \\ Reference / 324 \\ 10: Airy Functions / 325 \\ 10.1 Introduction / 325 \\ 10.2 Numerical Computation / 329 \\ 10.3 Mathematical Tables / 336 \\ References / 340 \\ 11: Struve Functions / 341 \\ 11.1 Struve Functions / 341 \\ 11.2 Modified Struve Functions / 353 \\ 11.3 Mathematical Tables / 362 \\ References / 365 \\ 12: Hypergeometric and Confluent Hypergeometric Functions / 366 \\ 12.1 Definition of Hypergeometric Functions / 366 \\ 12.2 Properties of Hypergeometric Functions / 368 \\ 12.3 Linear Transformation Formulas / 369 \\ 12.4 Recurrence Relations for Hypergeometric Functions / 372 \\ 12.5 Special Functions Expressed as Hypergeometric Functions / 373 \\ 12.6 Numerical Computation of Hypergeometric Functions / 374 \\ 12.7 Definition of Confluent Hypergeometric Functions / 385 \\ 12.8 Properties of Confluent Hypergeometric Functions / 387 \\ 12.9 Recurrence Relations for Confluent Hypergeometric Functions / 389 \\ 12.10 Special Functions Expressed as Confluent Hypergeometric Functions / 394 \\ 12.11 Definition of Whittaker Functions / 395 \\ 12.12 Numerical Computation of Confluent Hypergeometric Functions / 398 \\ 12.13 Mathematical Tables / 411 \\ References and Further Reading / 424 \\ 13: Parabolic Cylinder Functions / 425 \\ 13.1 Introduction / 425 \\ 13.2 Definitions of Parabolic Cylinder Functions / 428 \\ 13.3 Basic Properties / 432 \\ 13.4 Series and Asymptotic Expansions / 437 \\ 13.5 Numerical Computation / 438 \\ 13.6 Mathematical Tables / 455 \\ References and Further Reading / 474 \\ 14: Mathieu Functions / 475 \\ 14.1 Definition of Mathieu Functions / 475 \\ 14.2 Determination of Expansion Coefficients and Characteristic Values / 477 \\ 14.3 Approximate Calculation of Characteristic Values / 482 \\ 14.4 Expansion of Mathieu Functions When $|q| < 1$ / 485 \\ 14.5 Properties of Mathieu Functions / 487 \\ 14.6 Definition of Modified Mathieu Functions / 489 \\ 14.7 Properties of Modified Mathieu Functions / 496 \\ 14.8 Numerical Computation: Algorithms and Computer Programs / 501 \\ 14.9 Mathematical Tables / 520 \\ References and Further Reading / 535 \\ 15: Spheroidal Wave Functions / 536 \\ 15.1 Spheroidal Coordinate Systems / 536 \\ 15.2 Wave Equation and Its Solution in Spheroidal Coordinates / 540 \\ 15.3 Definitions of Angular and Radial Prolate Spheroidal Wave Functions / 542 \\ 15.4 Determination of Characteristic Values and Expansion Coefficients / 550 \\ 15.5 Evaluation of Prolate Radial Wave Functions of the Second Kind for Small $c \xi$ / 556 \\ 15.6 Definitions of Angular and Radial Oblate Spheroidal Wave Functions / 559 \\ 15.7 Evaluation of Oblate Radial Wave Functions of the Second Kind for Small $c \xi$ / 561 \\ 15.8 Numerical Computation: Algorithms and Computer Programs / 569 \\ 15.9 Mathematical Tables / 594 \\ References / 619 \\ 16: Error Function and Fresnel Integrals / 620 \\ 16.1 Introduction to Error Function / 620 \\ 16.2 Numerical Computation of Error Function / 621 \\ 16.3 Gaussian Probability Integral / 624 \\ 16.4 Introduction to Fresnel Integrals / 625 \\ 16.5 Series and Asymptotic Expansions of Fresnel Integrals / 629 \\ 16.6 Numerical Computation of Fresnel Integrals / 630 \\ 16.7 Zeros of Error Function and Fresnel Integrals / 635 \\ 16.8 Mathematical Tables / 636 \\ References and Further Reading / 643 \\ 17: Cosine and Sine Integrals / 644 \\ 17.1 Introduction / 644 \\ 17.2 Series and Asymptotic Expansions / 646 \\ 17.3 Numerical Computation / 647 \\ 17.4 Mathematical Table / 651 \\ References and Further Readings / 653 \\ 18: Elliptic Integrals and Jacobian Elliptic Functions / 654 \\ 18.1 Introduction to Elliptic Integrals / 654 \\ 18.2 Series Expansion of Elliptic Integrals / 659 \\ 18.3 Numerical Computation of Elliptic Integrals / 661 \\ 18.4 Introduction to Jacobian Elliptic Functions / 666 \\ 18.5 Numerical Computation of Jacobian Elliptic Functions / 670 \\ 18.6 Mathematical Tables / 672 \\ References and Further Reading / 679 \\ 19: Exponential Integrals / 680 \\ 19.1 Introduction / 680 \\ 19.2 Series, Asymptotic, and Continued Fraction Expressions / 682 \\ 19.3 Rational Approximations / 683 \\ 19.4 Numerical Computation / 684 \\ 19.5 Mathematical Tables / 688 \\ References / 693 \\ 20: Summary of Methods for Computing Special Functions / 694 \\ Appendix A: Derivation of Some Special Differential Equations / 697 \\ A.1 Helmholtz Equation and Separation of Variables / 697 \\ A.2 Circular Cylindrical Coordinates / 698 \\ A.3 Elliptic Cylindrical Coordinates / 700 \\ A.4 Parabolic Cylindrical Coordinates / 700 \\ A.5 Spherical Coordinates / 701 \\ A.6 Prolate Spheroidal Coordinates / 701 \\ A.7 Oblate Spheroidal Coordinates / 702 \\ A.8 Parabolic Coordinates / 703 \\ References / 703 \\ Appendix B: Root-Finding Methods / 704 \\ B.1 Newton's Method / 704 \\ B.2 Modified Newton's Method / 706 \\ B.3 Secant Method / 706 \\ Reference / 706 \\ Appendix C: About the Software / 707 \\ Index / 709 \\ Index of Computer Programs / 715

entry:
@Book{Zhang:1996:CSF,
  author =       "Shanjie Zhang and Jianming Jin",
  title =        "Computation of Special Functions",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xxvi + 717",
  year =         "1996",
  ISBN =         "0-471-11963-6",
  ISBN-13 =      "978-0-471-11963-0",
  LCCN =         "QA351.C45 1996",
  bibdate =      "Wed Mar 22 14:39:04 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  price =        "US\$94.00",
  acknowledgement = ack-nhfb,
  shorttableofcontents = "Preface / xi \\
                 Acknowledgments / xvii \\
                 List of Computer Programs / xix \\
                 1: Bernoulli and Euler Numbers / 1 \\
                 2: Orthogonal Polynomials / 12 \\
                 3: Gamma, Beta, and Psi Functions / 44 \\
                 4: Legendre Functions / 77 \\
                 5: Bessel Functions / 126 \\
                 6: Modified Bessel Functions / 202 \\
                 7: Integrals of Bessel Functions / 252 \\
                 8: Spherical Bessel Functions / 273 \\
                 9: Kelvin Functions / 307 \\
                 10: Airy Functions / 325 \\
                 11: Struve Functions / 341 \\
                 12: Hypergeometric and Confluent Hypergeometric / 366
                 \\
                 13: Parabolic Cylinder Functions / 425 \\
                 14: Mathieu Functions / 475 \\
                 15: Spheroidal Wave Functions / 536 \\
                 16: Error Function and Fresnel Integrals / 620 \\
                 17: Cosine and Sine Integrals / 644 \\
                 18: Elliptic Integrals and Jacobian Elliptic Functions
                 19: Exponential Integrals / 680 \\
                 20: Summary of Methods for Computing Special Functions
                 Appendix A: Derivation of Some Special Differential
                 Appendix B: Root-Finding Methods / 704 \\
                 Reference / 706 \\
                 Appendix C: About the Software / 707 \\
                 Index / 709 \\
                 Index of Computer Programs / 715",
  tableofcontents = "Preface / xi \\
                 Acknowledgments / xvii \\
                 List of Computer Programs / xix \\
                 1: Bernoulli and Euler Numbers / 1 \\
                 1.1 Bernoulli Numbers / 1 \\
                 1.2 Euler Numbers / 6 \\
                 1.3 Mathematical Table / 10 \\
                 References / 11 \\
                 2: Orthogonal Polynomials / 12 \\
                 2.1 Introduction / 12 \\
                 2.2 Chebyshev Polynomials / 13 \\
                 2.3 Laguerre Polynomials / 18 \\
                 2.4 Hermite Polynomials / 20 \\
                 2.5 Numerical Computation / 23 \\
                 2.6 Application in Numerical Integration / 27 \\
                 References / 43 \\
                 3: Gamma, Beta, and Psi Functions / 44 \\
                 3.1 Gamma Function / 44 \\
                 3.2 Beta Function / 53 \\
                 3.3 Psi Function / 55 \\
                 3.4 Incomplete Gamma Function / 61 \\
                 3.5 Incomplete Beta Function / 64 \\
                 3.6 Mathematical Tables / 66 \\
                 References and Further Reading / 76 \\
                 4: Legendre Functions / 77 \\
                 4.1 Introduction / 77 \\
                 4.2 Legendre Functions of the First Kind / 78 \\
                 4.3 Legendre Functions of the Second Kind / 83 \\
                 4.4 Associated Legendre Functions of the First Kind /
                 89 \\
                 4.5 Associated Legendre Functions of the Second Kind /
                 96 \\
                 4.6 Legendre Functions with an Arbitrary Degree / 104
                 \\
                 4.7 Mathematical Tables / 113 \\
                 References and Further Reading / 125 \\
                 5: Bessel Functions / 126 \\
                 5.1 Introduction / 126 \\
                 5.2 Computation of $J_0(x)$, $J_1(x)$, $Y_0(x)$, and
                 $Y_1(x)$ / 131 \\
                 5.3 Computation of $J_n(x)$ and $Y_n(x)$ with Real
                 Arguments / 140 \\
                 5.4 Computation of $Y_n(z)$ and$ Y_n(z)$ with Complex
                 Arguments / 149 \\
                 5.5 Computation of $J_\nu(z)$ and $J_\nu(z)$ with an
                 Arbitrary Order / 161 \\
                 5.6 Assessment of Validity and Accuracy of Computation
                 / 175 \\
                 5.7 Zeros of Bessel Functions / 180 \\
                 5.8 Lambda Functions / 182 \\
                 5.9 Mathematical Tables / 184 \\
                 References and Further Reading / 201 \\
                 6: Modified Bessel Functions / 202 \\
                 6.1 Introduction / 202 \\
                 6.2 Computation of $I_0(x)$, $I_1(x)$, $K_0(x)$, and
                 $K_1(x)$ / 207 \\
                 6.3 Computation of $I_n(x)$ and $K_n(x)$ with Real
                 Arguments / 213 \\
                 6.4 Computation of $I_n(z)$ and $K_n(z)$ with Complex
                 Arguments / 217 \\
                 6.5 Computation of $I_\nu(z)$ and $K_\nu(z)$ with an
                 Arbitrary Order / 225 \\
                 6.6 Computation of $H_\nu^{(1)}(z)$ and
                 $H_\nu^{(2)}(z)$ for Complex Arguments / 235 \\
                 6.7 Mathematical Tables / 239 \\
                 References and Further Reading / 251 \\
                 7: Integrals of Bessel Functions / 252 \\
                 7.1 Simple Integrals of Bessel Functions / 252 \\
                 7.2 Simple Integrals of Modified Bessel Functions / 261
                 \\
                 7.3 Curves and Tables / 268 \\
                 References / 272 \\
                 8: Spherical Bessel Functions / 273 \\
                 8.1 Spherical Bessel Functions / 273 \\
                 8.2 Riccati--Bessel Functions / 283 \\
                 8.3 Modified Spherical Bessel Functions / 286 \\
                 8.4 Mathematical Tables / 295 \\
                 References and Further Reading / 306 \\
                 9: Kelvin Functions / 307 \\
                 9.1 Introduction / 307 \\
                 9.2 Mathematical Properties / 311 \\
                 9.3 Asymptotic Expansions / 312 \\
                 9.4 Numerical Computation / 315 \\
                 9.5 Zeros of Kelvin Functions / 321 \\
                 9.6 Mathematical Tables / 321 \\
                 Reference / 324 \\
                 10: Airy Functions / 325 \\
                 10.1 Introduction / 325 \\
                 10.2 Numerical Computation / 329 \\
                 10.3 Mathematical Tables / 336 \\
                 References / 340 \\
                 11: Struve Functions / 341 \\
                 11.1 Struve Functions / 341 \\
                 11.2 Modified Struve Functions / 353 \\
                 11.3 Mathematical Tables / 362 \\
                 References / 365 \\
                 12: Hypergeometric and Confluent Hypergeometric
                 Functions / 366 \\
                 12.1 Definition of Hypergeometric Functions / 366 \\
                 12.2 Properties of Hypergeometric Functions / 368 \\
                 12.3 Linear Transformation Formulas / 369 \\
                 12.4 Recurrence Relations for Hypergeometric Functions
                 / 372 \\
                 12.5 Special Functions Expressed as Hypergeometric
                 Functions / 373 \\
                 12.6 Numerical Computation of Hypergeometric Functions
                 / 374 \\
                 12.7 Definition of Confluent Hypergeometric Functions /
                 385 \\
                 12.8 Properties of Confluent Hypergeometric Functions /
                 387 \\
                 12.9 Recurrence Relations for Confluent Hypergeometric
                 Functions / 389 \\
                 12.10 Special Functions Expressed as Confluent
                 Hypergeometric Functions / 394 \\
                 12.11 Definition of Whittaker Functions / 395 \\
                 12.12 Numerical Computation of Confluent Hypergeometric
                 Functions / 398 \\
                 12.13 Mathematical Tables / 411 \\
                 References and Further Reading / 424 \\
                 13: Parabolic Cylinder Functions / 425 \\
                 13.1 Introduction / 425 \\
                 13.2 Definitions of Parabolic Cylinder Functions / 428
                 \\
                 13.3 Basic Properties / 432 \\
                 13.4 Series and Asymptotic Expansions / 437 \\
                 13.5 Numerical Computation / 438 \\
                 13.6 Mathematical Tables / 455 \\
                 References and Further Reading / 474 \\
                 14: Mathieu Functions / 475 \\
                 14.1 Definition of Mathieu Functions / 475 \\
                 14.2 Determination of Expansion Coefficients and
                 Characteristic Values / 477 \\
                 14.3 Approximate Calculation of Characteristic Values /
                 482 \\
                 14.4 Expansion of Mathieu Functions When $|q| < 1$ /
                 485 \\
                 14.5 Properties of Mathieu Functions / 487 \\
                 14.6 Definition of Modified Mathieu Functions / 489 \\
                 14.7 Properties of Modified Mathieu Functions / 496 \\
                 14.8 Numerical Computation: Algorithms and Computer
                 Programs / 501 \\
                 14.9 Mathematical Tables / 520 \\
                 References and Further Reading / 535 \\
                 15: Spheroidal Wave Functions / 536 \\
                 15.1 Spheroidal Coordinate Systems / 536 \\
                 15.2 Wave Equation and Its Solution in Spheroidal
                 Coordinates / 540 \\
                 15.3 Definitions of Angular and Radial Prolate
                 Spheroidal Wave Functions / 542 \\
                 15.4 Determination of Characteristic Values and
                 Expansion Coefficients / 550 \\
                 15.5 Evaluation of Prolate Radial Wave Functions of the
                 Second Kind for Small $c \xi$ / 556 \\
                 15.6 Definitions of Angular and Radial Oblate
                 Spheroidal Wave Functions / 559 \\
                 15.7 Evaluation of Oblate Radial Wave Functions of the
                 Second Kind for Small $c \xi$ / 561 \\
                 15.8 Numerical Computation: Algorithms and Computer
                 Programs / 569 \\
                 15.9 Mathematical Tables / 594 \\
                 References / 619 \\
                 16: Error Function and Fresnel Integrals / 620 \\
                 16.1 Introduction to Error Function / 620 \\
                 16.2 Numerical Computation of Error Function / 621 \\
                 16.3 Gaussian Probability Integral / 624 \\
                 16.4 Introduction to Fresnel Integrals / 625 \\
                 16.5 Series and Asymptotic Expansions of Fresnel
                 Integrals / 629 \\
                 16.6 Numerical Computation of Fresnel Integrals / 630
                 \\
                 16.7 Zeros of Error Function and Fresnel Integrals /
                 635 \\
                 16.8 Mathematical Tables / 636 \\
                 References and Further Reading / 643 \\
                 17: Cosine and Sine Integrals / 644 \\
                 17.1 Introduction / 644 \\
                 17.2 Series and Asymptotic Expansions / 646 \\
                 17.3 Numerical Computation / 647 \\
                 17.4 Mathematical Table / 651 \\
                 References and Further Readings / 653 \\
                 18: Elliptic Integrals and Jacobian Elliptic Functions
                 / 654 \\
                 18.1 Introduction to Elliptic Integrals / 654 \\
                 18.2 Series Expansion of Elliptic Integrals / 659 \\
                 18.3 Numerical Computation of Elliptic Integrals / 661
                 \\
                 18.4 Introduction to Jacobian Elliptic Functions / 666
                 \\
                 18.5 Numerical Computation of Jacobian Elliptic
                 Functions / 670 \\
                 18.6 Mathematical Tables / 672 \\
                 References and Further Reading / 679 \\
                 19: Exponential Integrals / 680 \\
                 19.1 Introduction / 680 \\
                 19.2 Series, Asymptotic, and Continued Fraction
                 Expressions / 682 \\
                 19.3 Rational Approximations / 683 \\
                 19.4 Numerical Computation / 684 \\
                 19.5 Mathematical Tables / 688 \\
                 References / 693 \\
                 20: Summary of Methods for Computing Special Functions
                 / 694 \\
                 Appendix A: Derivation of Some Special Differential
                 Equations / 697 \\
                 A.1 Helmholtz Equation and Separation of Variables /
                 697 \\
                 A.2 Circular Cylindrical Coordinates / 698 \\
                 A.3 Elliptic Cylindrical Coordinates / 700 \\
                 A.4 Parabolic Cylindrical Coordinates / 700 \\
                 A.5 Spherical Coordinates / 701 \\
                 A.6 Prolate Spheroidal Coordinates / 701 \\
                 A.7 Oblate Spheroidal Coordinates / 702 \\
                 A.8 Parabolic Coordinates / 703 \\
                 References / 703 \\
                 Appendix B: Root-Finding Methods / 704 \\
                 B.1 Newton's Method / 704 \\
                 B.2 Modified Newton's Method / 706 \\
                 B.3 Secant Method / 706 \\
                 Reference / 706 \\
                 Appendix C: About the Software / 707 \\
                 Index / 709 \\
                 Index of Computer Programs / 715",
  xxauthor =     "Shan-chieh Chang and Shanjie Zhang and Jianming Jin",
  xxnote =       "There is online bookstore and library catalog
                 confusion over the authors of this book. The
                 publisher's Web page at
                 http://catalog.wiley.com/remsrch.cgi has Shan-jie Zhang
                 (Nanjing Univ., China) / Jianming Jin (Univ. of
                 Illinois at Urbana-Champaign), and a price of
                 US\$125.00. It looks like Shan-chieh Chang is merely a
                 different English transcription of Shanjie Zhang.
                 http://www.fatbrain.com/ lists this book for US\$99.95.
                 My copy of the book lists the authors as Shanjie Zhang
                 and Jianming Jin in four places.",
}


bibtype: article
filename: elefunt.bib
label: Zhang:1996:NTM
author: J. Zhang
title: A note on the tau-method approximations for the Bessel functions $ Y_0 (z) $ and $ Y_1 (z) $
journal: j-COMPUT-MATH-APPL
volume: 31
number: 9
pages: 63--70
month: may
monthnumber: 5
year: 1996
CODEN: CMAPDK
DOI: https://doi.org/10.1016/0898-1221(96)00043-0
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Sun Jun 12 08:43:36 2011
bibtimestamp: 2011.06.12 08:43:36 ???
URL: http://www.sciencedirect.com/science/article/pii/0898122196000430
fjournal: Computers and Mathematics with Applications
keywords: Automated $tau $-method; Bessel functions; Chebyshev series; Symbolic Faber polynomials
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: J. Zhang
rawtitle: A note on the tau-method approximations for the {Bessel} functions {$ Y_0 (z) $} and {$ Y_1 (z) $}
abstract:
This paper is to complete and improve the work reported in [1,2], using the Lanczos $ tau $-method (in Coleman's version) to approximate the Bessel functions $ Y_0 (z) $ and $ Y_1 (z) $. We introduce symbolic representations of the scaled Faber polynomials on any fan-shaped section of the complex plane. These Faber polynomials are used as the perturbation terms in the $ tau $-method. Numerical comparison among the power series, the Chebyshev series and the $ tau $-method are conducted to show the accuracy improvement achieved by this new version of the $ tau $-method. Some concluding remarks and suggestions on future research are given.

rawabstract:
This paper is to complete and improve the work reported in [1,2], using the Lanczos $ \tau $-method (in Coleman's version) to approximate the Bessel functions $ Y_0 (z) $ and $ Y_1 (z) $. We introduce symbolic representations of the scaled Faber polynomials on any fan-shaped section of the complex plane. These Faber polynomials are used as the perturbation terms in the $ \tau $-method. Numerical comparison among the power series, the Chebyshev series and the $ \tau $-method are conducted to show the accuracy improvement achieved by this new version of the $ \tau $-method. Some concluding remarks and suggestions on future research are given.

entry:
@Article{Zhang:1996:NTM,
  author =       "J. Zhang",
  title =        "A note on the tau-method approximations for the
                 {Bessel} functions {$ Y_0 (z) $} and {$ Y_1 (z) $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "31",
  number =       "9",
  pages =        "63--70",
  month =        may,
  year =         "1996",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/0898-1221(96)00043-0",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Sun Jun 12 08:43:36 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/0898122196000430",
  abstract =     "This paper is to complete and improve the work
                 reported in [1,2], using the Lanczos $ \tau $-method
                 (in Coleman's version) to approximate the Bessel
                 functions $ Y_0 (z) $ and $ Y_1 (z) $. We introduce
                 symbolic representations of the scaled Faber
                 polynomials on any fan-shaped section of the complex
                 plane. These Faber polynomials are used as the
                 perturbation terms in the $ \tau $-method. Numerical
                 comparison among the power series, the Chebyshev series
                 and the $ \tau $-method are conducted to show the
                 accuracy improvement achieved by this new version of
                 the $ \tau $-method. Some concluding remarks and
                 suggestions on future research are given.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "Automated $\tau$-method; Bessel functions; Chebyshev
                 series; Symbolic Faber polynomials",
}


bibtype: article
filename: elefunt.bib
label: Zhang:1996:SNC
author: Jun Zhang
title: Symbolic and numerical computation on Bessel functions of complex argument and large magnitude
journal: j-J-COMPUT-APPL-MATH
volume: 75
number: 1
pages: 99--118
day: 12
month: nov
monthnumber: 11
year: 1996
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:58 MST 2017
bibtimestamp: 2017.02.25 12:35:58 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042796000635
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Jun Zhang
rawtitle: Symbolic and numerical computation on {Bessel} functions of complex argument and large magnitude
entry:
@Article{Zhang:1996:SNC,
  author =       "Jun Zhang",
  title =        "Symbolic and numerical computation on {Bessel}
                 functions of complex argument and large magnitude",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "75",
  number =       "1",
  pages =        "99--118",
  day =          "12",
  month =        nov,
  year =         "1996",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:58 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796000635",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Abad:1997:NEC
author: Julio Abad and Javier Sesma
title: A new expansion of the confluent hypergeometric function in terms of modified Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 78
number: 1
pages: 97--101
day: 3
month: feb
monthnumber: 2
year: 1997
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:35:59 MST 2017
bibtimestamp: 2017.02.25 12:35:59 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042796001331
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Julio Abad and Javier Sesma
rawtitle: A new expansion of the confluent hypergeometric function in terms of modified {Bessel} functions
entry:
@Article{Abad:1997:NEC,
  author =       "Julio Abad and Javier Sesma",
  title =        "A new expansion of the confluent hypergeometric
                 function in terms of modified {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "78",
  number =       "1",
  pages =        "97--101",
  day =          "3",
  month =        feb,
  year =         "1997",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:35:59 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796001331",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Alzer:1997:HMI
author: Horst Alzer
title: A harmonic mean inequality for the gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 87
number: 2
pages: 195--198
day: 23
month: dec
monthnumber: 12
year: 1997
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:36:06 MST 2017
bibtimestamp: 2017.02.25 12:36:06 MST
note: See corrigendum cite Alzer:1998:CHM.
URL: http://www.sciencedirect.com/science/article/pii/S0377042796001811
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Horst Alzer
rawnote: See corrigendum \cite{Alzer:1998:CHM}.
rawtitle: A harmonic mean inequality for the gamma function
entry:
@Article{Alzer:1997:HMI,
  author =       "Horst Alzer",
  title =        "A harmonic mean inequality for the gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "87",
  number =       "2",
  pages =        "195--198",
  day =          "23",
  month =        dec,
  year =         "1997",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  note =         "See corrigendum \cite{Alzer:1998:CHM}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042796001811",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Alzer:1997:SIG
author: Horst Alzer
title: On some inequalities for the gamma and psi functions
journal: j-MATH-COMPUT
volume: 66
number: 217
pages: 373--389
month: jan
monthnumber: 1
year: 1997
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33B15 (26D07)
MRnumber: 97e:33004
MRreviewer: Peter Schroth
bibdate: Fri Jul 16 10:38:40 MDT 1999
bibsource: http://www.ams.org/mcom/1997-66-217; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.07.16 10:38:40 MDT
URL: http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00807-7&u=/mcom/1997-66-217/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Horst Alzer
rawtitle: On some inequalities for the gamma and psi functions
entry:
@Article{Alzer:1997:SIG,
  author =       "Horst Alzer",
  title =        "On some inequalities for the gamma and psi functions",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "217",
  pages =        "373--389",
  month =        jan,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B15 (26D07)",
  MRnumber =     "97e:33004",
  MRreviewer =   "Peter Schroth",
  bibdate =      "Fri Jul 16 10:38:40 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-217;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00807-7&u=/mcom/1997-66-217/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Alzer:1997:SII
author: Horst Alzer
title: On some inequalities for the incomplete gamma function
journal: j-MATH-COMPUT
volume: 66
number: 218
pages: 771--778
month: apr
monthnumber: 4
year: 1997
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33B20 (26D07)
MRnumber: 97h:33004
bibdate: Fri Jul 16 10:38:42 MDT 1999
bibsource: http://www.ams.org/mcom/1997-66-218; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.07.16 10:38:42 MDT
URL: http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00814-4&u=/mcom/1997-66-218/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Horst Alzer
rawtitle: On some inequalities for the incomplete gamma function
entry:
@Article{Alzer:1997:SII,
  author =       "Horst Alzer",
  title =        "On some inequalities for the incomplete gamma
                 function",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "218",
  pages =        "771--778",
  month =        apr,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33B20 (26D07)",
  MRnumber =     "97h:33004",
  bibdate =      "Fri Jul 16 10:38:42 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-218;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00814-4&u=/mcom/1997-66-218/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Bailey:1997:RCV
author: David Bailey and Peter Borwein and Simon Plouffe
title: On the rapid computation of various polylogarithmic constants
journal: j-MATH-COMPUT
volume: 66
number: 218
pages: 903--913
month: apr
monthnumber: 4
year: 1997
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11Yxx
MRnumber: 1 415 794
bibdate: Fri Jul 16 10:38:42 MDT 1999
bibtimestamp: 1999.07.16 10:38:42 MDT
URL: http://www.ams.org/journals/mcom/1997-66-218/S0025-5718-97-00856-9/S0025-5718-97-00856-9.pdf
fjournal: Mathematics of Computation
keywords: BBP formula
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: David Bailey and Peter Borwein and Simon Plouffe
rawtitle: On the rapid computation of various polylogarithmic constants
bibsource:
http://www.ams.org/mcom/1997-66-218; http://www.jstor.org/journals/00029890.htm; https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib

entry:
@Article{Bailey:1997:RCV,
  author =       "David Bailey and Peter Borwein and Simon Plouffe",
  title =        "On the rapid computation of various polylogarithmic
                 constants",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "218",
  pages =        "903--913",
  month =        apr,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Yxx",
  MRnumber =     "1 415 794",
  bibdate =      "Fri Jul 16 10:38:42 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-218;
                 http://www.jstor.org/journals/00029890.htm;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  URL =          "http://www.ams.org/journals/mcom/1997-66-218/S0025-5718-97-00856-9/S0025-5718-97-00856-9.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "BBP formula",
  xxnote =       "See \cite{Adamchik:1997:SF}.",
}


bibtype: article
filename: elefunt.bib
label: Blinn:1997:JBC
author: James F. Blinn
title: Jim Blinn's Corner: Floating-Point Tricks
journal: j-IEEE-CGA
volume: 17
number: 4
pages: 80--84
month: jul
monthnumber: 7
year: 1997
CODEN: ICGADZ
DOI: https://doi.org/10.1109/38.595279
ISSN: 0272-1716 (print), 1558-1756 (electronic) OR 02721716 (print), 15581756 (electronic)
ISSNL: 0272-1716 OR 02721716
bibdate: Sat Jul 16 08:40:52 MDT 2005
bibtimestamp: 2005.07.16 08:40:52 MDT
fjournal: IEEE Computer Graphics and Applications
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/portal/web/csdl/magazines/cga
rawauthor: James F. Blinn
rawtitle: {Jim Blinn}'s Corner: Floating-Point Tricks
note:
Discusses use of IEEE 754 single-precision floating-point bit patterns as integers for implementations of fast, but low-accuracy, functions useful in computer graphics.

rawnote:
Discusses use of IEEE 754 single-precision floating-point bit patterns as integers for implementations of fast, but low-accuracy, functions useful in computer graphics.

entry:
@Article{Blinn:1997:JBC,
  author =       "James F. Blinn",
  title =        "{Jim Blinn}'s Corner: Floating-Point Tricks",
  journal =      j-IEEE-CGA,
  volume =       "17",
  number =       "4",
  pages =        "80--84",
  month =        jul # "\slash " # aug,
  year =         "1997",
  CODEN =        "ICGADZ",
  DOI =          "https://doi.org/10.1109/38.595279",
  ISSN =         "0272-1716 (print), 1558-1756 (electronic)",
  ISSN-L =       "0272-1716",
  bibdate =      "Sat Jul 16 08:40:52 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Discusses use of IEEE 754 single-precision
                 floating-point bit patterns as integers for
                 implementations of fast, but low-accuracy, functions
                 useful in computer graphics.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Computer Graphics and Applications",
  journal-URL =  "http://www.computer.org/portal/web/csdl/magazines/cga",
  summary =      "The author discusses IEEE floating point
                 representation that stores numbers in what amounts to
                 scientific notation. He considers the sign bit, the
                 logarithm function, function approximations, errors and
                 refinements \ldots{}",
}


bibtype: incollection
filename: elefunt.bib
label: Borwein:1997:AGMa
author: J. M. Borwein and P. B. Borwein
title: The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions
crossref: Berggren:1997:PSB
pages: 537--552
year: 1997
DOI: https://doi.org/10.1007/978-1-4757-2736-4_56
bibdate: Thu Aug 11 09:36:22 MDT 2016
bibtimestamp: 2016.08.11 09:36:22 MDT
note: Reprint of cite Borwein:1984:AGM.
URL: http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_56
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawauthor: J. M. Borwein and P. B. Borwein
rawnote: Reprint of \cite{Borwein:1984:AGM}.
rawtitle: The Arithmetic--Geometric Mean and Fast Computation of Elementary Functions
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InCollection{Borwein:1997:AGMa,
  author =       "J. M. Borwein and P. B. Borwein",
  title =        "The Arithmetic--Geometric Mean and Fast Computation of
                 Elementary Functions",
  crossref =     "Berggren:1997:PSB",
  pages =        "537--552",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4757-2736-4_56",
  bibdate =      "Thu Aug 11 09:36:22 MDT 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Reprint of \cite{Borwein:1984:AGM}.",
  URL =          "http://link.springer.com/chapter/10.1007/978-1-4757-2736-4_56",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: article
filename: elefunt.bib
label: Bshouty:1997:TBA
author: Nader H. Bshouty and Yishay Mansour and Baruch Schieber and Prasoon Tiwari
title: A tight bound for approximating the square root
journal: j-INFO-PROC-LETT
volume: 63
number: 4
pages: 211--213
day: 10
month: sep
monthnumber: 9
year: 1997
CODEN: IFPLAT
ISSN: 0020-0190 (print), 1872-6119 (electronic) OR 00200190 (print), 18726119 (electronic)
ISSNL: 0020-0190 OR 00200190
MRclass: 68Q25 (65B15 68Q40)
MRnumber: 1 477 306
bibdate: Sat Nov 7 17:55:54 MST 1998
bibtimestamp: 1998.11.07 17:55:54 MST
fjournal: Information Processing Letters
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00200190
rawauthor: Nader H. Bshouty and Yishay Mansour and Baruch Schieber and Prasoon Tiwari
rawtitle: A tight bound for approximating the square root
bibsource:
http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Bshouty:1997:TBA,
  author =       "Nader H. Bshouty and Yishay Mansour and Baruch
                 Schieber and Prasoon Tiwari",
  title =        "A tight bound for approximating the square root",
  journal =      j-INFO-PROC-LETT,
  volume =       "63",
  number =       "4",
  pages =        "211--213",
  day =          "10",
  month =        sep,
  year =         "1997",
  CODEN =        "IFPLAT",
  ISSN =         "0020-0190 (print), 1872-6119 (electronic)",
  ISSN-L =       "0020-0190",
  MRclass =      "68Q25 (65B15 68Q40)",
  MRnumber =     "1 477 306",
  bibdate =      "Sat Nov 7 17:55:54 MST 1998",
  bibsource =    "http://www.elsevier.com:80/inca/publications/store/5/0/5/6/1/2/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Information Processing Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00200190",
}


bibtype: article
filename: elefunt.bib
label: El-Gabali:1997:MTA
author: Magdi A. El-Gabali
title: Multiple-term approximations for Appell's $ F_1 $ function
journal: j-J-AUSTRAL-MATH-SOC-SER-B
volume: 39
number: 1
pages: 135--148
month: jul
monthnumber: 7
year: 1997
CODEN: JAMMDU
DOI: https://doi.org/10.1017/S0334270000009267
ISSN: 0334-2700 OR 03342700
ISSNL: 0334-2700 OR 03342700
bibdate: Fri Apr 26 16:13:39 MDT 2019
bibtimestamp: 2019.04.26 16:13:39 MDT
fjournal: Journal of the Australian Mathematical Society. Series B, Applied Mathematics
acknowledgement: ack-nhfb
ajournal: J. Austral Math. Soc. Ser. B
journalURL: http://journals.cambridge.org/action/displayJournal?jid=ANZ
onlinedate: 17 February 2009
rawauthor: Magdi A. El-Gabali
rawtitle: Multiple-term approximations for {Appell}'s {$ F_1 $} function
bibsource:
https://www.math.utah.edu/pub/tex/bib/anziamj.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
https://www.cambridge.org/core/journals/anziam-journal/article/multipleterm-approximations-for-appells-f1-function/8E218109899D68FD0DC15B6E9D61E8BD

entry:
@Article{El-Gabali:1997:MTA,
  author =       "Magdi A. El-Gabali",
  title =        "Multiple-term approximations for {Appell}'s {$ F_1 $}
                 function",
  journal =      j-J-AUSTRAL-MATH-SOC-SER-B,
  volume =       "39",
  number =       "1",
  pages =        "135--148",
  month =        jul,
  year =         "1997",
  CODEN =        "JAMMDU",
  DOI =          "https://doi.org/10.1017/S0334270000009267",
  ISSN =         "0334-2700",
  ISSN-L =       "0334-2700",
  bibdate =      "Fri Apr 26 16:13:39 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/anziamj.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://www.cambridge.org/core/journals/anziam-journal/article/multipleterm-approximations-for-appells-f1-function/8E218109899D68FD0DC15B6E9D61E8BD",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Austral Math. Soc. Ser. B",
  fjournal =     "Journal of the Australian Mathematical Society. Series
                 B, Applied Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=ANZ",
  onlinedate =   "17 February 2009",
}


bibtype: article
filename: elefunt.bib
label: Fdil:1997:SRC
author: A. Fdil
title: Some results of convergence acceleration for a general $ Theta $-type algorithm
journal: j-APPL-NUM-MATH
volume: 23
number: 2
pages: 219--240
day: 21
month: mar
monthnumber: 3
year: 1997
CODEN: ANMAEL
ISSN: 0168-9274 (print), 1873-5460 (electronic) OR 01689274 (print), 18735460 (electronic)
ISSNL: 0168-9274 OR 01689274
MRclass: 65B10 (65D32)
MRnumber: 1 437 884
bibdate: Wed Jul 28 14:36:42 MDT 1999
bibtimestamp: 1999.07.28 14:36:42 MDT
URL: http://www.elsevier.com/cas/tree/store/apnum/sub/1997/23/2/738.pdf
fjournal: Applied Numerical Mathematics: Transactions of IMACS
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01689274/
rawauthor: A. Fdil
rawtitle: Some results of convergence acceleration for a general {$ \Theta $}-type algorithm
bibsource:
http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1997&volume=23&issue=2; https://www.math.utah.edu/pub/tex/bib/applnummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Fdil:1997:SRC,
  author =       "A. Fdil",
  title =        "Some results of convergence acceleration for a general
                 {$ \Theta $}-type algorithm",
  journal =      j-APPL-NUM-MATH,
  volume =       "23",
  number =       "2",
  pages =        "219--240",
  day =          "21",
  month =        mar,
  year =         "1997",
  CODEN =        "ANMAEL",
  ISSN =         "0168-9274 (print), 1873-5460 (electronic)",
  ISSN-L =       "0168-9274",
  MRclass =      "65B10 (65D32)",
  MRnumber =     "1 437 884",
  bibdate =      "Wed Jul 28 14:36:42 MDT 1999",
  bibsource =    "http://www.elsevier.com/cgi-bin/cas/tree/store/apnum/cas_free/browse/browse.cgi?year=1997&volume=23&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/applnummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/cas/tree/store/apnum/sub/1997/23/2/738.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Numerical Mathematics: Transactions of IMACS",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01689274/",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Forrey:1997:CHF
author: Robert C. Forrey
title: Computing the hypergeometric function
journal: j-J-COMPUT-PHYS
volume: 137
number: 1
pages: 79--100
month: oct
monthnumber: 10
year: 1997
CODEN: JCTPAH
DOI: https://doi.org/10.1006/jcph.1997.5794
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
MRclass: 33C05 (33-04 65D20)
MRnumber: MR1481885 (99g:33004)
bibdate: Thu Dec 01 09:06:55 2011
bibtimestamp: 2011.12.01 09:06:55 ???
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Robert C. Forrey
rawtitle: Computing the hypergeometric function
remark:
The author gives a FORTRAN program for computing $_2 F_1$ for real variable and parameters, using rapidly-convergent power series in six separate intervals.

entry:
@Article{Forrey:1997:CHF,
  author =       "Robert C. Forrey",
  title =        "Computing the hypergeometric function",
  journal =      j-J-COMPUT-PHYS,
  volume =       "137",
  number =       "1",
  pages =        "79--100",
  month =        oct,
  year =         "1997",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1006/jcph.1997.5794",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  MRclass =      "33C05 (33-04 65D20)",
  MRnumber =     "MR1481885 (99g:33004)",
  bibdate =      "Thu Dec 01 09:06:55 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
  remark =       "The author gives a FORTRAN program for computing $_2
                 F_1$ for real variable and parameters, using
                 rapidly-convergent power series in six separate
                 intervals.",
}


bibtype: article
filename: elefunt.bib
label: Ghanem:1997:SBF
author: Riadh Ben Ghanem and Clement Frappier
title: Spherical Bessel functions and explicit quadrature formula
journal: j-MATH-COMPUT
volume: 66
number: 217
pages: 289--296
month: jan
monthnumber: 1
year: 1997
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 33C10 (41A55 65D32)
MRnumber: 97c:33005
MRreviewer: N. Hayek Calil
bibdate: Fri Jul 16 10:38:40 MDT 1999
bibsource: http://www.ams.org/mcom/1997-66-217; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.07.16 10:38:40 MDT
URL: http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00794-1&u=/mcom/1997-66-217/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Riadh Ben Ghanem and Cl{\'e}ment Frappier
rawtitle: Spherical {Bessel} functions and explicit quadrature formula
entry:
@Article{Ghanem:1997:SBF,
  author =       "Riadh Ben Ghanem and Cl{\'e}ment Frappier",
  title =        "Spherical {Bessel} functions and explicit quadrature
                 formula",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "217",
  pages =        "289--296",
  month =        jan,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "33C10 (41A55 65D32)",
  MRnumber =     "97c:33005",
  MRreviewer =   "N. Hayek Calil",
  bibdate =      "Fri Jul 16 10:38:40 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1997-66-217;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-97-00794-1&u=/mcom/1997-66-217/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Goano:1997:RA7
author: Michele Goano
title: Remark on Algorithm 745
journal: j-TOMS
volume: 23
number: 2
pages: 295--295
month: jun
monthnumber: 6
year: 1997
CODEN: ACMSCU
DOI: https://doi.org/10.1145/264029.643581
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Tue Mar 9 10:19:38 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.03.09 10:19:38 ???
note: See cite Goano:1995:ACC.
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Michele Goano
rawnote: See \cite{Goano:1995:ACC}.
rawtitle: Remark on {Algorithm 745}
entry:
@Article{Goano:1997:RA7,
  author =       "Michele Goano",
  title =        "Remark on {Algorithm 745}",
  journal =      j-TOMS,
  volume =       "23",
  number =       "2",
  pages =        "295--295",
  month =        jun,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/264029.643581",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Tue Mar 9 10:19:38 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Goano:1995:ACC}.",
  acknowledgement = ack-rfb # " and " # ack-kr # "\slash " # ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Hare:1997:CPB
author: D. E. G. Hare
title: Computing the Principal Branch of log-Gamma
journal: j-J-ALG
volume: 25
number: 2
pages: 221--236
month: nov
monthnumber: 11
year: 1997
CODEN: JOALDV
DOI: https://doi.org/10.1006/jagm.1997.0881
ISSN: 0196-6774 (print), 1090-2678 (electronic) OR 01966774 (print), 10902678 (electronic)
ISSNL: 0196-6774 OR 01966774
bibdate: Tue Dec 11 09:16:52 MST 2012
bibtimestamp: 2012.12.11 09:16:52 MST
URL: http://www.sciencedirect.com/science/article/pii/S0196677497908816
fjournal: Journal of Algorithms
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/01966774
rawauthor: D. E. G. Hare
rawtitle: Computing the Principal Branch of {log-Gamma}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jalg.bib; https://www.math.utah.edu/pub/tex/bib/maple-extract.bib

abstract:
The log-Gamma function is an important special function of mathematics, and its principal branch is required in many applications. We develop here the mathematics required to evaluate the principal branch to arbitrary precision, including a new bound for the error in Stirling's asymptotic series. We conclude with a discussion of the implementation of the principal branch of the log-Gamma function in the Maple symbolic algebra system, starting with version Maple V, Release 3.

rawabstract:
The log-Gamma function is an important special function of mathematics, and its principal branch is required in many applications. We develop here the mathematics required to evaluate the principal branch to arbitrary precision, including a new bound for the error in Stirling's asymptotic series. We conclude with a discussion of the implementation of the principal branch of the log-Gamma function in the Maple symbolic algebra system, starting with version Maple V, Release 3.

entry:
@Article{Hare:1997:CPB,
  author =       "D. E. G. Hare",
  title =        "Computing the Principal Branch of {log-Gamma}",
  journal =      j-J-ALG,
  volume =       "25",
  number =       "2",
  pages =        "221--236",
  month =        nov,
  year =         "1997",
  CODEN =        "JOALDV",
  DOI =          "https://doi.org/10.1006/jagm.1997.0881",
  ISSN =         "0196-6774 (print), 1090-2678 (electronic)",
  ISSN-L =       "0196-6774",
  bibdate =      "Tue Dec 11 09:16:52 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jalg.bib;
                 https://www.math.utah.edu/pub/tex/bib/maple-extract.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0196677497908816",
  abstract =     "The log-Gamma function is an important special
                 function of mathematics, and its principal branch is
                 required in many applications. We develop here the
                 mathematics required to evaluate the principal branch
                 to arbitrary precision, including a new bound for the
                 error in Stirling's asymptotic series. We conclude with
                 a discussion of the implementation of the principal
                 branch of the log-Gamma function in the Maple symbolic
                 algebra system, starting with version Maple V, Release
                 3.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Algorithms",
  journal-URL =  "http://www.sciencedirect.com/science/journal/01966774",
}


bibtype: article
filename: elefunt.bib
label: Harris:1997:NAC
author: Frank E. Harris
title: New Approach to Calculation of the Leaky Aquifer Function
journal: j-IJQC
volume: 63
number: 5
pages: 913--916
year: 1997
CODEN: IJQCB2
DOI: https://doi.org/10.1002/(SICI)1097-461X(1997)63:5<913::AID-QUA1>3.0.CO%3B2-Z
ISSN: 0020-7608 (print), 1097-461X (electronic) OR 00207608 (print), 1097461X (electronic)
ISSNL: 0020-7608 OR 00207608
bibdate: Tue Oct 4 06:59:09 MDT 2011
bibtimestamp: 2011.10.04 06:59:09 MDT
fjournal: International Journal of Quantum Chemistry
acknowledgement: ack-nhfb
ajournal: Int. J. Quantum Chem.
journalURL: http://www.interscience.wiley.com/jpages/0020-7608/
journalabr: Int J Quant Chem
onlinedate: 6 Dec 1998
rawauthor: Frank E. Harris
rawtitle: New Approach to Calculation of the Leaky Aquifer Function
bibsource:
Compendex database; http://www.interscience.wiley.com/jpages/0020-7608; http://www3.interscience.wiley.com/journalfinder.html; https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ijqc.bib; https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib

URL:
http://www3.interscience.wiley.com/cgi-bin/abstract?ID=42641; http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=42641&PLACEBO=IE.pdf

entry:
@Article{Harris:1997:NAC,
  author =       "Frank E. Harris",
  title =        "New Approach to Calculation of the Leaky Aquifer
                 Function",
  journal =      j-IJQC,
  volume =       "63",
  number =       "5",
  pages =        "913--916",
  month =        "????",
  year =         "1997",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/(SICI)1097-461X(1997)63:5<913::AID-QUA1>3.0.CO%3B2-Z",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Tue Oct 4 06:59:09 MDT 2011",
  bibsource =    "Compendex database;
                 http://www.interscience.wiley.com/jpages/0020-7608;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib",
  URL =          "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=42641;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=42641&PLACEBO=IE.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Quantum Chem.",
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  journalabr =   "Int J Quant Chem",
  onlinedate =   "6 Dec 1998",
}


bibtype: article
filename: elefunt.bib
label: Ito:1997:EIA
author: M. Ito and N. Takagi and S. Yajima
journal: j-IEEE-TRANS-COMPUT
volume: 46
number: 4
pages: 495--498
month: apr
monthnumber: 4
year: 1997
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.588066
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 10:06:22 MDT 2011
bibtimestamp: 2011.07.06 10:06:22 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588066
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: M. Ito and N. Takagi and S. Yajima
title:
Efficient initial approximation for multiplicative division and square root by a multiplication with operand modification

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib

rawtitle:
Efficient initial approximation for multiplicative division and square root by a multiplication with operand modification

entry:
@Article{Ito:1997:EIA,
  author =       "M. Ito and N. Takagi and S. Yajima",
  title =        "Efficient initial approximation for multiplicative
                 division and square root by a multiplication with
                 operand modification",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "46",
  number =       "4",
  pages =        "495--498",
  month =        apr,
  year =         "1997",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.588066",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 10:06:22 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=588066",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "An efficient initial approximation method for
                 multiplicative division and square root is proposed. It
                 is a modification of the piecewise linear
                 approximation. The multiplication and the addition
                 required for the linear approximation are replaced by
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Karp:1997:HPD
author: Alan H. Karp and Peter Markstein
title: High-Precision Division and Square Root
journal: j-TOMS
volume: 23
number: 4
pages: 561--589
month: dec
monthnumber: 12
year: 1997
CODEN: ACMSCU
DOI: https://doi.org/10.1145/279232.279237
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Thu Nov 8 14:50:37 2007
bibtimestamp: 2007.11.08 14:50:37 ???
fjournal: ACM Transactions on Mathematical Software (TOMS)
keywords: algorithms, performance, division, quad precision, square root.
acknowledgement: ack-rfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Alan H. Karp and Peter Markstein
rawtitle: High-Precision Division and Square Root
bibsource:
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

URL:
http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps; http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/

abstract:
We present division and square root algorithms for calculation with more bits than are handled by the floating-point hardware. These algorithms avoid the need to multiply two high-precision numbers, speeding up the last iteration by as much as a factor of 10. We also show how to produce the floating-point number closest to the exact result with relatively few additional operations.

subject:
G.1.0 [Numerical Analysis]: General -- computer arithmetic. G.4 [Mathematics of Computing]: Mathematical Software.

rawabstract:
We present division and square root algorithms for calculation with more bits than are handled by the floating-point hardware. These algorithms avoid the need to multiply two high-precision numbers, speeding up the last iteration by as much as a factor of 10. We also show how to produce the floating-point number closest to the exact result with relatively few additional operations.

entry:
@Article{Karp:1997:HPD,
  author =       "Alan H. Karp and Peter Markstein",
  title =        "High-Precision Division and Square Root",
  journal =      j-TOMS,
  volume =       "23",
  number =       "4",
  pages =        "561--589",
  month =        dec,
  year =         "1997",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/279232.279237",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Thu Nov 8 14:50:37 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://www.acm.org/pubs/articles/journals/toms/forthcoming/a0-karp/a0-karp.ps;
                 http://www.acm.org/pubs/citations/journals/toms/1997-23-4/p561-karp/",
  abstract =     "We present division and square root algorithms for
                 calculation with more bits than are handled by the
                 floating-point hardware. These algorithms avoid the
                 need to multiply two high-precision numbers, speeding
                 up the last iteration by as much as a factor of 10. We
                 also show how to produce the floating-point number
                 closest to the exact result with relatively few
                 additional operations.",
  accepted =     "June 1997",
  acknowledgement = ack-rfb # " and " # ack-kr,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "algorithms, performance, division, quad precision,
                 square root.",
  subject =      "G.1.0 [Numerical Analysis]: General -- computer
                 arithmetic. G.4 [Mathematics of Computing]:
                 Mathematical Software.",
}


bibtype: article
filename: elefunt.bib
label: Kolbig:1997:TEH
author: K. S. Kolbig
journal: j-MATH-COMPUT
volume: 66
number: 220
pages: 1767--1767
month: oct
monthnumber: 10
year: 1997
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 44-00 (33-00)
MRnumber: 1 434 945
bibdate: Tue Dec 2 11:25:56 MST 1997
bibtimestamp: 1997.12.02 11:25:56 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: K. S. K{\"o}lbig
title:
Table errata: booktitle Handbook of elliptic integrals for engineers and scientists [Second edition, Springer, New York, 1971, MR bf 43 #3506] by P. F. Byrd and M. D. Friedman

rawtitle:
Table errata: {{\booktitle{Handbook of elliptic integrals for engineers and scientists}} [Second edition, Springer, New York, 1971, MR {\bf 43} \#3506] by P. F. Byrd and M. D. Friedman}

entry:
@Article{Kolbig:1997:TEH,
  author =       "K. S. K{\"o}lbig",
  title =        "Table errata: {{\booktitle{Handbook of elliptic
                 integrals for engineers and scientists}} [Second
                 edition, Springer, New York, 1971, MR {\bf 43} \#3506]
                 by P. F. Byrd and M. D. Friedman}",
  journal =      j-MATH-COMPUT,
  volume =       "66",
  number =       "220",
  pages =        "1767--1767",
  month =        oct,
  year =         "1997",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "44-00 (33-00)",
  MRnumber =     "1 434 945",
  bibdate =      "Tue Dec 2 11:25:56 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Lee:1997:PRF
author: M. Howard Lee
title: Polylogarithms and Riemann's $ zeta $ function
journal: j-PHYS-REV-E
volume: 56
number: 4
pages: 3909--3912
month: oct
monthnumber: 10
year: 1997
CODEN: PLEEE8
DOI: https://doi.org/10.1103/physreve.56.3909
ISSN: 1539-3755 (print), 1550-2376 (electronic) OR 15393755 (print), 15502376 (electronic)
ISSNL: 1539-3755 OR 15393755
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
fjournal: Physical Review E (Statistical physics, plasmas, fluids, and related interdisciplinary topics)
journalURL: http://pre.aps.org/browse
rawauthor: M. Howard Lee
rawtitle: Polylogarithms and {Riemann}'s $ \zeta $ function
remark:
The paper presents increasingly complicated closed forms of $ Li _n(x) $ for negative $n$ to $ n = - 8$, and reports that no general form for negative $n$ is apparent. See https://oeis.org/A131758 for related functions and sequences. Maple and Mathematica can produce such formulas with code like simplify(expand(polylog(-13,x))) and PolyLog[-13, x].

entry:
@Article{Lee:1997:PRF,
  author =       "M. Howard Lee",
  title =        "Polylogarithms and {Riemann}'s $ \zeta $ function",
  journal =      j-PHYS-REV-E,
  volume =       "56",
  number =       "4",
  pages =        "3909--3912",
  month =        oct,
  year =         "1997",
  CODEN =        "PLEEE8",
  DOI =          "https://doi.org/10.1103/physreve.56.3909",
  ISSN =         "1539-3755 (print), 1550-2376 (electronic)",
  ISSN-L =       "1539-3755",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  fjournal =     "Physical Review E (Statistical physics, plasmas,
                 fluids, and related interdisciplinary topics)",
  journal-URL =  "http://pre.aps.org/browse",
  remark =       "The paper presents increasingly complicated closed
                 forms of $ \Li_n(x) $ for negative $n$ to $ n = - 8$,
                 and reports that no general form for negative $n$ is
                 apparent. See https://oeis.org/A131758 for related
                 functions and sequences. Maple and Mathematica can
                 produce such formulas with code like
                 simplify(expand(polylog(-13,x))) and PolyLog[-13, x].",
}


bibtype: article
filename: elefunt.bib
label: Lether:1997:CNM
author: Frank G. Lether
title: Constrained near-minimax rational approximations to Dawson's integral
journal: j-APPL-MATH-COMP
volume: 88
number: 2--3
pages: 267--274
day: 30
month: dec
monthnumber: 12
year: 1997
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/S0096-3003(96)00330-X
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Tue Nov 20 21:02:59 MST 2012
bibtimestamp: 2012.11.20 21:02:59 MST
URL: http://www.sciencedirect.com/science/article/pii/S009630039600330X
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003/
rawauthor: Frank G. Lether
rawtitle: Constrained near-minimax rational approximations to {Dawson}'s integral
bibsource:
https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Lether:1997:CNM,
  author =       "Frank G. Lether",
  title =        "Constrained near-minimax rational approximations to
                 {Dawson}'s integral",
  journal =      j-APPL-MATH-COMP,
  volume =       "88",
  number =       "2--3",
  pages =        "267--274",
  day =          "30",
  month =        dec,
  year =         "1997",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/S0096-3003(96)00330-X",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Nov 20 21:02:59 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S009630039600330X",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}


bibtype: inproceedings
filename: elefunt.bib
label: Li:1997:ISP
author: Yamin Li and Wanming Chu
title: Implementation of single precision floating point square root on FPGAs
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 226--232
year: 1997
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Yamin Li and Wanming Chu
rawtitle: Implementation of single precision floating point square root on {FPGAs}
booktitle:
Proceedings of the 5th Annual IEEE Symposium on FPGAs for Custom Computing Machines, 16--18 April 1997

rawbooktitle:
Proceedings of the 5th Annual {IEEE} Symposium on {FPGAs} for Custom Computing Machines, 16--18 April 1997

entry:
@InProceedings{Li:1997:ISP,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the 5th Annual {IEEE} Symposium on
                 {FPGAs} for Custom Computing Machines, 16--18 April
                 1997",
  title =        "Implementation of single precision floating point
                 square root on {FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "226--232",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  summary =      "The square root operation is hard to implement on
                 FPGAs because of the complexity of the algorithms. In
                 this paper, we present a non-restoring square root
                 algorithm and two very simple single precision floating
                 point square root implementations \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Li:1997:PAI
author: Yamin Li and Wanming Chu
title: Parallel-array implementations of a non-restoring square root algorithm
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 690--695
year: 1997
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Yamin Li and Wanming Chu
rawtitle: Parallel-array implementations of a non-restoring square root algorithm
booktitle:
Proceedings of the 1997 IEEE International Conference on Computer Design: VLSI in Computers and Processors: ICCD '97

rawbooktitle:
Proceedings of the 1997 {IEEE} International Conference on Computer Design: {VLSI} in Computers and Processors: {ICCD '97}

entry:
@InProceedings{Li:1997:PAI,
  author =       "Yamin Li and Wanming Chu",
  booktitle =    "Proceedings of the 1997 {IEEE} International
                 Conference on Computer Design: {VLSI} in Computers and
                 Processors: {ICCD '97}",
  title =        "Parallel-array implementations of a non-restoring
                 square root algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "690--695",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "In this paper we present a parallel-array
                 implementation of a new non-restoring square root
                 algorithm (PASQRT). The carry-save adder (CSA) is used
                 in the parallel array. The PASQRT has several features
                 unlike other implementations. First, it does \ldots{}",
}


bibtype: incollection
filename: elefunt.bib
label: Lozier:1997:PST
author: Daniel W. Lozier
title: A Proposed Software Test Service for Special Functions
crossref: Boisvert:1997:QNS
pages: 167--178
year: 1997
bibdate: Fri Jul 09 06:00:46 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:00:46 ???
remark: See preprint cite Lozier:1996:PST.
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier
rawtitle: A Proposed Software Test Service for Special Functions
entry:
@InCollection{Lozier:1997:PST,
  author =       "Daniel W. Lozier",
  title =        "A Proposed Software Test Service for Special
                 Functions",
  crossref =     "Boisvert:1997:QNS",
  pages =        "167--178",
  year =         "1997",
  bibdate =      "Fri Jul 09 06:00:46 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "See preprint \cite{Lozier:1996:PST}.",
}


bibtype: techreport
filename: elefunt.bib
label: Lozier:1997:TRN
author: Daniel W. Lozier
title: Toward a Revised NBS Handbook of Mathematical Functions
type: Technical Report
number: NISTIR 6072
institution: pub-NIST
address: pub-NIST:adr
pages: 8
month: sep
monthnumber: 9
year: 1997
bibdate: Fri Jul 09 06:35:07 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:35:07 ???
URL: http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6072.ps.gz
acknowledgement: ack-nhfb
rawauthor: Daniel W. Lozier
rawtitle: Toward a Revised {NBS} Handbook of Mathematical Functions
entry:
@TechReport{Lozier:1997:TRN,
  author =       "Daniel W. Lozier",
  title =        "Toward a Revised {NBS} Handbook of Mathematical
                 Functions",
  type =         "Technical Report",
  number =       "NISTIR 6072",
  institution =  pub-NIST,
  address =      pub-NIST:adr,
  pages =        "8",
  month =        sep,
  year =         "1997",
  bibdate =      "Fri Jul 09 06:35:07 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6072.ps.gz",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: MacLeod:1997:AEE
author: Allan J. MacLeod
title: Accurate and efficient evaluation of the Bose--Einstein functions $ g_3 / 2 $ and $ g_5 / 2 $
journal: j-COMPUT-PHYS
volume: 11
number: 4
pages: 385--??
month: jul
monthnumber: 7
year: 1997
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.168609
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:46:08 MDT 2019
bibtimestamp: 2019.04.10 08:46:08 MDT
URL: https://aip.scitation.org/doi/10.1063/1.168609
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: Allan J. MacLeod
rawtitle: Accurate and efficient evaluation of the {Bose--Einstein} functions $ g_{3 / 2} $ and $ g_{5 / 2} $
entry:
@Article{MacLeod:1997:AEE,
  author =       "Allan J. MacLeod",
  title =        "Accurate and efficient evaluation of the
                 {Bose--Einstein} functions $ g_{3 / 2} $ and $ g_{5 /
                 2} $",
  journal =      j-COMPUT-PHYS,
  volume =       "11",
  number =       "4",
  pages =        "385--??",
  month =        jul,
  year =         "1997",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168609",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:46:08 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168609",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: inproceedings
filename: elefunt.bib
label: Matsubara:1997:LPZ
author: G. Matsubara and N. Ide
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 198--209
year: 1997
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: G. Matsubara and N. Ide
booktitle:
Proceedings of the Third International Symposium on Advanced Research in Asynchronous Circuits and Systems, 7--10 April 1997

title:
A low power zero-overhead self-timed division and square root unit combining a single-rail static circuit with a dual-rail dynamic circuit

rawbooktitle:
Proceedings of the Third International Symposium on Advanced Research in Asynchronous Circuits and Systems, 7--10 April 1997

rawtitle:
A low power zero-overhead self-timed division and square root unit combining a single-rail static circuit with a dual-rail dynamic circuit

entry:
@InProceedings{Matsubara:1997:LPZ,
  author =       "G. Matsubara and N. Ide",
  booktitle =    "Proceedings of the Third International Symposium on
                 Advanced Research in Asynchronous Circuits and Systems,
                 7--10 April 1997",
  title =        "A low power zero-overhead self-timed division and
                 square root unit combining a single-rail static circuit
                 with a dual-rail dynamic circuit",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "198--209",
  year =         "1997",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "An asynchronous pipeline scheme that combines a low
                 power static circuit with a high-speed dual-rail
                 dynamic circuit is proposed. The scheme utilizes a
                 dual-rail circuit only in the critical path of an SRT
                 division and square root calculation unit. \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Muller:1997:EFA
author: Jean-Michel Muller
title: Elementary Functions: Algorithms and Implementation
publisher: pub-BIRKHAUSER
address: pub-BIRKHAUSER:adr
pages: xv + 204
year: 1997
ISBN: 0-8176-3990-X OR 081763990X
ISBN13: 978-0-8176-3990-7 OR 9780817639907
LCCN: QA331.M866 1997
bibdate: Fri Jul 25 12:00:55 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.07.25 12:00:55 ???
acknowledgement: ack-nhfb
rawauthor: Jean-Michel Muller
rawtitle: Elementary Functions: Algorithms and Implementation
URL:
http://www.birkhauser.com/cgi-win/ISBN/0-8176-3990-X; http://www.ens-lyon.fr/~jmmuller/book_functions.html

TOC:
1 Introduction / 1 2 Computer Arithmetic / 9 2.1 Floating-Point Arithmetic / 9 2.1.1 Floating-point formats / 9 2.1.2 Rounding modes / 10 2.1.3 Subnormal numbers and exceptions / 12 2.1.4 ULPs / 13 2.1.5 Testing your computational environment / 13 2.2 Redundant Number Systems / 13 2.2.1 Signed-digit number systems / 14 2.2.2 Radix-2 redundant number systems / 15 I Algorithms Based on Polynomial Approximation and/or Table Lookup / 19 3 Polynomial Approximations / 21 3.1 Least Squares Polynomial Approximations / 22 3.1.1 Legendre polynomials / 23 3.1.2 Chebyshev polynomials / 23 3.1.3 Jacobi polynomials / 23 3.2 Least Maximum Approximations / 24 3.3 Speed of Convergence / 31 3.4 Rational Approximations / 34 3.5 Actual Computation / 38 3.6 Example: the Cyrix FastMath Processor / 41 3.7 Algorithms and Architectures / 43 3.7.1 The $E$-Method / 45 3.7.2 Estrin's Method / 47 3.8 Miscellaneous / 47 4 Table-Based Methods / 51 4.1 Introduction / 51 4.2 Table-Driven Algorithms / 53 4.2.1 Tang's algorithm for $exp (x)$ in IEEE floating-point arithmetic / 55 4.2.2 $ln (x)$ on $[1, 2]$ / 57 4.2.3 $sin (x)$ on $[0, pi /4]$ / 58 4.3 Gal's Accurate Tables Method / 58 4.4 Methods Requiring Specialized Hardware / 62 4.4.1 Wong and Goto, logarithm / 62 4.4.2 Wong and Goto, exponential / 65 II Shift-and-Add Algorithms / 69 5 Shift-and-Add algorithms / 71 5.1 The Restoring and Nonrestoring Algorithms / 73 5.2 Simple Algorithms for Exponentials and Logarithms / 77 5.2.1 The restoring algorithm for exponentials / 77 5.2.2 The restoring algorithm for logarithms / 79 5.3 Faster Algorithms '. / 81 5.3.1 Faster computation of exponentials / 81 5.3.2 Faster computation of logarithms / 87 5.4 Baker's Predictive Algorithm / 90 5.5 Bibliographic notes / 98 6 The CORDIC Algorithm / 101 6.1 Introduction / 101 6.2 The Conventional Iteration / 101 6.3 Scale Factor Compensation / 107 6.4 CORDIC With Redundant Number Systems / 109 6.4.1 Signed-digit implementation / 111 6.4.2 Carry-save implementation / 111 6.4.3 The variable scale factor problem / 112 6.5 The Double Rotation Method / 112 6.6 Branching CORDIC / 115 6.7 Differential CORDIC / 118 6.8 Computation of $cos ^-1$ and $sin ^-1$ / 122 6.9 Variations on CORDIC / 124 7 Other Shift-and-Add Algorithms / 127 7.1 High-Radix Algorithms / 127 7.1.1 Ercegovac's radix-16 algorithms / 127 7.2 The BKM Algorithm / 131 7.2.1 The BKM iteration / 133 7.2.2 Computation of the exponential function (E-mode) / 133 7.2.3 Computation of the logarithm function (L-mode) / 137 7.2.4 Application to the computation of elementary functions / 138 III Range Reduction, Final Rounding and Exceptions / 141 8 Range Reduction / 143 8.1 Introduction / 143 8.2 Cody and Waite's Method for Range Reduction / 148 8.3 Worst Cases for Range Reduction / 149 8.3.1 A few basic notions on continued fractions / 149 8.3.2 Finding worst cases using continued fractions / 151 8.4 The Payne and Hanek Algorithm / 154 8.5 The Modular Algorithm / 158 8.5.1 Fixed-point reduction / 158 8.5.2 Floating-point reduction / 161 8.5.3 Architectures for Modular Reduction / 161 9 Final Rounding / 163 9.1 Introduction / 163 9.2 Monotonicity / 164 9.3 Exact Rounding: Presentation of the Problem / 165 9.4 Some Experiments / 168 9.5 A ``Probabilistic'' Approach / 168 9.6 Upper Bounds on $m$ / 171 9.6.1 Frequency of failures / 173 9.6.2 Computing with one million bits / 173 10 Miscellaneous / 175 10.1 Exceptions / 175 10.1.1 NaNs / 176 10.1.2 Exact results / 177 10.2 Notes on $x^y$ / 178 10.3 Multiple Precision / 180

rawTOC:
1 Introduction / 1 \\ 2 Computer Arithmetic / 9 \\ 2.1 Floating-Point Arithmetic / 9 \\ 2.1.1 Floating-point formats / 9 \\ 2.1.2 Rounding modes / 10 \\ 2.1.3 Subnormal numbers and exceptions / 12 \\ 2.1.4 ULPs / 13 \\ 2.1.5 Testing your computational environment / 13 \\ 2.2 Redundant Number Systems / 13 \\ 2.2.1 Signed-digit number systems / 14 \\ 2.2.2 Radix-2 redundant number systems / 15 \\ I Algorithms Based on Polynomial Approximation and/or Table Lookup / 19 \\ 3 Polynomial Approximations / 21 \\ 3.1 Least Squares Polynomial Approximations / 22 \\ 3.1.1 Legendre polynomials / 23 \\ 3.1.2 Chebyshev polynomials / 23 \\ 3.1.3 Jacobi polynomials / 23 \\ 3.2 Least Maximum Approximations / 24 \\ 3.3 Speed of Convergence / 31 \\ 3.4 Rational Approximations / 34 \\ 3.5 Actual Computation / 38 \\ 3.6 Example: the Cyrix FastMath Processor / 41 \\ 3.7 Algorithms and Architectures / 43 \\ 3.7.1 The $E$-Method / 45 \\ 3.7.2 Estrin's Method / 47 \\ 3.8 Miscellaneous / 47 \\ 4 Table-Based Methods / 51 \\ 4.1 Introduction / 51 \\ 4.2 Table-Driven Algorithms / 53 \\ 4.2.1 Tang's algorithm for $\exp(x)$ in IEEE floating-point arithmetic / 55 \\ 4.2.2 $\ln(x)$ on $[1, 2]$ / 57 \\ 4.2.3 $\sin(x)$ on $[0, \pi/4]$ / 58 \\ 4.3 Gal's Accurate Tables Method / 58 \\ 4.4 Methods Requiring Specialized Hardware / 62 \\ 4.4.1 Wong and Goto, logarithm / 62 \\ 4.4.2 Wong and Goto, exponential / 65 \\ II Shift-and-Add Algorithms / 69 \\ 5 Shift-and-Add algorithms / 71 \\ 5.1 The Restoring and Nonrestoring Algorithms / 73 \\ 5.2 Simple Algorithms for Exponentials and Logarithms / 77 \\ 5.2.1 The restoring algorithm for exponentials / 77 \\ 5.2.2 The restoring algorithm for logarithms / 79 \\ 5.3 Faster Algorithms '. / 81 \\ 5.3.1 Faster computation of exponentials / 81 \\ 5.3.2 Faster computation of logarithms / 87 \\ 5.4 Baker's Predictive Algorithm / 90 \\ 5.5 Bibliographic notes / 98 \\ 6 The CORDIC Algorithm / 101 \\ 6.1 Introduction / 101 \\ 6.2 The Conventional Iteration / 101 \\ 6.3 Scale Factor Compensation / 107 \\ 6.4 CORDIC With Redundant Number Systems / 109 \\ 6.4.1 Signed-digit implementation / 111 \\ 6.4.2 Carry-save implementation / 111 \\ 6.4.3 The variable scale factor problem / 112 \\ 6.5 The Double Rotation Method / 112 \\ 6.6 Branching CORDIC / 115 \\ 6.7 Differential CORDIC / 118 \\ 6.8 Computation of $\cos^{-1}$ and $\sin^{-1}$ / 122 \\ 6.9 Variations on CORDIC / 124 \\ 7 Other Shift-and-Add Algorithms / 127 \\ 7.1 High-Radix Algorithms / 127 \\ 7.1.1 Ercegovac's radix-16 algorithms / 127 \\ 7.2 The BKM Algorithm / 131 \\ 7.2.1 The BKM iteration / 133 \\ 7.2.2 Computation of the exponential function (E-mode) / 133 \\ 7.2.3 Computation of the logarithm function (L-mode) / 137 \\ 7.2.4 Application to the computation of elementary functions / 138 \\ III Range Reduction, Final Rounding and Exceptions / 141 \\ 8 Range Reduction / 143 \\ 8.1 Introduction / 143 \\ 8.2 Cody and Waite's Method for Range Reduction / 148 \\ 8.3 Worst Cases for Range Reduction / 149 \\ 8.3.1 A few basic notions on continued fractions / 149 \\ 8.3.2 Finding worst cases using continued fractions / 151 \\ 8.4 The Payne and Hanek Algorithm / 154 \\ 8.5 The Modular Algorithm / 158 \\ 8.5.1 Fixed-point reduction / 158 \\ 8.5.2 Floating-point reduction / 161 \\ 8.5.3 Architectures for Modular Reduction / 161 \\ 9 Final Rounding / 163 \\ 9.1 Introduction / 163 \\ 9.2 Monotonicity / 164 \\ 9.3 Exact Rounding: Presentation of the Problem / 165 \\ 9.4 Some Experiments / 168 \\ 9.5 A ``Probabilistic'' Approach / 168 \\ 9.6 Upper Bounds on $m$ / 171 \\ 9.6.1 Frequency of failures / 173 \\ 9.6.2 Computing with one million bits / 173 \\ 10 Miscellaneous / 175 \\ 10.1 Exceptions / 175 \\ 10.1.1 NaNs / 176 \\ 10.1.2 Exact results / 177 \\ 10.2 Notes on $x^y$ / 178 \\ 10.3 Multiple Precision / 180

entry:
@Book{Muller:1997:EFA,
  author =       "Jean-Michel Muller",
  title =        "Elementary Functions: Algorithms and Implementation",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "xv + 204",
  year =         "1997",
  ISBN =         "0-8176-3990-X",
  ISBN-13 =      "978-0-8176-3990-7",
  LCCN =         "QA331.M866 1997",
  bibdate =      "Fri Jul 25 12:00:55 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  price =        "US\$59.95",
  URL =          "http://www.birkhauser.com/cgi-win/ISBN/0-8176-3990-X;
                 http://www.ens-lyon.fr/~jmmuller/book_functions.html",
  acknowledgement = ack-nhfb,
  tableofcontents = "1 Introduction / 1 \\
                 2 Computer Arithmetic / 9 \\
                 2.1 Floating-Point Arithmetic / 9 \\
                 2.1.1 Floating-point formats / 9 \\
                 2.1.2 Rounding modes / 10 \\
                 2.1.3 Subnormal numbers and exceptions / 12 \\
                 2.1.4 ULPs / 13 \\
                 2.1.5 Testing your computational environment / 13 \\
                 2.2 Redundant Number Systems / 13 \\
                 2.2.1 Signed-digit number systems / 14 \\
                 2.2.2 Radix-2 redundant number systems / 15 \\
                 I Algorithms Based on Polynomial Approximation and/or
                 Table Lookup / 19 \\
                 3 Polynomial Approximations / 21 \\
                 3.1 Least Squares Polynomial Approximations / 22 \\
                 3.1.1 Legendre polynomials / 23 \\
                 3.1.2 Chebyshev polynomials / 23 \\
                 3.1.3 Jacobi polynomials / 23 \\
                 3.2 Least Maximum Approximations / 24 \\
                 3.3 Speed of Convergence / 31 \\
                 3.4 Rational Approximations / 34 \\
                 3.5 Actual Computation / 38 \\
                 3.6 Example: the Cyrix FastMath Processor / 41 \\
                 3.7 Algorithms and Architectures / 43 \\
                 3.7.1 The $E$-Method / 45 \\
                 3.7.2 Estrin's Method / 47 \\
                 3.8 Miscellaneous / 47 \\
                 4 Table-Based Methods / 51 \\
                 4.1 Introduction / 51 \\
                 4.2 Table-Driven Algorithms / 53 \\
                 4.2.1 Tang's algorithm for $\exp(x)$ in IEEE
                 floating-point arithmetic / 55 \\
                 4.2.2 $\ln(x)$ on $[1, 2]$ / 57 \\
                 4.2.3 $\sin(x)$ on $[0, \pi/4]$ / 58 \\
                 4.3 Gal's Accurate Tables Method / 58 \\
                 4.4 Methods Requiring Specialized Hardware / 62 \\
                 4.4.1 Wong and Goto, logarithm / 62 \\
                 4.4.2 Wong and Goto, exponential / 65 \\
                 II Shift-and-Add Algorithms / 69 \\
                 5 Shift-and-Add algorithms / 71 \\
                 5.1 The Restoring and Nonrestoring Algorithms / 73 \\
                 5.2 Simple Algorithms for Exponentials and Logarithms /
                 77 \\
                 5.2.1 The restoring algorithm for exponentials / 77 \\
                 5.2.2 The restoring algorithm for logarithms / 79 \\
                 5.3 Faster Algorithms '. / 81 \\
                 5.3.1 Faster computation of exponentials / 81 \\
                 5.3.2 Faster computation of logarithms / 87 \\
                 5.4 Baker's Predictive Algorithm / 90 \\
                 5.5 Bibliographic notes / 98 \\
                 6 The CORDIC Algorithm / 101 \\
                 6.1 Introduction / 101 \\
                 6.2 The Conventional Iteration / 101 \\
                 6.3 Scale Factor Compensation / 107 \\
                 6.4 CORDIC With Redundant Number Systems / 109 \\
                 6.4.1 Signed-digit implementation / 111 \\
                 6.4.2 Carry-save implementation / 111 \\
                 6.4.3 The variable scale factor problem / 112 \\
                 6.5 The Double Rotation Method / 112 \\
                 6.6 Branching CORDIC / 115 \\
                 6.7 Differential CORDIC / 118 \\
                 6.8 Computation of $\cos^{-1}$ and $\sin^{-1}$ / 122
                 \\
                 6.9 Variations on CORDIC / 124 \\
                 7 Other Shift-and-Add Algorithms / 127 \\
                 7.1 High-Radix Algorithms / 127 \\
                 7.1.1 Ercegovac's radix-16 algorithms / 127 \\
                 7.2 The BKM Algorithm / 131 \\
                 7.2.1 The BKM iteration / 133 \\
                 7.2.2 Computation of the exponential function (E-mode)
                 / 133 \\
                 7.2.3 Computation of the logarithm function (L-mode) /
                 137 \\
                 7.2.4 Application to the computation of elementary
                 functions / 138 \\
                 III Range Reduction, Final Rounding and Exceptions /
                 141 \\
                 8 Range Reduction / 143 \\
                 8.1 Introduction / 143 \\
                 8.2 Cody and Waite's Method for Range Reduction / 148
                 \\
                 8.3 Worst Cases for Range Reduction / 149 \\
                 8.3.1 A few basic notions on continued fractions / 149
                 \\
                 8.3.2 Finding worst cases using continued fractions /
                 151 \\
                 8.4 The Payne and Hanek Algorithm / 154 \\
                 8.5 The Modular Algorithm / 158 \\
                 8.5.1 Fixed-point reduction / 158 \\
                 8.5.2 Floating-point reduction / 161 \\
                 8.5.3 Architectures for Modular Reduction / 161 \\
                 9 Final Rounding / 163 \\
                 9.1 Introduction / 163 \\
                 9.2 Monotonicity / 164 \\
                 9.3 Exact Rounding: Presentation of the Problem / 165
                 \\
                 9.4 Some Experiments / 168 \\
                 9.5 A ``Probabilistic'' Approach / 168 \\
                 9.6 Upper Bounds on $m$ / 171 \\
                 9.6.1 Frequency of failures / 173 \\
                 9.6.2 Computing with one million bits / 173 \\
                 10 Miscellaneous / 175 \\
                 10.1 Exceptions / 175 \\
                 10.1.1 NaNs / 176 \\
                 10.1.2 Exact results / 177 \\
                 10.2 Notes on $x^y$ / 178 \\
                 10.3 Multiple Precision / 180",
}


bibtype: inproceedings
filename: elefunt.bib
label: Schulte:1997:AFA
author: M. J. Schulte and James E. Stine
title: Accurate Function Approximations by Symmetric Table Lookup and Addition
crossref: Thiele:1997:IIC
pages: 144--153
year: 1997
bibdate: Sun Mar 04 10:55:40 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.03.04 10:55:40 ???
URL: http://mesa.ece.wisc.edu/publications/cp_1997-02.pdf
acknowledgement: ack-nhfb
rawauthor: M. J. Schulte and James E. Stine
rawtitle: Accurate Function Approximations by Symmetric Table Lookup and Addition
entry:
@InProceedings{Schulte:1997:AFA,
  author =       "M. J. Schulte and James E. Stine",
  title =        "Accurate Function Approximations by Symmetric Table
                 Lookup and Addition",
  crossref =     "Thiele:1997:IIC",
  pages =        "144--153",
  year =         "1997",
  bibdate =      "Sun Mar 04 10:55:40 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1997-02.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: inproceedings
filename: elefunt.bib
label: Schulte:1997:SBT
author: M. Schulte and J. Stine
title: Symmetric Bipartite Tables for Accurate Function Approximation
crossref: Lang:1997:ISC
pages: 175--183
year: 1997
bibdate: Mon May 20 05:45:32 MDT 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2002.05.20 05:45:32 MDT
URL: http://mesa.ece.wisc.edu/publications/cp_1997-01.pdf
acknowledgement: ack-nhfb
rawauthor: M. Schulte and J. Stine
rawtitle: Symmetric Bipartite Tables for Accurate Function Approximation
entry:
@InProceedings{Schulte:1997:SBT,
  author =       "M. Schulte and J. Stine",
  title =        "Symmetric Bipartite Tables for Accurate Function
                 Approximation",
  crossref =     "Lang:1997:ISC",
  pages =        "175--183",
  year =         "1997",
  bibdate =      "Mon May 20 05:45:32 MDT 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1997-01.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Segura:1997:CEM
author: J. Segura and P. Fernandez de Cordoba and Yu. L. Ratis
title: A code to evaluate modified Bessel functions based on the continued fraction method
journal: j-COMP-PHYS-COMM
volume: 105
number: 2--3
pages: 263--272
day: 1
month: oct
monthnumber: 10
year: 1997
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(97)00069-6
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:30:19 MST 2012
bibtimestamp: 2012.02.13 21:30:19 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465597000696
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: J. Segura and P. Fern{\'a}ndez de C{\'o}rdoba and Yu. L. Ratis
rawtitle: A code to evaluate modified {Bessel} functions based on the continued fraction method
abstract:
We present an algorithm to evaluate the modified Bessel functions $ I _ n u $ and $ K_nu $ of integral and half-integral order based on the calculation of the continued fraction for the $ I _ n u $'s, the Wronskian and the application of forward recurrence relations for the $ K_nu $'s and backward recurrence for the $ I _ n u $'s. The main feature of the algorithm is that it does not require recalculations using normalization relations nor trial values to start the recurrences; the code evaluates in each step (already normalized) Bessel functions. The accuracy of the method ($ 10^-16 $ for half-integral order and better than $ 2 times 10^-7 $ for integral order in our code) is limited only by the precision in the initial values for the recurrence and the maximum order available for a given value of the argument is restricted only by the maximum real number available in the computer.

rawabstract:
We present an algorithm to evaluate the modified Bessel functions $ I \_ n u $ and $ K_\nu $ of integral and half-integral order based on the calculation of the continued fraction for the $ I \_ n u $'s, the Wronskian and the application of forward recurrence relations for the $ K_\nu $'s and backward recurrence for the $ I \_ n u $'s. The main feature of the algorithm is that it does not require recalculations using normalization relations nor trial values to start the recurrences; the code evaluates in each step (already normalized) Bessel functions. The accuracy of the method ($ 10^{-16} $ for half-integral order and better than $ 2 \times 10^{-7} $ for integral order in our code) is limited only by the precision in the initial values for the recurrence and the maximum order available for a given value of the argument is restricted only by the maximum real number available in the computer.

entry:
@Article{Segura:1997:CEM,
  author =       "J. Segura and P. Fern{\'a}ndez de C{\'o}rdoba and Yu.
                 L. Ratis",
  title =        "A code to evaluate modified {Bessel} functions based
                 on the continued fraction method",
  journal =      j-COMP-PHYS-COMM,
  volume =       "105",
  number =       "2--3",
  pages =        "263--272",
  day =          "1",
  month =        oct,
  year =         "1997",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(97)00069-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:19 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465597000696",
  abstract =     "We present an algorithm to evaluate the modified
                 Bessel functions $ I \_ n u $ and $ K_\nu $ of integral
                 and half-integral order based on the calculation of the
                 continued fraction for the $ I \_ n u $'s, the
                 Wronskian and the application of forward recurrence
                 relations for the $ K_\nu $'s and backward recurrence
                 for the $ I \_ n u $'s. The main feature of the
                 algorithm is that it does not require recalculations
                 using normalization relations nor trial values to start
                 the recurrences; the code evaluates in each step
                 (already normalized) Bessel functions. The accuracy of
                 the method ($ 10^{-16} $ for half-integral order and
                 better than $ 2 \times 10^{-7} $ for integral order in
                 our code) is limited only by the precision in the
                 initial values for the recurrence and the maximum order
                 available for a given value of the argument is
                 restricted only by the maximum real number available in
                 the computer.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Soderquist:1997:DSR
author: Peter Soderquist and Miriam Leeser
journal: j-IEEE-MICRO
volume: 17
number: 4
pages: 56--66
month: jul
monthnumber: 7
year: 1997
CODEN: IEMIDZ
DOI: https://doi.org/10.1109/40.612224
ISSN: 0272-1732 (print), 1937-4143 (electronic) OR 02721732 (print), 19374143 (electronic)
ISSNL: 0272-1732 OR 02721732
bibdate: Thu Dec 14 06:08:58 MST 2000
bibtimestamp: 2000.12.14 06:08:58 MST
URL: http://pascal.computer.org/mi/books/mi1997/pdf/m4056.pdf
fjournal: IEEE Micro
acknowledgement: ack-nhfb
journalURL: http://www.computer.org/csdl/mags/mi/index.html
rawauthor: Peter Soderquist and Miriam Leeser
title:
Division and Square Root: Choosing the Right Implementation: Exploring the major design choices for microprocessor implementations of floating-point division and square root

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib; Science Citation Index database (1980--2000)

rawtitle:
Division and Square Root: Choosing the Right Implementation: Exploring the major design choices for microprocessor implementations of floating-point division and square root

entry:
@Article{Soderquist:1997:DSR,
  author =       "Peter Soderquist and Miriam Leeser",
  title =        "Division and Square Root: Choosing the Right
                 Implementation: Exploring the major design choices for
                 microprocessor implementations of floating-point
                 division and square root",
  journal =      j-IEEE-MICRO,
  volume =       "17",
  number =       "4",
  pages =        "56--66",
  month =        jul # "\slash " # aug,
  year =         "1997",
  CODEN =        "IEMIDZ",
  DOI =          "https://doi.org/10.1109/40.612224",
  ISSN =         "0272-1732 (print), 1937-4143 (electronic)",
  ISSN-L =       "0272-1732",
  bibdate =      "Thu Dec 14 06:08:58 MST 2000",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeemicro.bib;
                 Science Citation Index database (1980--2000)",
  URL =          "http://pascal.computer.org/mi/books/mi1997/pdf/m4056.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Micro",
  journal-URL =  "http://www.computer.org/csdl/mags/mi/index.html",
}


bibtype: book
filename: elefunt.bib
label: Thompson:1997:ACMa
author: William J. (William Jackson) Thompson
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xiv + 903
year: 1997
ISBN: 0-471-00260-7 (cloth) OR 0471002607 (cloth)
ISBN13: 978-0-471-00260-4 (cloth) OR 9780471002604 (cloth)
LCCN: QA331.T385 1997
bibdate: Fri May 21 07:11:19 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.05.21 07:11:19 MDT
acknowledgement: ack-nhfb
annote: A Wiley-Interscience publication. Includes CD-ROM.
rawauthor: William J. (William Jackson) Thompson
title:
Atlas for Computing Mathematical Functions: an Illustrated Guidebook for Practitioners: with Programs in C and Mathematica

keywords:
C (Computer program language); Functions -- Computer programs; Mathematica (Computer program language); Science -- Mathematics -- Computer programs

TOC:
Preface / xiii INTRODUCTION The Atlas of Functions / 1 What This Atlas Contains / 1 How to Use the Atlas / 2 About the Production of the Atlas / 2 The Computer Interface / 3 What the CD-ROM Contains / 3 How to Locate a Function / 3 Exploring Functions with Mathematica / 4 The C Functions: No Assembly Required / 7 Hints for Fortran and Pascal Programmers / 3 File Names for PC-Based Systems / 12 Reliability of Programs: Disclaimer / 12 References on the Computer Interface / 12 PART I. THE FUNCTIONS 1 Introduction to the Functions / 15 How the Function Descriptions Are Organized / 16 2 A Visual Tour of the Atlas / 17 3 Computing Strategies / 25 3.1 General Computing Strategies / 25 3.2 Iteration and Recursion / 27 3.3 Continued Fractions and Rational Approximations / 30 3.4 Using Asymptotic Expansions / 31 3.5 Euler--Maclaurin Summation Formula / 32 3.6 Accuracy and Precision of the Functions / 33 3.7 Mathematical Constants Used in the Atlas / 34 References on Computing Strategies / 34 4 Elementary Transcendental Functions / 35 4.1 Exponential and Logarithmic Functions / 35 4.1.1 Exponentials / 36 4.1.2 Logarithms / 38 4.2 Circular and Inverse Circular Functions / 40 42.1 Circular Functions / 40 4.2.2 Inverse Circular Functions / 44 4.3 Hyperbolic and Inverse Hyperbolic Functions / 49 4.3.1 Hyperbolic Functions / 49 4.3.2 Inverse Hyperbolic Functions / 53 References on Elementary Transcendental Functions / 58 S Exponential Integrals and Related Functions / 59 5.1 Exponential and Logarithmic Integrals / 59 5.1.1 Exponential Integral of the First Kind / 59 5.1.2 Exponential Integral of the Second Kind / 64 5.1.3 Logarithmic Integral / 69 5.2 Cosine and Sine Integrals / 72 References on Exponential Integrals and Related Functions / 78 6 Gamma and Beta Functions / 79 6.1 Gamma Function and Beta Function / 79 6.1.1 Gamma Function / 79 6.1.2 Beta Function / 84 6.2 Psi (Digamma) and Polygamma Functions / 86 6.2.1 Psi Function / 87 6.2.2 Polygamma Functions / 91 6.3 Incomplete Gamma and Beta Functions / 97 6.3.1 Incomplete Gamma Function / 97 6.3.2 Incomplete Beta Function / 102 References on Gamma and Beta Functions / 106 7 Combinatorial Functions / 109 7.1 Factorials and Rising Factorials / 109 7.1.1 Factorial Function / 110 7.1.2 Rising Factorial Function / 113 7.2 Binomial and Multinomial Coefficients / 115 7.2.1 Binomial Coefficients / 115 7.2.2 Multinomial Coefficients / 118 7.3 Stirling Numbers of First and Second Kinds / 121 7.3.1 Stirling Numbers of the First Kind / 121 7.3.2 Stirling Numbers of the Second Kind / 124 7.4 Fibonacci and Lucas Polynomials / 126 7.4.1 Fibonacci Polynomials and Fibonacci Numbers / 126 7.4.2 Lucas Polynomials and Lucas Numbers / 128 References on Combinatorial Functions / 130 8 Number Theory Functions / 133 8.1 Bernoulli Numbers and Bernoulli Polynomials / 133 8.1.1 Bernoulli Numbers / 133 8.1.2 Bernoulli Polynomials / 137 8.2 Euler Numbers and Euler Polynomials / 139 8.2.1 Euler Numbers / 139 8.2.2 Euler Polynomials / 142 8.3 Riemann Zeta Function / 144 8.4 Other Sums of Reciprocal Powers / 147 8.5 Polylogarithms / 151 References on Number Theory Functions / 156 9 Probability Distributions / 159 9.1 Overview of Probability Distribution Functions / 160 9.2 Discrete Probability Distributions / 160 9.2.1 Binomial Distribution / 162 9.2.2 Negative Binomial (Pascal) Distribution / 164 9.2.3 Geometric Distribution / 166 9.2.4 Hypergeometric Distribution / 168 9.2.5 Logarithmic Series Distribution / 171 9.2.6 Poisson Distribution / 173 9.3 Normal Probability Distributions / 175 9.3.1 Gauss (Normal) Probability Function / 177 9.3.2 Bivariate Normal Probability Function / 179 9.3.3 Chi-Square Probability Functions / 182 9.3.4 $F$-(Variance-Ratio) Distribution Functions / 188 9.3.5 Student's $t$-Distribution Functions / 192 9.3.6 Lognormal Distribution / 196 9.4 Other Continuous Probability Distributions / 199 9.4.1 Cauchy (Lorentz) Distribution / 200 9.4.2 Exponential Distribution / 203 9.4.3 Pareto Distribution / 205 9.4.4 Weibull Distribution / 208 9.4.5 Logistic Distribution / 211 9.4.6 Laplace Distribution / 213 9.4.7 Kolmogorov--Smirnov Distribution / 215 9.4.8 Beta Distribution / 218 References on Probability Distribution Functions / 221 10 Error Function, Fresnel and Dawson Integrals / 223 10.1 Error Function / 223 10.2 Fresnel Integrals / 226 10.3 Dawson Integral / 234 References on Error Functions, Fresnel and Dawson Integrals / 238 11 Orthogonal Polynomials / 239 11.1 Overview of Orthogonal Polynomials / 239 11.2 Chebyshev Polynomials / 244 11.2.1 Chebyshev Polynomials of the First Kind / 245 11.2.2 Chebyshev Polynomials of the Second Kind / 247 11.3 Gegenbauer (Ultraspherical) Polynomials / 251 11.4 Hermite Polynomials / 254 11.5 Laguerre Polynomials / 257 11.6 Legendre Polynomials / 260 11.7 Jacobi Polynomials / 263 References on Orthogonal Polynomials / 267 12 Legendre Functions / 269 12.1 Overview of Legendre Functions / 269 12.1.1 Visualizing Legendre Functions of the First Kind / 270 12.1.2 Visualizing Legendre Functions of the Second Kind / 273 12.1.3 Legendre Functions and Coordinate Systems / 277 12.2 Spherical Legendre Functions / 278 12.2.1 Spherical Polar Coordinates / 278 12.2.2 Legendre Functions of the First Kind for Integer $m$ and $n$ / 279 12.2.3 Legendre Functions of the Second Kind for Integer $m$ and $n$ / 284 12.3 Toroidal Legendre Functions / 291 12.3.1 Toroidal Coordinates / 291 12.3.2 Toroidal Functions of the First Kind / 293 12.3.3 Toroidal Functions of the Second Kind / 296 12.4 Conical Legendre Functions / 300 12.4.1 Laplace Equation on a Cone / 300 12.4.2 Conical Functions / 301 References on Legendre Functions / 304 13 Spheroidal Wave Functions / 307 13.1 Overview of Spheroidal Wave Functions / 307 13.1.1 Spheroidal Coordinates / 308 13.1.2 Scalar Wave Equation in Spheroidal Coordinates / 309 13.1.3 Eigenvalues for Spheroidal Equations / 310 13.1.4 Auxiliary Functions for Eigenvalues / 320 13.2 Spheroidal Angular Functions / 321 13.2.1 Expansion Coefficients for Angular Functions / 321 13.2.2 Spheroidal Angular Functions / 331 13.3 Spheroidal Radial Functions / 336 13.3.1 Expansion Coefficients for Radial Functions / 336 13.3.2 Spheroidal Radial Functions / 340 References on Spheroidal Wave Functions / 344 14 Bessel Functions / 345 14.1 Overview of Bessel Functions / 345 14.2 Bessel Functions of Integer Order / 350 14.2.1 Regular Cylindrical Bessel Function / 351 14.2.2 Irregular Cylindrical Bessel Function / 357 14.2.3 Regular Hyperbolic Bessel Function / 361 14.2.4 Irregular Hyperbolic Bessel Function / 368 14.3 Kelvin Functions / 375 14.3.1 Regular Kelvin Functions / 375 14.3.2 Irregular Kelvin Functions / 385 14.4 Bessel Functions of Half-Integer Order / 394 14.4.1 Regular Spherical Bessel Function / 394 14.4.2 Irregular Spherical Bessel Function / 401 14.4.3 Regular Modified Spherical Bessel Function / 405 14.4.4 Irregular Modified Spherical Bessel Function / 412 14.5 Airy Functions / 416 14.5.1 Airy Functions / 416 14.5.2 Derivatives of Airy Functions / 425 References on Bessel Functions / 434 15 Struve, Anger, and Weber Functions / 435 15.1 Struve Functions / 435 15.1.1 Struve Function / 435 15.1.1 Modified Struve Function / 442 15.2 Anger and Weber Functions / 448 15.2.1 Overview of Anger and Weber Functions / 448 15.2.2 Anger Function / 449 15.2.3 Weber Function / 455 References on Struve, Anger, and Weber Functions / 458 16 Hypergeometric Functions and Coulomb Wave Functions / 461 16.1 Hypergeometric Functions / 461 16.2 Confluent Hypergeometric Functions / 465 16.2.1 Regular Function / 465 16.2.2 Irregular Function / 471 16.3 Coulomb Wave Functions / 478 16.3.1 Regular Functions and Derivatives / 478 16.3.2 Irregular Functions and Derivatives / 487 References on Hypergeometric Functions and Coulomb Wave Functions / 493 17 Elliptic Integrals and Elliptic Functions / 495 17.1 Overview of Elliptic Integrals and Elliptic Functions / 495 17.2 Elliptic Integrals / 496 17.2.1 Elliptic Integrals of the First Kind / 496 17.2.2 Elliptic Integrals of the Second Kind / 502 17.2.3 Jacobi Zeta Function / 506 17.2.4 Heuman Lambda Function / 510 17.2.5 Elliptic Integrals of the Third Kind / 513 17.3 Jacobi Elliptic Functions and Theta Functions / 517 17.3.1 Jacobi Elliptic Functions / 517 17.3.2 Theta Functions / 525 17.3.3 Logarithmic Derivatives of Theta Functions / 531 References on Elliptic Integrals and Elliptic Functions / 536 18 Parabolic Cylinder Functions / 539 18.1 Parabolic Cylinder Coordinates / 539 18.2 Parabolic Cylinder Functions / 540 18.2.1 Parabolic Cylinder Functions U / 540 18.2.2 Parabolic Cylinder Functions V / 546 References on Parabolic Cylinder Functions / 550 19 Miscellaneous Functions for Science and Engineering / 551 19.1 Debye Functions / 551 19.2 Sievert Integral / 554 19.3 Abramowitz Function / 557 19.4 Spence Integeral / 562 19.5 Clausen Integral / 565 19.6 Voigt (Plasma Dispersion) Function / 570 19.7 Angular Momentum Coupling Coefficients 576 / 539 19.7.1 3-j Coefficients / 578 19.7.2 6-j Coefficients / 582 19.7.3 9-j Coefficients / 586 References on Miscellaneous Functions for Science and Engineering PART II. THE COMPUTER INTERFACE 20 The Mathematica Notebooks / 593 20.1 Introduction to the Notebooks / 593 20.2 Exploring with the Notebook Cells / 594 20.3 The Annotated Notebooks / 594 20.4 Elementary Transcendental Functions / 595 20.5 Exponential Integrals and Related Functions / 602 20.6 Gamma and Beta Functions / 607 20.7 Combinatorial Functions / 618 20.8 Number Theory Functions / 627 20.9 Probability Distributions / 633 20.10 Error Function, Fresnel and Dawson Integrals / 663 20.11 Orthogonal Polynomials / 667 20.12 Legendre Functions / 676 20.14 Bessel Functions / 708 20.15 Struve, Anger, and Weber Functions / 747 20.16 Hypergeometric Functions and Coulomb Wave Functions / 756 20.17 Elliptic Integrals and Elliptic Functions / 765 20.18 Parabolic Cylinder Functions / 782 20.19 Miscellaneous Functions for Science and Engineering / 788 21 The C Driver Programs / 797 21.1 Introduction to the C Driver Programs / 797 21.2 How the C Drivers are Organized / 797 21.3 Annotations to the C Driver Programs / 798 21.4 Elementary Transcendental Functions / 798 21.4.1 Exponential and Logarithmic Functions / 798 21.4.2 Circular and Inverse Circular Functions / 799 21.4.3 Hyperbolic and Inverse Hyperbolic Functions / 800 21.5 Exponential Integrals and Related Functions / 802 21.5.1 Exponential and Logarithmic Integrals / 802 21.5.2 Cosine and Sine Integrals / 803 21.6 Gamma and Beta Functions / 804 21.6.1 Gamma Function and Beta Function / 804 21.6.2 Psi (Digamma) and Polygamma Functions / 805 21.6.3 Incomplete Gamma and Beta Functions / 807 21.7 Combinatorial Functions / 808 21.7.1 Factorials and Rising Factorials / 808 21.7.2 Binomial and Multinomial Coefficients / 809 21.7.3 Stirling Numbers of the First and Second Kinds / 811 21.7.4 Fibonacci and Lucas Polynomials / 811 21.8 Number Theory Functions / 813 21.8.1 Bernoulli Numbers and Bernoulli Polynomials / 813 21.8.2 Euler Numbers and Euler Polynomials / 814 21.8.3 Riemann Zeta Function / 814 21.8.4 Other Sums of Reciprocal Powers / 815 21.8.5 Polylogarithms / 816 21.9 Probability Distributions / 816 21.9.1 Organization of the PDFs / 816 21.9.2 Discrete Probability Distributions / 816 21.9.3 Normal Probability Distributions / 820 21.9.4 Other Continuous Probability Distributions / 825 21.10 Error Function, Fresnel and Dawson Integrals / 830 21.10.1 Error Function / 830 21.10.2 Fresnel Integrals / 831 21.10.3 Dawson Integral / 832 21.11 Orthogonal Polynomials / 833 21.11.1 Orthogonal Polynomial Functions / 833 21.11.2 Chebyshev Polynomials / 833 21.11.3 Gegenbauer (Ultraspherical) Polynomials / 834 21.11.4 Hermite Polynomials / 835 21.11.5 Laguerre Polynomials / 835 21.11.6 Legendre Polynomials / 836 21.11.7 Jacobi Polynomials / 837 21.12 Legendre Functions / 837 21.12.1 Overview of Legendre Functions / 838 21.12.2 Spherical Legendre Functions / 838 21.12.3 Toroidal Legendre Functions / 840 21.12.4 Conical Legendre Functions / 841 21.13 Spheroidal Wave Functions / 842 21.13.1 Overview of Spheroidal Wave Functions / 842 21.13.2 Spheroidal Angular Functions / 843 21.13.3 Spheroidal Radial Functions / 844 21.14 Bessel Functions / 846 21.14.1 Overview of Bessel Functions / 846 21.14.2 Bessel Functions of Integer Order / 846 21.14.3 Kelvin Functions / 850 21.14.4 Bessel Functions of Half-Integer Order / 852 21.14.5 Airy Functions / 856 21.15 Struve, Anger, and Weber Functions / 857 21.15.1 Struve Functions / 857 21.15.2 Anger and Weber Functions / 859 21.16 Hypergeometric Functions and Coulomb Wave Functions / 861 21.16.1 Hypergeometric Functions / 861 21.16.2 Confluent Hypergeometric Functions / 862 21.16.3 Coulomb Wave Functions / 863 21.17 Elliptic Integrals and Elliptic Functions / 864 21.17.1 Overview of Elliptic Integrals and Elliptic Functions / 864 21.17.2 Elliptic Integrals / 864 21.17.3 Jacobi Elliptic Functions and Theta Functions / 867 21.18 Parabolic Cylinder Functions / 870 21.18.1 Parabolic Cylinder Functions / 870 21.19 Miscellaneous Functions for Science and Engineering / 872 21.19.1 Debye Functions / 872 21.19.2 Sievert Integral / 873 21.19.3 Abramowitz Function / 873 21.19.4 Spence Integral / 874 21.19.5 Clausen Integral / 875 21.19.6 Voigt (Plasma Dispersion) Function / 876 21.19.7 Angular Momentum Coupling Coefficients / 876 APPENDIX: File Names for PC-Based Systems / 879 INDEXES Index of Function Notations / 883 Index of Programs and Dependencies / 886 Index of Subjects and Authors / 889

rawtitle:
Atlas for Computing Mathematical Functions: an Illustrated Guidebook for Practitioners: with Programs in {C} and {Mathematica}

rawTOC:
Preface / xiii \\ INTRODUCTION \\ The Atlas of Functions / 1 \\ What This Atlas Contains / 1 \\ How to Use the Atlas / 2 \\ About the Production of the Atlas / 2 \\ The Computer Interface / 3 \\ What the CD-ROM Contains / 3 \\ How to Locate a Function / 3 \\ Exploring Functions with Mathematica / 4 \\ The C Functions: No Assembly Required / 7 \\ Hints for Fortran and Pascal Programmers / 3 \\ File Names for PC-Based Systems / 12 \\ Reliability of Programs: Disclaimer / 12 \\ References on the Computer Interface / 12 \\ PART I. THE FUNCTIONS \\ 1 Introduction to the Functions / 15 \\ How the Function Descriptions Are Organized / 16 \\ 2 A Visual Tour of the Atlas / 17 \\ 3 Computing Strategies / 25 \\ 3.1 General Computing Strategies / 25 \\ 3.2 Iteration and Recursion / 27 \\ 3.3 Continued Fractions and Rational Approximations / 30 \\ 3.4 Using Asymptotic Expansions / 31 \\ 3.5 Euler--Maclaurin Summation Formula / 32 \\ 3.6 Accuracy and Precision of the Functions / 33 \\ 3.7 Mathematical Constants Used in the Atlas / 34 \\ References on Computing Strategies / 34 \\ 4 Elementary Transcendental Functions / 35 \\ 4.1 Exponential and Logarithmic Functions / 35 \\ 4.1.1 Exponentials / 36 \\ 4.1.2 Logarithms / 38 \\ 4.2 Circular and Inverse Circular Functions / 40 \\ 42.1 Circular Functions / 40 \\ 4.2.2 Inverse Circular Functions / 44 \\ 4.3 Hyperbolic and Inverse Hyperbolic Functions / 49 \\ 4.3.1 Hyperbolic Functions / 49 \\ 4.3.2 Inverse Hyperbolic Functions / 53 \\ References on Elementary Transcendental Functions / 58 \\ S Exponential Integrals and Related Functions / 59 \\ 5.1 Exponential and Logarithmic Integrals / 59 \\ 5.1.1 Exponential Integral of the First Kind / 59 \\ 5.1.2 Exponential Integral of the Second Kind / 64 \\ 5.1.3 Logarithmic Integral / 69 \\ 5.2 Cosine and Sine Integrals / 72 \\ References on Exponential Integrals and Related Functions / 78 \\ 6 Gamma and Beta Functions / 79 \\ 6.1 Gamma Function and Beta Function / 79 \\ 6.1.1 Gamma Function / 79 \\ 6.1.2 Beta Function / 84 \\ 6.2 Psi (Digamma) and Polygamma Functions / 86 \\ 6.2.1 Psi Function / 87 \\ 6.2.2 Polygamma Functions / 91 \\ 6.3 Incomplete Gamma and Beta Functions / 97 \\ 6.3.1 Incomplete Gamma Function / 97 \\ 6.3.2 Incomplete Beta Function / 102 \\ References on Gamma and Beta Functions / 106 \\ 7 Combinatorial Functions / 109 \\ 7.1 Factorials and Rising Factorials / 109 \\ 7.1.1 Factorial Function / 110 \\ 7.1.2 Rising Factorial Function / 113 \\ 7.2 Binomial and Multinomial Coefficients / 115 \\ 7.2.1 Binomial Coefficients / 115 \\ 7.2.2 Multinomial Coefficients / 118 \\ 7.3 Stirling Numbers of First and Second Kinds / 121 \\ 7.3.1 Stirling Numbers of the First Kind / 121 \\ 7.3.2 Stirling Numbers of the Second Kind / 124 \\ 7.4 Fibonacci and Lucas Polynomials / 126 \\ 7.4.1 Fibonacci Polynomials and Fibonacci Numbers / 126 \\ 7.4.2 Lucas Polynomials and Lucas Numbers / 128 \\ References on Combinatorial Functions / 130 \\ 8 Number Theory Functions / 133 \\ 8.1 Bernoulli Numbers and Bernoulli Polynomials / 133 \\ 8.1.1 Bernoulli Numbers / 133 \\ 8.1.2 Bernoulli Polynomials / 137 \\ 8.2 Euler Numbers and Euler Polynomials / 139 \\ 8.2.1 Euler Numbers / 139 \\ 8.2.2 Euler Polynomials / 142 \\ 8.3 Riemann Zeta Function / 144 \\ 8.4 Other Sums of Reciprocal Powers / 147 \\ 8.5 Polylogarithms / 151 \\ References on Number Theory Functions / 156 \\ 9 Probability Distributions / 159 \\ 9.1 Overview of Probability Distribution Functions / 160 \\ 9.2 Discrete Probability Distributions / 160 \\ 9.2.1 Binomial Distribution / 162 \\ 9.2.2 Negative Binomial (Pascal) Distribution / 164 \\ 9.2.3 Geometric Distribution / 166 \\ 9.2.4 Hypergeometric Distribution / 168 \\ 9.2.5 Logarithmic Series Distribution / 171 \\ 9.2.6 Poisson Distribution / 173 \\ 9.3 Normal Probability Distributions / 175 \\ 9.3.1 Gauss (Normal) Probability Function / 177 \\ 9.3.2 Bivariate Normal Probability Function / 179 \\ 9.3.3 Chi-Square Probability Functions / 182 \\ 9.3.4 $F$-(Variance-Ratio) Distribution Functions / 188 \\ 9.3.5 Student's $t$-Distribution Functions / 192 \\ 9.3.6 Lognormal Distribution / 196 \\ 9.4 Other Continuous Probability Distributions / 199 \\ 9.4.1 Cauchy (Lorentz) Distribution / 200 \\ 9.4.2 Exponential Distribution / 203 \\ 9.4.3 Pareto Distribution / 205 \\ 9.4.4 Weibull Distribution / 208 \\ 9.4.5 Logistic Distribution / 211 \\ 9.4.6 Laplace Distribution / 213 \\ 9.4.7 Kolmogorov--Smirnov Distribution / 215 \\ 9.4.8 Beta Distribution / 218 \\ References on Probability Distribution Functions / 221 \\ 10 Error Function, Fresnel and Dawson Integrals / 223 \\ 10.1 Error Function / 223 \\ 10.2 Fresnel Integrals / 226 \\ 10.3 Dawson Integral / 234 \\ References on Error Functions, Fresnel and Dawson Integrals / 238 \\ 11 Orthogonal Polynomials / 239 \\ 11.1 Overview of Orthogonal Polynomials / 239 \\ 11.2 Chebyshev Polynomials / 244 \\ 11.2.1 Chebyshev Polynomials of the First Kind / 245 \\ 11.2.2 Chebyshev Polynomials of the Second Kind / 247 \\ 11.3 Gegenbauer (Ultraspherical) Polynomials / 251 \\ 11.4 Hermite Polynomials / 254 \\ 11.5 Laguerre Polynomials / 257 \\ 11.6 Legendre Polynomials / 260 \\ 11.7 Jacobi Polynomials / 263 \\ References on Orthogonal Polynomials / 267 \\ 12 Legendre Functions / 269 \\ 12.1 Overview of Legendre Functions / 269 \\ 12.1.1 Visualizing Legendre Functions of the First Kind / 270 \\ 12.1.2 Visualizing Legendre Functions of the Second Kind / 273 \\ 12.1.3 Legendre Functions and Coordinate Systems / 277 \\ 12.2 Spherical Legendre Functions / 278 \\ 12.2.1 Spherical Polar Coordinates / 278 \\ 12.2.2 Legendre Functions of the First Kind for Integer $m$ and $n$ / 279 \\ 12.2.3 Legendre Functions of the Second Kind for Integer $m$ and $n$ / 284 \\ 12.3 Toroidal Legendre Functions / 291 \\ 12.3.1 Toroidal Coordinates / 291 \\ 12.3.2 Toroidal Functions of the First Kind / 293 \\ 12.3.3 Toroidal Functions of the Second Kind / 296 \\ 12.4 Conical Legendre Functions / 300 \\ 12.4.1 Laplace Equation on a Cone / 300 \\ 12.4.2 Conical Functions / 301 \\ References on Legendre Functions / 304 \\ 13 Spheroidal Wave Functions / 307 \\ 13.1 Overview of Spheroidal Wave Functions / 307 \\ 13.1.1 Spheroidal Coordinates / 308 \\ 13.1.2 Scalar Wave Equation in Spheroidal Coordinates / 309 \\ 13.1.3 Eigenvalues for Spheroidal Equations / 310 \\ 13.1.4 Auxiliary Functions for Eigenvalues / 320 \\ 13.2 Spheroidal Angular Functions / 321 \\ 13.2.1 Expansion Coefficients for Angular Functions / 321 \\ 13.2.2 Spheroidal Angular Functions / 331 \\ 13.3 Spheroidal Radial Functions / 336 \\ 13.3.1 Expansion Coefficients for Radial Functions / 336 \\ 13.3.2 Spheroidal Radial Functions / 340 \\ References on Spheroidal Wave Functions / 344 \\ 14 Bessel Functions / 345 \\ 14.1 Overview of Bessel Functions / 345 \\ 14.2 Bessel Functions of Integer Order / 350 \\ 14.2.1 Regular Cylindrical Bessel Function / 351 \\ 14.2.2 Irregular Cylindrical Bessel Function / 357 \\ 14.2.3 Regular Hyperbolic Bessel Function / 361 \\ 14.2.4 Irregular Hyperbolic Bessel Function / 368 \\ 14.3 Kelvin Functions / 375 \\ 14.3.1 Regular Kelvin Functions / 375 \\ 14.3.2 Irregular Kelvin Functions / 385 \\ 14.4 Bessel Functions of Half-Integer Order / 394 \\ 14.4.1 Regular Spherical Bessel Function / 394 \\ 14.4.2 Irregular Spherical Bessel Function / 401 \\ 14.4.3 Regular Modified Spherical Bessel Function / 405 \\ 14.4.4 Irregular Modified Spherical Bessel Function / 412 \\ 14.5 Airy Functions / 416 \\ 14.5.1 Airy Functions / 416 \\ 14.5.2 Derivatives of Airy Functions / 425 \\ References on Bessel Functions / 434 \\ 15 Struve, Anger, and Weber Functions / 435 \\ 15.1 Struve Functions / 435 \\ 15.1.1 Struve Function / 435 \\ 15.1.1 Modified Struve Function / 442 \\ 15.2 Anger and Weber Functions / 448 \\ 15.2.1 Overview of Anger and Weber Functions / 448 \\ 15.2.2 Anger Function / 449 \\ 15.2.3 Weber Function / 455 \\ References on Struve, Anger, and Weber Functions / 458 \\ 16 Hypergeometric Functions and Coulomb Wave Functions / 461 \\ 16.1 Hypergeometric Functions / 461 \\ 16.2 Confluent Hypergeometric Functions / 465 \\ 16.2.1 Regular Function / 465 \\ 16.2.2 Irregular Function / 471 \\ 16.3 Coulomb Wave Functions / 478 \\ 16.3.1 Regular Functions and Derivatives / 478 \\ 16.3.2 Irregular Functions and Derivatives / 487 \\ References on Hypergeometric Functions and Coulomb Wave Functions / 493 \\ 17 Elliptic Integrals and Elliptic Functions / 495 \\ 17.1 Overview of Elliptic Integrals and Elliptic Functions / 495 \\ 17.2 Elliptic Integrals / 496 \\ 17.2.1 Elliptic Integrals of the First Kind / 496 \\ 17.2.2 Elliptic Integrals of the Second Kind / 502 \\ 17.2.3 Jacobi Zeta Function / 506 \\ 17.2.4 Heuman Lambda Function / 510 \\ 17.2.5 Elliptic Integrals of the Third Kind / 513 \\ 17.3 Jacobi Elliptic Functions and Theta Functions / 517 \\ 17.3.1 Jacobi Elliptic Functions / 517 \\ 17.3.2 Theta Functions / 525 \\ 17.3.3 Logarithmic Derivatives of Theta Functions / 531 \\ References on Elliptic Integrals and Elliptic Functions / 536 \\ 18 Parabolic Cylinder Functions / 539 \\ 18.1 Parabolic Cylinder Coordinates / 539 \\ 18.2 Parabolic Cylinder Functions / 540 \\ 18.2.1 Parabolic Cylinder Functions U / 540 \\ 18.2.2 Parabolic Cylinder Functions V / 546 \\ References on Parabolic Cylinder Functions / 550 \\ 19 Miscellaneous Functions for Science and Engineering / 551 \\ 19.1 Debye Functions / 551 \\ 19.2 Sievert Integral / 554 \\ 19.3 Abramowitz Function / 557 \\ 19.4 Spence Integeral / 562 \\ 19.5 Clausen Integral / 565 \\ 19.6 Voigt (Plasma Dispersion) Function / 570 \\ 19.7 Angular Momentum Coupling Coefficients 576 / 539 \\ 19.7.1 3-j Coefficients / 578 \\ 19.7.2 6-j Coefficients / 582 \\ 19.7.3 9-j Coefficients / 586 \\ References on Miscellaneous Functions for Science and Engineering \\ PART II. THE COMPUTER INTERFACE \\ 20 The Mathematica Notebooks / 593 \\ 20.1 Introduction to the Notebooks / 593 \\ 20.2 Exploring with the Notebook Cells / 594 \\ 20.3 The Annotated Notebooks / 594 \\ 20.4 Elementary Transcendental Functions / 595 \\ 20.5 Exponential Integrals and Related Functions / 602 \\ 20.6 Gamma and Beta Functions / 607 \\ 20.7 Combinatorial Functions / 618 \\ 20.8 Number Theory Functions / 627 \\ 20.9 Probability Distributions / 633 \\ 20.10 Error Function, Fresnel and Dawson Integrals / 663 \\ 20.11 Orthogonal Polynomials / 667 \\ 20.12 Legendre Functions / 676 \\ 20.14 Bessel Functions / 708 \\ 20.15 Struve, Anger, and Weber Functions / 747 \\ 20.16 Hypergeometric Functions and Coulomb Wave Functions / 756 \\ 20.17 Elliptic Integrals and Elliptic Functions / 765 \\ 20.18 Parabolic Cylinder Functions / 782 \\ 20.19 Miscellaneous Functions for Science and Engineering / 788 \\ 21 The C Driver Programs / 797 \\ 21.1 Introduction to the C Driver Programs / 797 \\ 21.2 How the C Drivers are Organized / 797 \\ 21.3 Annotations to the C Driver Programs / 798 \\ 21.4 Elementary Transcendental Functions / 798 \\ 21.4.1 Exponential and Logarithmic Functions / 798 \\ 21.4.2 Circular and Inverse Circular Functions / 799 \\ 21.4.3 Hyperbolic and Inverse Hyperbolic Functions / 800 \\ 21.5 Exponential Integrals and Related Functions / 802 \\ 21.5.1 Exponential and Logarithmic Integrals / 802 \\ 21.5.2 Cosine and Sine Integrals / 803 \\ 21.6 Gamma and Beta Functions / 804 \\ 21.6.1 Gamma Function and Beta Function / 804 \\ 21.6.2 Psi (Digamma) and Polygamma Functions / 805 \\ 21.6.3 Incomplete Gamma and Beta Functions / 807 \\ 21.7 Combinatorial Functions / 808 \\ 21.7.1 Factorials and Rising Factorials / 808 \\ 21.7.2 Binomial and Multinomial Coefficients / 809 \\ 21.7.3 Stirling Numbers of the First and Second Kinds / 811 \\ 21.7.4 Fibonacci and Lucas Polynomials / 811 \\ 21.8 Number Theory Functions / 813 \\ 21.8.1 Bernoulli Numbers and Bernoulli Polynomials / 813 \\ 21.8.2 Euler Numbers and Euler Polynomials / 814 \\ 21.8.3 Riemann Zeta Function / 814 \\ 21.8.4 Other Sums of Reciprocal Powers / 815 \\ 21.8.5 Polylogarithms / 816 \\ 21.9 Probability Distributions / 816 \\ 21.9.1 Organization of the PDFs / 816 \\ 21.9.2 Discrete Probability Distributions / 816 \\ 21.9.3 Normal Probability Distributions / 820 \\ 21.9.4 Other Continuous Probability Distributions / 825 \\ 21.10 Error Function, Fresnel and Dawson Integrals / 830 \\ 21.10.1 Error Function / 830 \\ 21.10.2 Fresnel Integrals / 831 \\ 21.10.3 Dawson Integral / 832 \\ 21.11 Orthogonal Polynomials / 833 \\ 21.11.1 Orthogonal Polynomial Functions / 833 \\ 21.11.2 Chebyshev Polynomials / 833 \\ 21.11.3 Gegenbauer (Ultraspherical) Polynomials / 834 \\ 21.11.4 Hermite Polynomials / 835 \\ 21.11.5 Laguerre Polynomials / 835 \\ 21.11.6 Legendre Polynomials / 836 \\ 21.11.7 Jacobi Polynomials / 837 \\ 21.12 Legendre Functions / 837 \\ 21.12.1 Overview of Legendre Functions / 838 \\ 21.12.2 Spherical Legendre Functions / 838 \\ 21.12.3 Toroidal Legendre Functions / 840 \\ 21.12.4 Conical Legendre Functions / 841 \\ 21.13 Spheroidal Wave Functions / 842 \\ 21.13.1 Overview of Spheroidal Wave Functions / 842 \\ 21.13.2 Spheroidal Angular Functions / 843 \\ 21.13.3 Spheroidal Radial Functions / 844 \\ 21.14 Bessel Functions / 846 \\ 21.14.1 Overview of Bessel Functions / 846 \\ 21.14.2 Bessel Functions of Integer Order / 846 \\ 21.14.3 Kelvin Functions / 850 \\ 21.14.4 Bessel Functions of Half-Integer Order / 852 \\ 21.14.5 Airy Functions / 856 \\ 21.15 Struve, Anger, and Weber Functions / 857 \\ 21.15.1 Struve Functions / 857 \\ 21.15.2 Anger and Weber Functions / 859 \\ 21.16 Hypergeometric Functions and Coulomb Wave Functions / 861 \\ 21.16.1 Hypergeometric Functions / 861 \\ 21.16.2 Confluent Hypergeometric Functions / 862 \\ 21.16.3 Coulomb Wave Functions / 863 \\ 21.17 Elliptic Integrals and Elliptic Functions / 864 \\ 21.17.1 Overview of Elliptic Integrals and Elliptic Functions / 864 \\ 21.17.2 Elliptic Integrals / 864 \\ 21.17.3 Jacobi Elliptic Functions and Theta Functions / 867 \\ 21.18 Parabolic Cylinder Functions / 870 \\ 21.18.1 Parabolic Cylinder Functions / 870 \\ 21.19 Miscellaneous Functions for Science and Engineering / 872 \\ 21.19.1 Debye Functions / 872 \\ 21.19.2 Sievert Integral / 873 \\ 21.19.3 Abramowitz Function / 873 \\ 21.19.4 Spence Integral / 874 \\ 21.19.5 Clausen Integral / 875 \\ 21.19.6 Voigt (Plasma Dispersion) Function / 876 \\ 21.19.7 Angular Momentum Coupling Coefficients / 876 \\ APPENDIX: File Names for PC-Based Systems / 879 \\ INDEXES \\ Index of Function Notations / 883 \\ Index of Programs and Dependencies / 886 \\ Index of Subjects and Authors / 889

entry:
@Book{Thompson:1997:ACMa,
  author =       "William J. (William Jackson) Thompson",
  title =        "Atlas for Computing Mathematical Functions: an
                 Illustrated Guidebook for Practitioners: with Programs
                 in {C} and {Mathematica}",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiv + 903",
  year =         "1997",
  ISBN =         "0-471-00260-7 (cloth)",
  ISBN-13 =      "978-0-471-00260-4 (cloth)",
  LCCN =         "QA331.T385 1997",
  bibdate =      "Fri May 21 07:11:19 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  annote =       "A Wiley-Interscience publication. Includes CD-ROM.",
  keywords =     "C (Computer program language); Functions -- Computer
                 programs; Mathematica (Computer program language);
                 Science -- Mathematics -- Computer programs",
  tableofcontents = "Preface / xiii \\
                 INTRODUCTION \\
                 The Atlas of Functions / 1 \\
                 What This Atlas Contains / 1 \\
                 How to Use the Atlas / 2 \\
                 About the Production of the Atlas / 2 \\
                 The Computer Interface / 3 \\
                 What the CD-ROM Contains / 3 \\
                 How to Locate a Function / 3 \\
                 Exploring Functions with Mathematica / 4 \\
                 The C Functions: No Assembly Required / 7 \\
                 Hints for Fortran and Pascal Programmers / 3 \\
                 File Names for PC-Based Systems / 12 \\
                 Reliability of Programs: Disclaimer / 12 \\
                 References on the Computer Interface / 12 \\
                 PART I. THE FUNCTIONS \\
                 1 Introduction to the Functions / 15 \\
                 How the Function Descriptions Are Organized / 16 \\
                 2 A Visual Tour of the Atlas / 17 \\
                 3 Computing Strategies / 25 \\
                 3.1 General Computing Strategies / 25 \\
                 3.2 Iteration and Recursion / 27 \\
                 3.3 Continued Fractions and Rational Approximations /
                 30 \\
                 3.4 Using Asymptotic Expansions / 31 \\
                 3.5 Euler--Maclaurin Summation Formula / 32 \\
                 3.6 Accuracy and Precision of the Functions / 33 \\
                 3.7 Mathematical Constants Used in the Atlas / 34 \\
                 References on Computing Strategies / 34 \\
                 4 Elementary Transcendental Functions / 35 \\
                 4.1 Exponential and Logarithmic Functions / 35 \\
                 4.1.1 Exponentials / 36 \\
                 4.1.2 Logarithms / 38 \\
                 4.2 Circular and Inverse Circular Functions / 40 \\
                 42.1 Circular Functions / 40 \\
                 4.2.2 Inverse Circular Functions / 44 \\
                 4.3 Hyperbolic and Inverse Hyperbolic Functions / 49
                 \\
                 4.3.1 Hyperbolic Functions / 49 \\
                 4.3.2 Inverse Hyperbolic Functions / 53 \\
                 References on Elementary Transcendental Functions / 58
                 \\
                 S Exponential Integrals and Related Functions / 59 \\
                 5.1 Exponential and Logarithmic Integrals / 59 \\
                 5.1.1 Exponential Integral of the First Kind / 59 \\
                 5.1.2 Exponential Integral of the Second Kind / 64 \\
                 5.1.3 Logarithmic Integral / 69 \\
                 5.2 Cosine and Sine Integrals / 72 \\
                 References on Exponential Integrals and Related
                 Functions / 78 \\
                 6 Gamma and Beta Functions / 79 \\
                 6.1 Gamma Function and Beta Function / 79 \\
                 6.1.1 Gamma Function / 79 \\
                 6.1.2 Beta Function / 84 \\
                 6.2 Psi (Digamma) and Polygamma Functions / 86 \\
                 6.2.1 Psi Function / 87 \\
                 6.2.2 Polygamma Functions / 91 \\
                 6.3 Incomplete Gamma and Beta Functions / 97 \\
                 6.3.1 Incomplete Gamma Function / 97 \\
                 6.3.2 Incomplete Beta Function / 102 \\
                 References on Gamma and Beta Functions / 106 \\
                 7 Combinatorial Functions / 109 \\
                 7.1 Factorials and Rising Factorials / 109 \\
                 7.1.1 Factorial Function / 110 \\
                 7.1.2 Rising Factorial Function / 113 \\
                 7.2 Binomial and Multinomial Coefficients / 115 \\
                 7.2.1 Binomial Coefficients / 115 \\
                 7.2.2 Multinomial Coefficients / 118 \\
                 7.3 Stirling Numbers of First and Second Kinds / 121
                 \\
                 7.3.1 Stirling Numbers of the First Kind / 121 \\
                 7.3.2 Stirling Numbers of the Second Kind / 124 \\
                 7.4 Fibonacci and Lucas Polynomials / 126 \\
                 7.4.1 Fibonacci Polynomials and Fibonacci Numbers / 126
                 \\
                 7.4.2 Lucas Polynomials and Lucas Numbers / 128 \\
                 References on Combinatorial Functions / 130 \\
                 8 Number Theory Functions / 133 \\
                 8.1 Bernoulli Numbers and Bernoulli Polynomials / 133
                 \\
                 8.1.1 Bernoulli Numbers / 133 \\
                 8.1.2 Bernoulli Polynomials / 137 \\
                 8.2 Euler Numbers and Euler Polynomials / 139 \\
                 8.2.1 Euler Numbers / 139 \\
                 8.2.2 Euler Polynomials / 142 \\
                 8.3 Riemann Zeta Function / 144 \\
                 8.4 Other Sums of Reciprocal Powers / 147 \\
                 8.5 Polylogarithms / 151 \\
                 References on Number Theory Functions / 156 \\
                 9 Probability Distributions / 159 \\
                 9.1 Overview of Probability Distribution Functions /
                 160 \\
                 9.2 Discrete Probability Distributions / 160 \\
                 9.2.1 Binomial Distribution / 162 \\
                 9.2.2 Negative Binomial (Pascal) Distribution / 164 \\
                 9.2.3 Geometric Distribution / 166 \\
                 9.2.4 Hypergeometric Distribution / 168 \\
                 9.2.5 Logarithmic Series Distribution / 171 \\
                 9.2.6 Poisson Distribution / 173 \\
                 9.3 Normal Probability Distributions / 175 \\
                 9.3.1 Gauss (Normal) Probability Function / 177 \\
                 9.3.2 Bivariate Normal Probability Function / 179 \\
                 9.3.3 Chi-Square Probability Functions / 182 \\
                 9.3.4 $F$-(Variance-Ratio) Distribution Functions / 188
                 \\
                 9.3.5 Student's $t$-Distribution Functions / 192 \\
                 9.3.6 Lognormal Distribution / 196 \\
                 9.4 Other Continuous Probability Distributions / 199
                 \\
                 9.4.1 Cauchy (Lorentz) Distribution / 200 \\
                 9.4.2 Exponential Distribution / 203 \\
                 9.4.3 Pareto Distribution / 205 \\
                 9.4.4 Weibull Distribution / 208 \\
                 9.4.5 Logistic Distribution / 211 \\
                 9.4.6 Laplace Distribution / 213 \\
                 9.4.7 Kolmogorov--Smirnov Distribution / 215 \\
                 9.4.8 Beta Distribution / 218 \\
                 References on Probability Distribution Functions / 221
                 \\
                 10 Error Function, Fresnel and Dawson Integrals / 223
                 \\
                 10.1 Error Function / 223 \\
                 10.2 Fresnel Integrals / 226 \\
                 10.3 Dawson Integral / 234 \\
                 References on Error Functions, Fresnel and Dawson
                 Integrals / 238 \\
                 11 Orthogonal Polynomials / 239 \\
                 11.1 Overview of Orthogonal Polynomials / 239 \\
                 11.2 Chebyshev Polynomials / 244 \\
                 11.2.1 Chebyshev Polynomials of the First Kind / 245
                 \\
                 11.2.2 Chebyshev Polynomials of the Second Kind / 247
                 \\
                 11.3 Gegenbauer (Ultraspherical) Polynomials / 251 \\
                 11.4 Hermite Polynomials / 254 \\
                 11.5 Laguerre Polynomials / 257 \\
                 11.6 Legendre Polynomials / 260 \\
                 11.7 Jacobi Polynomials / 263 \\
                 References on Orthogonal Polynomials / 267 \\
                 12 Legendre Functions / 269 \\
                 12.1 Overview of Legendre Functions / 269 \\
                 12.1.1 Visualizing Legendre Functions of the First Kind
                 / 270 \\
                 12.1.2 Visualizing Legendre Functions of the Second
                 Kind / 273 \\
                 12.1.3 Legendre Functions and Coordinate Systems / 277
                 \\
                 12.2 Spherical Legendre Functions / 278 \\
                 12.2.1 Spherical Polar Coordinates / 278 \\
                 12.2.2 Legendre Functions of the First Kind for Integer
                 $m$ and $n$ / 279 \\
                 12.2.3 Legendre Functions of the Second Kind for
                 Integer $m$ and $n$ / 284 \\
                 12.3 Toroidal Legendre Functions / 291 \\
                 12.3.1 Toroidal Coordinates / 291 \\
                 12.3.2 Toroidal Functions of the First Kind / 293 \\
                 12.3.3 Toroidal Functions of the Second Kind / 296 \\
                 12.4 Conical Legendre Functions / 300 \\
                 12.4.1 Laplace Equation on a Cone / 300 \\
                 12.4.2 Conical Functions / 301 \\
                 References on Legendre Functions / 304 \\
                 13 Spheroidal Wave Functions / 307 \\
                 13.1 Overview of Spheroidal Wave Functions / 307 \\
                 13.1.1 Spheroidal Coordinates / 308 \\
                 13.1.2 Scalar Wave Equation in Spheroidal Coordinates /
                 309 \\
                 13.1.3 Eigenvalues for Spheroidal Equations / 310 \\
                 13.1.4 Auxiliary Functions for Eigenvalues / 320 \\
                 13.2 Spheroidal Angular Functions / 321 \\
                 13.2.1 Expansion Coefficients for Angular Functions /
                 321 \\
                 13.2.2 Spheroidal Angular Functions / 331 \\
                 13.3 Spheroidal Radial Functions / 336 \\
                 13.3.1 Expansion Coefficients for Radial Functions /
                 336 \\
                 13.3.2 Spheroidal Radial Functions / 340 \\
                 References on Spheroidal Wave Functions / 344 \\
                 14 Bessel Functions / 345 \\
                 14.1 Overview of Bessel Functions / 345 \\
                 14.2 Bessel Functions of Integer Order / 350 \\
                 14.2.1 Regular Cylindrical Bessel Function / 351 \\
                 14.2.2 Irregular Cylindrical Bessel Function / 357 \\
                 14.2.3 Regular Hyperbolic Bessel Function / 361 \\
                 14.2.4 Irregular Hyperbolic Bessel Function / 368 \\
                 14.3 Kelvin Functions / 375 \\
                 14.3.1 Regular Kelvin Functions / 375 \\
                 14.3.2 Irregular Kelvin Functions / 385 \\
                 14.4 Bessel Functions of Half-Integer Order / 394 \\
                 14.4.1 Regular Spherical Bessel Function / 394 \\
                 14.4.2 Irregular Spherical Bessel Function / 401 \\
                 14.4.3 Regular Modified Spherical Bessel Function / 405
                 \\
                 14.4.4 Irregular Modified Spherical Bessel Function /
                 412 \\
                 14.5 Airy Functions / 416 \\
                 14.5.1 Airy Functions / 416 \\
                 14.5.2 Derivatives of Airy Functions / 425 \\
                 References on Bessel Functions / 434 \\
                 15 Struve, Anger, and Weber Functions / 435 \\
                 15.1 Struve Functions / 435 \\
                 15.1.1 Struve Function / 435 \\
                 15.1.1 Modified Struve Function / 442 \\
                 15.2 Anger and Weber Functions / 448 \\
                 15.2.1 Overview of Anger and Weber Functions / 448 \\
                 15.2.2 Anger Function / 449 \\
                 15.2.3 Weber Function / 455 \\
                 References on Struve, Anger, and Weber Functions / 458
                 \\
                 16 Hypergeometric Functions and Coulomb Wave Functions
                 / 461 \\
                 16.1 Hypergeometric Functions / 461 \\
                 16.2 Confluent Hypergeometric Functions / 465 \\
                 16.2.1 Regular Function / 465 \\
                 16.2.2 Irregular Function / 471 \\
                 16.3 Coulomb Wave Functions / 478 \\
                 16.3.1 Regular Functions and Derivatives / 478 \\
                 16.3.2 Irregular Functions and Derivatives / 487 \\
                 References on Hypergeometric Functions and Coulomb Wave
                 Functions / 493 \\
                 17 Elliptic Integrals and Elliptic Functions / 495 \\
                 17.1 Overview of Elliptic Integrals and Elliptic
                 Functions / 495 \\
                 17.2 Elliptic Integrals / 496 \\
                 17.2.1 Elliptic Integrals of the First Kind / 496 \\
                 17.2.2 Elliptic Integrals of the Second Kind / 502 \\
                 17.2.3 Jacobi Zeta Function / 506 \\
                 17.2.4 Heuman Lambda Function / 510 \\
                 17.2.5 Elliptic Integrals of the Third Kind / 513 \\
                 17.3 Jacobi Elliptic Functions and Theta Functions /
                 517 \\
                 17.3.1 Jacobi Elliptic Functions / 517 \\
                 17.3.2 Theta Functions / 525 \\
                 17.3.3 Logarithmic Derivatives of Theta Functions / 531
                 \\
                 References on Elliptic Integrals and Elliptic Functions
                 / 536 \\
                 18 Parabolic Cylinder Functions / 539 \\
                 18.1 Parabolic Cylinder Coordinates / 539 \\
                 18.2 Parabolic Cylinder Functions / 540 \\
                 18.2.1 Parabolic Cylinder Functions U / 540 \\
                 18.2.2 Parabolic Cylinder Functions V / 546 \\
                 References on Parabolic Cylinder Functions / 550 \\
                 19 Miscellaneous Functions for Science and Engineering
                 / 551 \\
                 19.1 Debye Functions / 551 \\
                 19.2 Sievert Integral / 554 \\
                 19.3 Abramowitz Function / 557 \\
                 19.4 Spence Integeral / 562 \\
                 19.5 Clausen Integral / 565 \\
                 19.6 Voigt (Plasma Dispersion) Function / 570 \\
                 19.7 Angular Momentum Coupling Coefficients 576 / 539
                 \\
                 19.7.1 3-j Coefficients / 578 \\
                 19.7.2 6-j Coefficients / 582 \\
                 19.7.3 9-j Coefficients / 586 \\
                 References on Miscellaneous Functions for Science and
                 Engineering \\
                 PART II. THE COMPUTER INTERFACE \\
                 20 The Mathematica Notebooks / 593 \\
                 20.1 Introduction to the Notebooks / 593 \\
                 20.2 Exploring with the Notebook Cells / 594 \\
                 20.3 The Annotated Notebooks / 594 \\
                 20.4 Elementary Transcendental Functions / 595 \\
                 20.5 Exponential Integrals and Related Functions / 602
                 \\
                 20.6 Gamma and Beta Functions / 607 \\
                 20.7 Combinatorial Functions / 618 \\
                 20.8 Number Theory Functions / 627 \\
                 20.9 Probability Distributions / 633 \\
                 20.10 Error Function, Fresnel and Dawson Integrals /
                 663 \\
                 20.11 Orthogonal Polynomials / 667 \\
                 20.12 Legendre Functions / 676 \\
                 20.14 Bessel Functions / 708 \\
                 20.15 Struve, Anger, and Weber Functions / 747 \\
                 20.16 Hypergeometric Functions and Coulomb Wave
                 Functions / 756 \\
                 20.17 Elliptic Integrals and Elliptic Functions / 765
                 \\
                 20.18 Parabolic Cylinder Functions / 782 \\
                 20.19 Miscellaneous Functions for Science and
                 Engineering / 788 \\
                 21 The C Driver Programs / 797 \\
                 21.1 Introduction to the C Driver Programs / 797 \\
                 21.2 How the C Drivers are Organized / 797 \\
                 21.3 Annotations to the C Driver Programs / 798 \\
                 21.4 Elementary Transcendental Functions / 798 \\
                 21.4.1 Exponential and Logarithmic Functions / 798 \\
                 21.4.2 Circular and Inverse Circular Functions / 799
                 \\
                 21.4.3 Hyperbolic and Inverse Hyperbolic Functions /
                 800 \\
                 21.5 Exponential Integrals and Related Functions / 802
                 \\
                 21.5.1 Exponential and Logarithmic Integrals / 802 \\
                 21.5.2 Cosine and Sine Integrals / 803 \\
                 21.6 Gamma and Beta Functions / 804 \\
                 21.6.1 Gamma Function and Beta Function / 804 \\
                 21.6.2 Psi (Digamma) and Polygamma Functions / 805 \\
                 21.6.3 Incomplete Gamma and Beta Functions / 807 \\
                 21.7 Combinatorial Functions / 808 \\
                 21.7.1 Factorials and Rising Factorials / 808 \\
                 21.7.2 Binomial and Multinomial Coefficients / 809 \\
                 21.7.3 Stirling Numbers of the First and Second Kinds /
                 811 \\
                 21.7.4 Fibonacci and Lucas Polynomials / 811 \\
                 21.8 Number Theory Functions / 813 \\
                 21.8.1 Bernoulli Numbers and Bernoulli Polynomials /
                 813 \\
                 21.8.2 Euler Numbers and Euler Polynomials / 814 \\
                 21.8.3 Riemann Zeta Function / 814 \\
                 21.8.4 Other Sums of Reciprocal Powers / 815 \\
                 21.8.5 Polylogarithms / 816 \\
                 21.9 Probability Distributions / 816 \\
                 21.9.1 Organization of the PDFs / 816 \\
                 21.9.2 Discrete Probability Distributions / 816 \\
                 21.9.3 Normal Probability Distributions / 820 \\
                 21.9.4 Other Continuous Probability Distributions / 825
                 \\
                 21.10 Error Function, Fresnel and Dawson Integrals /
                 830 \\
                 21.10.1 Error Function / 830 \\
                 21.10.2 Fresnel Integrals / 831 \\
                 21.10.3 Dawson Integral / 832 \\
                 21.11 Orthogonal Polynomials / 833 \\
                 21.11.1 Orthogonal Polynomial Functions / 833 \\
                 21.11.2 Chebyshev Polynomials / 833 \\
                 21.11.3 Gegenbauer (Ultraspherical) Polynomials / 834
                 \\
                 21.11.4 Hermite Polynomials / 835 \\
                 21.11.5 Laguerre Polynomials / 835 \\
                 21.11.6 Legendre Polynomials / 836 \\
                 21.11.7 Jacobi Polynomials / 837 \\
                 21.12 Legendre Functions / 837 \\
                 21.12.1 Overview of Legendre Functions / 838 \\
                 21.12.2 Spherical Legendre Functions / 838 \\
                 21.12.3 Toroidal Legendre Functions / 840 \\
                 21.12.4 Conical Legendre Functions / 841 \\
                 21.13 Spheroidal Wave Functions / 842 \\
                 21.13.1 Overview of Spheroidal Wave Functions / 842 \\
                 21.13.2 Spheroidal Angular Functions / 843 \\
                 21.13.3 Spheroidal Radial Functions / 844 \\
                 21.14 Bessel Functions / 846 \\
                 21.14.1 Overview of Bessel Functions / 846 \\
                 21.14.2 Bessel Functions of Integer Order / 846 \\
                 21.14.3 Kelvin Functions / 850 \\
                 21.14.4 Bessel Functions of Half-Integer Order / 852
                 \\
                 21.14.5 Airy Functions / 856 \\
                 21.15 Struve, Anger, and Weber Functions / 857 \\
                 21.15.1 Struve Functions / 857 \\
                 21.15.2 Anger and Weber Functions / 859 \\
                 21.16 Hypergeometric Functions and Coulomb Wave
                 Functions / 861 \\
                 21.16.1 Hypergeometric Functions / 861 \\
                 21.16.2 Confluent Hypergeometric Functions / 862 \\
                 21.16.3 Coulomb Wave Functions / 863 \\
                 21.17 Elliptic Integrals and Elliptic Functions / 864
                 \\
                 21.17.1 Overview of Elliptic Integrals and Elliptic
                 Functions / 864 \\
                 21.17.2 Elliptic Integrals / 864 \\
                 21.17.3 Jacobi Elliptic Functions and Theta Functions /
                 867 \\
                 21.18 Parabolic Cylinder Functions / 870 \\
                 21.18.1 Parabolic Cylinder Functions / 870 \\
                 21.19 Miscellaneous Functions for Science and
                 Engineering / 872 \\
                 21.19.1 Debye Functions / 872 \\
                 21.19.2 Sievert Integral / 873 \\
                 21.19.3 Abramowitz Function / 873 \\
                 21.19.4 Spence Integral / 874 \\
                 21.19.5 Clausen Integral / 875 \\
                 21.19.6 Voigt (Plasma Dispersion) Function / 876 \\
                 21.19.7 Angular Momentum Coupling Coefficients / 876
                 \\
                 APPENDIX: File Names for PC-Based Systems / 879 \\
                 INDEXES \\
                 Index of Function Notations / 883 \\
                 Index of Programs and Dependencies / 886 \\
                 Index of Subjects and Authors / 889",
}


bibtype: book
filename: elefunt.bib
label: Thompson:1997:ACMb
author: William J. (William Jackson) Thompson
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xiv + 888
year: 1997
ISBN: 0-471-18171-4 (cloth) OR 0471181714 (cloth)
ISBN13: 978-0-471-18171-2 (cloth) OR 9780471181712 (cloth)
LCCN: QA331.T386 1997
bibdate: Fri May 21 07:11:19 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.05.21 07:11:19 MDT
note: Includes CD-ROM.
acknowledgement: ack-nhfb
rawauthor: William J. (William Jackson) Thompson
rawnote: Includes CD-ROM.
title:
Atlas for Computing Mathematical Functions: an Illustrated Guide for Practitioners with Programs in Fortran 90 and Mathematica

keywords:
FORTRAN (Computer program language); Functions -- Computer programs; Mathematica (Computer program language); Science -- Mathematics -- Computer programs

annote:
A Wiley-Interscience publication. System requirements for accompanying computer disc: Windows; Macintosh compatible.

rawtitle:
Atlas for Computing Mathematical Functions: an Illustrated Guide for Practitioners with Programs in {Fortran 90} and {Mathematica}

entry:
@Book{Thompson:1997:ACMb,
  author =       "William J. (William Jackson) Thompson",
  title =        "Atlas for Computing Mathematical Functions: an
                 Illustrated Guide for Practitioners with Programs in
                 {Fortran 90} and {Mathematica}",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiv + 888",
  year =         "1997",
  ISBN =         "0-471-18171-4 (cloth)",
  ISBN-13 =      "978-0-471-18171-2 (cloth)",
  LCCN =         "QA331.T386 1997",
  bibdate =      "Fri May 21 07:11:19 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Includes CD-ROM.",
  acknowledgement = ack-nhfb,
  annote =       "A Wiley-Interscience publication. System requirements
                 for accompanying computer disc: Windows; Macintosh
                 compatible.",
  keywords =     "FORTRAN (Computer program language); Functions --
                 Computer programs; Mathematica (Computer program
                 language); Science -- Mathematics -- Computer
                 programs",
}


bibtype: book
filename: elefunt.bib
label: Yoshida:1997:HFM
author: Masaaki Yoshida
title: Hypergeometric Functions, My Love: Modular Interpretations of Configuration Spaces
volume: E 32
publisher: pub-VIEWEG
address: pub-VIEWEG:adr
pages: xvi + 292
year: 1997
ISBN: 3-528-06925-2 OR 3528069252
ISBN13: 978-3-528-06925-4 OR 9783528069254
ISSN: 0179-2156 OR 01792156
LCCN: QA353.H9 Y67 1997
bibdate: Sat Oct 30 21:12:24 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 21:12:24 MDT
series: Aspects of mathematics
subject: Hypergeometric functions; Configuration space
acknowledgement: ack-nhfb
rawauthor: Masaaki Yoshida
rawtitle: Hypergeometric Functions, My Love: Modular Interpretations of Configuration Spaces
TOC:
Part 1: The Story of the Configuration Space $X(2,4)$ of Four Points on the Projective Line I. Configuration Spaces --- The Simplest Case II. Elliptic Curves III. Modular Interpretations of X(2,4) IV. Hypergeometric Integrals and Loaded Cycles 2 The Story of the Configuration Space X(2,n) of n Points on the Projective Line V. The Configuration Space X(2,5) VI. Modular Interpretation of the Configuration Space X(2,n) 3 The Story of the Configuration Space X(3,6) of Six Lines on the Projective Plane VII The Configuration Space X(3,6) VIII. Hypergeometric Functions of Type (3,6) IX. Modular Interpretation of the Configuration Space X(3,6)

rawTOC:
Part 1: The Story of the Configuration Space $X(2,4)$ of Four Points on the Projective Line \\ I. Configuration Spaces --- The Simplest Case \\ II. Elliptic Curves \\ III. Modular Interpretations of X(2,4) \\ IV. Hypergeometric Integrals and Loaded Cycles \\ 2 The Story of the Configuration Space X(2,n) of n Points on the Projective Line \\ V. The Configuration Space X(2,5) \\ VI. Modular Interpretation of the Configuration Space X(2,n) \\ 3 The Story of the Configuration Space X(3,6) of Six Lines on the Projective Plane \\ VII The Configuration Space X(3,6) \\ VIII. Hypergeometric Functions of Type (3,6) \\ IX. Modular Interpretation of the Configuration Space X(3,6)

entry:
@Book{Yoshida:1997:HFM,
  author =       "Masaaki Yoshida",
  title =        "Hypergeometric Functions, My Love: Modular
                 Interpretations of Configuration Spaces",
  volume =       "E 32",
  publisher =    pub-VIEWEG,
  address =      pub-VIEWEG:adr,
  pages =        "xvi + 292",
  year =         "1997",
  ISBN =         "3-528-06925-2",
  ISBN-13 =      "978-3-528-06925-4",
  ISSN =         "0179-2156",
  LCCN =         "QA353.H9 Y67 1997",
  bibdate =      "Sat Oct 30 21:12:24 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Aspects of mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions; Configuration space",
  tableofcontents = "Part 1: The Story of the Configuration Space
                 $X(2,4)$ of Four Points on the Projective Line \\
                 I. Configuration Spaces --- The Simplest Case \\
                 II. Elliptic Curves \\
                 III. Modular Interpretations of X(2,4) \\
                 IV. Hypergeometric Integrals and Loaded Cycles \\
                 2 The Story of the Configuration Space X(2,n) of n
                 Points on the Projective Line \\
                 V. The Configuration Space X(2,5) \\
                 VI. Modular Interpretation of the Configuration Space
                 X(2,n) \\
                 3 The Story of the Configuration Space X(3,6) of Six
                 Lines on the Projective Plane \\
                 VII The Configuration Space X(3,6) \\
                 VIII. Hypergeometric Functions of Type (3,6) \\
                 IX. Modular Interpretation of the Configuration Space
                 X(3,6)",
}


bibtype: article
filename: elefunt.bib
label: Yousif:1997:BFF
author: Hashim A. Yousif and Richard Melka
title: Bessel function of the first kind with complex argument
journal: j-COMP-PHYS-COMM
volume: 106
number: 3
pages: 199--206
month: nov
monthnumber: 11
year: 1997
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(97)00087-8
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:30:21 MST 2012
bibtimestamp: 2012.02.13 21:30:21 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465597000878
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Hashim A. Yousif and Richard Melka
rawtitle: {Bessel} function of the first kind with complex argument
abstract:
A new method of computing integral order Bessel functions of the first kind $ J_n(z) $ when either the absolute value of the real part or the imaginary part of the argument $ z = x + i y $ is small, is described. This method is based on computing the Bessel functions from asymptotic expressions when $ x sim 0 $ (or $ y sim 0 $ ). These expansions are derived from the integral definition of Bessel functions. This method is necessary because some existing algorithms and methods fail to give correct results for small $x$ or small $y$. In addition, our overall method of computing Bessel functions of any order and argument is discussed and the logarithmic derivative is used in computing these functions. The starting point of the backward recurrence relations needed to evaluate the Bessel function and their logarithmic derivatives are investigated in order to obtain accurate numerical results. Our numerical method, together with established techniques of computing the Bessel functions, is easy to implement, efficient, and produces reliable results for all $z$.

rawabstract:
A new method of computing integral order Bessel functions of the first kind $ J_n(z) $ when either the absolute value of the real part or the imaginary part of the argument $ z = x + i y $ is small, is described. This method is based on computing the Bessel functions from asymptotic expressions when $ x \sim 0 $ (or $ y \sim 0 $ ). These expansions are derived from the integral definition of Bessel functions. This method is necessary because some existing algorithms and methods fail to give correct results for small $x$ or small $y$. In addition, our overall method of computing Bessel functions of any order and argument is discussed and the logarithmic derivative is used in computing these functions. The starting point of the backward recurrence relations needed to evaluate the Bessel function and their logarithmic derivatives are investigated in order to obtain accurate numerical results. Our numerical method, together with established techniques of computing the Bessel functions, is easy to implement, efficient, and produces reliable results for all $z$.

entry:
@Article{Yousif:1997:BFF,
  author =       "Hashim A. Yousif and Richard Melka",
  title =        "{Bessel} function of the first kind with complex
                 argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "106",
  number =       "3",
  pages =        "199--206",
  month =        nov,
  year =         "1997",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(97)00087-8",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:21 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465597000878",
  abstract =     "A new method of computing integral order Bessel
                 functions of the first kind $ J_n(z) $ when either the
                 absolute value of the real part or the imaginary part
                 of the argument $ z = x + i y $ is small, is described.
                 This method is based on computing the Bessel functions
                 from asymptotic expressions when $ x \sim 0 $ (or $ y
                 \sim 0 $ ). These expansions are derived from the
                 integral definition of Bessel functions. This method is
                 necessary because some existing algorithms and methods
                 fail to give correct results for small $x$ or small
                 $y$. In addition, our overall method of computing
                 Bessel functions of any order and argument is discussed
                 and the logarithmic derivative is used in computing
                 these functions. The starting point of the backward
                 recurrence relations needed to evaluate the Bessel
                 function and their logarithmic derivatives are
                 investigated in order to obtain accurate numerical
                 results. Our numerical method, together with
                 established techniques of computing the Bessel
                 functions, is easy to implement, efficient, and
                 produces reliable results for all $z$.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Zhang:1997:CSA
author: Jun Zhang and John A. Belward
title: Chebyshev series approximations for the Bessel function $ Y_n(z) $ of complex argument
journal: j-APPL-MATH-COMP
volume: 88
number: 2--3
pages: 275--286
day: 30
month: dec
monthnumber: 12
year: 1997
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/S0096-3003(96)00335-9
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Tue Nov 20 21:02:59 MST 2012
bibtimestamp: 2012.11.20 21:02:59 MST
URL: http://www.sciencedirect.com/science/article/pii/S0096300396003359
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: Jun Zhang and John A. Belward
rawtitle: {Chebyshev} series approximations for the {Bessel} function {$ Y_n(z) $} of complex argument
bibsource:
http://www.sciencedirect.com/science/journal/00963003; https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Zhang:1997:CSA,
  author =       "Jun Zhang and John A. Belward",
  title =        "{Chebyshev} series approximations for the {Bessel}
                 function {$ Y_n(z) $} of complex argument",
  journal =      j-APPL-MATH-COMP,
  volume =       "88",
  number =       "2--3",
  pages =        "275--286",
  day =          "30",
  month =        dec,
  year =         "1997",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/S0096-3003(96)00335-9",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Nov 20 21:02:59 MST 2012",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300396003359",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}


bibtype: article
filename: elefunt.bib
label: Aberbour:1998:PMF
author: M. Aberbour and A. Houelle and H. Mehrez and N. Vaucher and A. Guyot
journal: j-IEEE-TRANS-VLSI-SYST
volume: 6
number: 1
pages: 114--121
month: mar
monthnumber: 3
year: 1998
CODEN: IEVSE9
DOI: https://doi.org/10.1109/92.661253
ISSN: 1063-8210 (print), 1557-9999 (electronic) OR 10638210 (print), 15579999 (electronic)
ISSNL: 1063-8210 OR 10638210
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Very Large Scale Integration (VLSI) Systems
acknowledgement: ack-nhfb
rawauthor: M. Aberbour and A. Houelle and H. Mehrez and N. Vaucher and A. Guyot
title:
On portable macrocell FPU generators for division and square root operators complying to the full IEEE-754 standard

rawtitle:
On portable macrocell {FPU} generators for division and square root operators complying to the full {IEEE-754} standard

entry:
@Article{Aberbour:1998:PMF,
  author =       "M. Aberbour and A. Houelle and H. Mehrez and N.
                 Vaucher and A. Guyot",
  title =        "On portable macrocell {FPU} generators for division
                 and square root operators complying to the full
                 {IEEE-754} standard",
  journal =      j-IEEE-TRANS-VLSI-SYST,
  volume =       "6",
  number =       "1",
  pages =        "114--121",
  month =        mar,
  year =         "1998",
  CODEN =        "IEVSE9",
  DOI =          "https://doi.org/10.1109/92.661253",
  ISSN =         "1063-8210 (print), 1557-9999 (electronic)",
  ISSN-L =       "1063-8210",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Very Large Scale Integration
                 (VLSI) Systems",
  summary =      "In this paper, we investigate the design of macrocell
                 generators of division and square root floating-point
                 operators. The number representation used in our
                 operators is the IEEE-754-1985 standard for binary
                 floating-point numbers. The design and \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Adamchik:1998:PFN
author: Victor S. Adamchik
title: Polygamma functions of negative order
journal: j-J-COMPUT-APPL-MATH
volume: 100
number: 2
pages: 191--199
day: 21
month: dec
monthnumber: 12
year: 1998
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:39:42 MST 2017
bibtimestamp: 2017.02.25 12:39:42 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042798001927
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Victor S. Adamchik
rawtitle: {Polygamma} functions of negative order
entry:
@Article{Adamchik:1998:PFN,
  author =       "Victor S. Adamchik",
  title =        "{Polygamma} functions of negative order",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "100",
  number =       "2",
  pages =        "191--199",
  day =          "21",
  month =        dec,
  year =         "1998",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:39:42 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042798001927",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Alzer:1998:CHM
author: Horst Alzer
journal: j-J-COMPUT-APPL-MATH
volume: 90
number: 2
pages: 265--265
day: 17
month: apr
monthnumber: 4
year: 1998
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(98)00040-5
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:36:08 MST 2017
bibtimestamp: 2017.02.25 12:36:08 MST
note: See cite Alzer:1997:HMI.
URL: http://www.sciencedirect.com/science/article/pii/S0377042798000405
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Horst Alzer
rawnote: See \cite{Alzer:1997:HMI}.
title:
Corrigendum: A harmonic mean inequality for the gamma function [J. Comput. Appl. Math. bf 87 (1997) 195--198]

rawtitle:
Corrigendum: {A harmonic mean inequality for the gamma function [J. Comput. Appl. Math. {\bf 87} (1997) 195--198]}

entry:
@Article{Alzer:1998:CHM,
  author =       "Horst Alzer",
  title =        "Corrigendum: {A harmonic mean inequality for the gamma
                 function [J. Comput. Appl. Math. {\bf 87} (1997)
                 195--198]}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "90",
  number =       "2",
  pages =        "265--265",
  day =          "17",
  month =        apr,
  year =         "1998",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(98)00040-5",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:08 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  note =         "See \cite{Alzer:1997:HMI}.",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042798000405",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: book
filename: elefunt.bib
label: Andrews:1998:SFM
author: Larry C. Andrews
title: Special functions of mathematics for engineers
publisher: pub-OXFORD
address: pub-OXFORD:adr
edition: Second
pages: xvii + 479
year: 1998
LCCN: QA351 .A75 1998
bibdate: Sat Oct 30 16:44:00 MDT 2010
bibtimestamp: 2010.10.30 16:44:00 MDT
remark: Originally published: New York : McGraw-Hill, c1992.
subject: Functions, Special
acknowledgement: ack-nhfb
rawauthor: Larry C. Andrews
rawtitle: Special functions of mathematics for engineers
ISBN:
0-19-856558-5 (Oxford hardcover), 0-8194-2616-4 (SPIE Press hardcover) OR 0198565585 (Oxford hardcover), 0819426164 (SPIE Press hardcover)

ISBN13:
978-0-19-856558-1 (Oxford hardcover), 978-0-8194-2616-1 (SPIE Press) OR 9780198565581 (Oxford hardcover), 9780819426161 (SPIE Press)

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; library.ox.ac.uk:210/ADVANCE; z3950.loc.gov:7090/Voyager

TOC:
Preface to the Second Edition Preface to the First Edition Notation for Special Functions Infinite Series, Improper Integrals, and Infinite Products The Gamma Function and Related Functions Other Functions Defined by Integrals Legendre Polynomials and Related Functions Other Orthogonal Polynomials Bessel Functions Bessel Functions of Other Kinds Applications Involving Bessel Functions The Hypergeometric Function The Confluent Hypergeometric Functions Generalized Hypergeometric Functions Applications Involving Hypergeometric-Type Functions Bibliography Appendix: A List of Special Function Formulas Selected Answers to Exercises Index

rawTOC:
Preface to the Second Edition \\ Preface to the First Edition \\ Notation for Special Functions \\ Infinite Series, Improper Integrals, and Infinite Products \\ The Gamma Function and Related Functions \\ Other Functions Defined by Integrals \\ Legendre Polynomials and Related Functions \\ Other Orthogonal Polynomials \\ Bessel Functions \\ Bessel Functions of Other Kinds \\ Applications Involving Bessel Functions \\ The Hypergeometric Function \\ The Confluent Hypergeometric Functions \\ Generalized Hypergeometric Functions \\ Applications Involving Hypergeometric-Type Functions \\ Bibliography \\ Appendix: A List of Special Function Formulas \\ Selected Answers to Exercises \\ Index

entry:
@Book{Andrews:1998:SFM,
  author =       "Larry C. Andrews",
  title =        "Special functions of mathematics for engineers",
  publisher =    pub-OXFORD,
  address =      pub-OXFORD:adr,
  edition =      "Second",
  pages =        "xvii + 479",
  year =         "1998",
  ISBN =         "0-19-856558-5 (Oxford hardcover), 0-8194-2616-4 (SPIE
                 Press hardcover)",
  ISBN-13 =      "978-0-19-856558-1 (Oxford hardcover),
                 978-0-8194-2616-1 (SPIE Press)",
  LCCN =         "QA351 .A75 1998",
  bibdate =      "Sat Oct 30 16:44:00 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 library.ox.ac.uk:210/ADVANCE;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  remark =       "Originally published: New York : McGraw-Hill, c1992.",
  subject =      "Functions, Special",
  tableofcontents = "Preface to the Second Edition \\
                 Preface to the First Edition \\
                 Notation for Special Functions \\
                 Infinite Series, Improper Integrals, and Infinite
                 Products \\
                 The Gamma Function and Related Functions \\
                 Other Functions Defined by Integrals \\
                 Legendre Polynomials and Related Functions \\
                 Other Orthogonal Polynomials \\
                 Bessel Functions \\
                 Bessel Functions of Other Kinds \\
                 Applications Involving Bessel Functions \\
                 The Hypergeometric Function \\
                 The Confluent Hypergeometric Functions \\
                 Generalized Hypergeometric Functions \\
                 Applications Involving Hypergeometric-Type Functions
                 \\
                 Bibliography \\
                 Appendix: A List of Special Function Formulas \\
                 Selected Answers to Exercises \\
                 Index",
}


bibtype: book
filename: elefunt.bib
label: Anonymous:1998:AMS
editor: Anonymous
title: Analytical methods and special functions
publisher: Gordon and Breach Science Publishers
address: Amsterdam, The Netherlands
year: 1998
ISSN: 1027-0264 OR 10270264
LCCN: A299.6 A533 v. 1 1998
bibdate: Sat Oct 30 19:02:18 2010
bibsource: http://cat.cisti-icist.nrc-cnrc.gc.ca/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:02:18 ???
acknowledgement: ack-nhfb
raweditor: Anonymous
rawtitle: Analytical methods and special functions
entry:
@Book{Anonymous:1998:AMS,
  editor =       "Anonymous",
  title =        "Analytical methods and special functions",
  publisher =    "Gordon and Breach Science Publishers",
  address =      "Amsterdam, The Netherlands",
  pages =        "????",
  year =         "1998",
  ISSN =         "1027-0264",
  LCCN =         "A299.6 A533 v. 1 1998",
  bibdate =      "Sat Oct 30 19:02:18 2010",
  bibsource =    "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Antelo:1998:CVH
author: E. Antelo and T. Lang and J. D. Bruguera
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 2
pages: 152--161
month: feb
monthnumber: 2
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.663761
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:53 MDT 2011
bibtimestamp: 2011.07.06 09:35:53 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663761
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: E. Antelo and T. Lang and J. D. Bruguera
title:
Computation of $ sqrt (x / d) $ in a very high radix combined division / square-root unit with scaling and selection by rounding

rawtitle:
Computation of $ \sqrt {(x / d)} $ in a very high radix combined division\slash square-root unit with scaling and selection by rounding

entry:
@Article{Antelo:1998:CVH,
  author =       "E. Antelo and T. Lang and J. D. Bruguera",
  title =        "Computation of $ \sqrt {(x / d)} $ in a very high
                 radix combined division\slash square-root unit with
                 scaling and selection by rounding",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "2",
  pages =        "152--161",
  month =        feb,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.663761",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:53 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=663761",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A very-high radix digit-recurrence algorithm for the
                 operation {\surd}(x/d) is developed, with residual
                 scaling and digit selection by rounding. This is an
                 extension of the division and square-root algorithms
                 presented previously, and for which a \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: BenGhanem:1998:QFU
author: Riadh Ben Ghanem
title: Quadrature formulae using zeros of Bessel functions as nodes
journal: j-MATH-COMPUT
volume: 67
number: 221
pages: 323--336
month: jan
monthnumber: 1
year: 1998
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65D32
MRnumber: 98c:65031
MRreviewer: Kai Diethelm
bibdate: Fri Jul 16 10:38:50 MDT 1999
bibsource: http://www.ams.org/mcom/1998-67-221; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.07.16 10:38:50 MDT
URL: http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00882-5&u=/mcom/1998-67-221/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Riadh {Ben Ghanem}
rawtitle: Quadrature formulae using zeros of {Bessel} functions as nodes
entry:
@Article{BenGhanem:1998:QFU,
  author =       "Riadh {Ben Ghanem}",
  title =        "Quadrature formulae using zeros of {Bessel} functions
                 as nodes",
  journal =      j-MATH-COMPUT,
  volume =       "67",
  number =       "221",
  pages =        "323--336",
  month =        jan,
  year =         "1998",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65D32",
  MRnumber =     "98c:65031",
  MRreviewer =   "Kai Diethelm",
  bibdate =      "Fri Jul 16 10:38:50 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1998-67-221;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00882-5&u=/mcom/1998-67-221/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: techreport
filename: elefunt.bib
label: Borwein:1998:CSR
author: Jonathan M. Borwein and David M. Bradley and Richard E. Crandall
title: Computational Strategies for the Riemann Zeta Function
type: Report
number: CECM-98-118
institution: inst-CECM
address: inst-CECM:adr
pages: 68
day: 30
month: oct
monthnumber: 10
year: 1998
bibdate: Mon Oct 24 11:29:15 2011
bibtimestamp: 2011.10.24 11:29:15 ???
note: Published in cite Borwein:2000:CSR.
URL: http://docserver.carma.newcastle.edu.au/211; http://people.reed.edu/~crandall/papers/attach01.pdf
acknowledgement: ack-nhfb
rawauthor: Jonathan M. Borwein and David M. Bradley and Richard E. Crandall
rawnote: Published in \cite{Borwein:2000:CSR}.
rawtitle: Computational Strategies for the {Riemann} Zeta Function
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the incidence of what we call ``value recycling.''

authordates:
Jonathan Michael Borwein (20 May 1951--2 August 2016); Richard Eugene Crandall (29 December 1947--20 December 2012)

rawabstract:
We provide a compendium of evaluation methods for the Riemann zeta function, presenting formulae ranging from historical attempts to recently found convergent series to curious oddities old and new. We concentrate primarily on practical computational issues, such issues depending on the domain of the argument, the desired speed of computation, and the incidence of what we call ``value recycling.''

entry:
@TechReport{Borwein:1998:CSR,
  author =       "Jonathan M. Borwein and David M. Bradley and Richard
                 E. Crandall",
  title =        "Computational Strategies for the {Riemann} Zeta
                 Function",
  type =         "Report",
  number =       "CECM-98-118",
  institution =  inst-CECM,
  address =      inst-CECM:adr,
  pages =        "68",
  day =          "30",
  month =        oct,
  year =         "1998",
  bibdate =      "Mon Oct 24 11:29:15 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/c/crandall-richard-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Borwein:2000:CSR}.",
  URL =          "http://docserver.carma.newcastle.edu.au/211;
                 http://people.reed.edu/~crandall/papers/attach01.pdf",
  abstract =     "We provide a compendium of evaluation methods for the
                 Riemann zeta function, presenting formulae ranging from
                 historical attempts to recently found convergent series
                 to curious oddities old and new. We concentrate
                 primarily on practical computational issues, such
                 issues depending on the domain of the argument, the
                 desired speed of computation, and the incidence of what
                 we call ``value recycling.''",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August 2016);
                 Richard Eugene Crandall (29 December 1947--20 December
                 2012)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
}


bibtype: incollection
filename: elefunt.bib
label: Buhring:1998:ACG
author: Wolfgang Buhring and H. M. Srivastava
editor: Themistocles M. Rassias
booktitle: Approximation theory and applications
publisher: Hadronic Press
address: Palm Harbor, FL, USA
pages: 17--35
year: 1998
ISBN: 1-57485-041-5 OR 1574850415
ISBN13: 978-1-57485-041-3 OR 9781574850413
LCCN: QA297.5 .A685 1998
MRclass: 33C20; 41-06 (00B15)
MRnumber: MR1924838 (2003i:33006); MR1924835 (2003c:41003)
bibdate: Thu Dec 01 10:08:00 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 10:08:00 ???
URL: http://catalog.hathitrust.org/api/volumes/oclc/42786578.html
remark: The paper treats $_p + 1F_p(z)$ for $ z approx 1 $. Available as arxiv:math/0102032.
acknowledgement: ack-nhfb
bookpages: v + 193
rawauthor: Wolfgang B{\"u}hring and H. M. Srivastava
rawbooktitle: Approximation theory and applications
raweditor: Themistocles M. Rassias
title:
Analytic Continuation of the Generalized Hypergeometric Series Near Unit Argument with Emphasis on the Zero-Balanced Series

rawtitle:
Analytic Continuation of the Generalized Hypergeometric Series Near Unit Argument with Emphasis on the Zero-Balanced Series

entry:
@InCollection{Buhring:1998:ACG,
  author =       "Wolfgang B{\"u}hring and H. M. Srivastava",
  editor =       "Themistocles M. Rassias",
  booktitle =    "Approximation theory and applications",
  title =        "Analytic Continuation of the Generalized
                 Hypergeometric Series Near Unit Argument with Emphasis
                 on the Zero-Balanced Series",
  publisher =    "Hadronic Press",
  address =      "Palm Harbor, FL, USA",
  bookpages =    "v + 193",
  pages =        "17--35",
  year =         "1998",
  ISBN =         "1-57485-041-5",
  ISBN-13 =      "978-1-57485-041-3",
  LCCN =         "QA297.5 .A685 1998",
  MRclass =      "33C20; 41-06 (00B15)",
  MRnumber =     "MR1924838 (2003i:33006); MR1924835 (2003c:41003)",
  bibdate =      "Thu Dec 01 10:08:00 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://catalog.hathitrust.org/api/volumes/oclc/42786578.html",
  acknowledgement = ack-nhfb,
  remark =       "The paper treats $_{p + 1F}_p(z)$ for $ z \approx 1 $.
                 Available as arxiv:math/0102032.",
}


bibtype: article
filename: elefunt.bib
label: Carsky:1998:IGF
author: Petr Carsky and Martin Polasek
title: Incomplete Gamma $ F_m(x) $ Functions for Real Negative and Complex Arguments
journal: j-J-COMPUT-PHYS
volume: 143
number: 1
pages: 259--265
day: 10
month: jun
monthnumber: 6
year: 1998
CODEN: JCTPAH
DOI: https://doi.org/10.1006/jcph.1998.5975
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Mon Jan 2 07:55:26 MST 2012
bibtimestamp: 2012.01.02 07:55:26 MST
URL: http://www.sciencedirect.com/science/article/pii/S0021999198959757
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Petr C{\'a}rsky and Martin Pol{\'a}sek
rawtitle: Incomplete Gamma {$ F_m(x) $} Functions for Real Negative and Complex Arguments
entry:
@Article{Carsky:1998:IGF,
  author =       "Petr C{\'a}rsky and Martin Pol{\'a}sek",
  title =        "Incomplete Gamma {$ F_m(x) $} Functions for Real
                 Negative and Complex Arguments",
  journal =      j-J-COMPUT-PHYS,
  volume =       "143",
  number =       "1",
  pages =        "259--265",
  day =          "10",
  month =        jun,
  year =         "1998",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1006/jcph.1998.5975",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 07:55:26 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021999198959757",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Cornea-Hasegan:1998:PIC
author: Marius Cornea-Hasegan
journal: j-INTEL-TECH-J
volume: Q2
number: Q2
pages: 11
year: 1998
ISSN: 1535-766X OR 1535766X
bibdate: Fri Jun 01 06:02:08 2001
bibtimestamp: 2001.06.01 06:02:08 ???
acknowledgement: ack-nhfb
rawauthor: Marius Cornea-Hasegan
title:
Proving the IEEE Correctness of Iterative Floating-Point Square Root, Divide, and Remainder Algorithms

URL:
http://developer.intel.com/technology/itj/q21998/articles/art_3.htm; http://developer.intel.com/technology/itj/q21998/pdf/ieee.pdf

rawtitle:
Proving the {IEEE} Correctness of Iterative Floating-Point Square Root, Divide, and Remainder Algorithms

entry:
@Article{Cornea-Hasegan:1998:PIC,
  author =       "Marius Cornea-Hasegan",
  title =        "Proving the {IEEE} Correctness of Iterative
                 Floating-Point Square Root, Divide, and Remainder
                 Algorithms",
  journal =      j-INTEL-TECH-J,
  volume =       "Q2",
  number =       "Q2",
  pages =        "11",
  year =         "1998",
  ISSN =         "1535-766X",
  bibdate =      "Fri Jun 01 06:02:08 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://developer.intel.com/technology/itj/q21998/articles/art_3.htm;
                 http://developer.intel.com/technology/itj/q21998/pdf/ieee.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Crenshaw:1998:ISR
author: Jack W. Crenshaw
title: Integer Square Roots
journal: j-EMBED-SYS-PROG
volume: 11
number: 2
pages: 15--32
month: feb
monthnumber: 2
year: 1998
CODEN: EYPRE4
ISSN: 1040-3272 OR 10403272
bibdate: Fri Nov 28 16:31:58 2003
bibtimestamp: 2003.11.28 16:31:58 ???
URL: http://www.embedded.com/98/9802fe2.htm
fjournal: Embedded Systems Programming
acknowledgement: ack-mfc
rawauthor: Jack W. Crenshaw
rawtitle: Integer Square Roots
entry:
@Article{Crenshaw:1998:ISR,
  author =       "Jack W. Crenshaw",
  title =        "Integer Square Roots",
  journal =      j-EMBED-SYS-PROG,
  volume =       "11",
  number =       "2",
  pages =        "15--32",
  month =        feb,
  year =         "1998",
  CODEN =        "EYPRE4",
  ISSN =         "1040-3272",
  bibdate =      "Fri Nov 28 16:31:58 2003",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.embedded.com/98/9802fe2.htm",
  acknowledgement = ack-mfc # " and " # ack-nhfb,
  fjournal =     "Embedded Systems Programming",
}


bibtype: article
filename: elefunt.bib
label: Dattoli:1998:GBF
author: G. Dattoli and A. Torre and S. Lorenzutta and G. Maino
title: Generalized Bessel functions and Kapteyn series
journal: j-COMPUT-MATH-APPL
volume: 35
number: 8
pages: 117--125
month: apr
monthnumber: 4
year: 1998
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:48:48 MST 2017
bibtimestamp: 2017.03.01 21:48:48 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122198000509
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: G. Dattoli and A. Torre and S. Lorenzutta and G. Maino
rawtitle: Generalized {Bessel} functions and {Kapteyn} series
entry:
@Article{Dattoli:1998:GBF,
  author =       "G. Dattoli and A. Torre and S. Lorenzutta and G.
                 Maino",
  title =        "Generalized {Bessel} functions and {Kapteyn} series",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "35",
  number =       "8",
  pages =        "117--125",
  month =        apr,
  year =         "1998",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:48:48 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122198000509",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Deleglise:1998:C
author: Marc Deleglise and Joel Rivat
title: Computing $ psi (x) $
journal: j-MATH-COMPUT
volume: 67
number: 224
pages: 1691--1696
month: oct
monthnumber: 10
year: 1998
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 11Y35 (11N56)
MRnumber: 1 474 649
bibdate: Fri Jul 16 10:38:58 MDT 1999
bibsource: http://www.ams.org/mcom/1998-67-224; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.07.16 10:38:58 MDT
URL: http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00977-6&u=/mcom/1998-67-224/
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Marc Del{\'e}glise and Jo{\"e}l Rivat
rawtitle: Computing $ \psi (x) $
entry:
@Article{Deleglise:1998:C,
  author =       "Marc Del{\'e}glise and Jo{\"e}l Rivat",
  title =        "Computing $ \psi (x) $",
  journal =      j-MATH-COMPUT,
  volume =       "67",
  number =       "224",
  pages =        "1691--1696",
  month =        oct,
  year =         "1998",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "11Y35 (11N56)",
  MRnumber =     "1 474 649",
  bibdate =      "Fri Jul 16 10:38:58 MDT 1999",
  bibsource =    "http://www.ams.org/mcom/1998-67-224;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/jourcgi/jour-pbprocess?fn=110&arg1=S0025-5718-98-00977-6&u=/mcom/1998-67-224/",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Fowler:1998:SRA
author: David Fowler and Eleanor Robson
title: Square Root Approximations in Old Babylonian Mathematics: YBC 7289 in Context
journal: j-HIST-MATH
volume: 25
number: 4
pages: 366--378
month: nov
monthnumber: 11
year: 1998
CODEN: HIMADS
ISSN: 0315-0860 (print), 1090-249X (electronic) OR 03150860 (print), 1090249X (electronic)
ISSNL: 0315-0860 OR 03150860
bibdate: Wed Jun 26 06:19:31 MDT 2013
bibtimestamp: 2013.06.26 06:19:31 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0315086098922091
fjournal: Historia Mathematica
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03150860
rawauthor: David Fowler and Eleanor Robson
rawtitle: Square Root Approximations in Old {Babylonian} Mathematics: {YBC 7289} in Context
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/histmath.bib

entry:
@Article{Fowler:1998:SRA,
  author =       "David Fowler and Eleanor Robson",
  title =        "Square Root Approximations in Old {Babylonian}
                 Mathematics: {YBC 7289} in Context",
  journal =      j-HIST-MATH,
  volume =       "25",
  number =       "4",
  pages =        "366--378",
  month =        nov,
  year =         "1998",
  CODEN =        "HIMADS",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:19:31 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086098922091",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
}


bibtype: inproceedings
filename: elefunt.bib
label: Gautschi:1998:IGF
author: Walter Gautschi
title: The incomplete gamma functions since Tricomi
crossref: Anonymous:1998:TIC
pages: 203--237
year: 1998
bibdate: Fri May 31 16:38:24 2024
bibtimestamp: 2024.05.31 16:38:24 ???
URL: https://web.archive.org/web/20070503103643/http://citeseer.ist.psu.edu/gautschi98incomplete.html
acknowledgement: ack-nhfb
rawauthor: Walter Gautschi
rawtitle: The incomplete gamma functions since {Tricomi}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@InProceedings{Gautschi:1998:IGF,
  author =       "Walter Gautschi",
  title =        "The incomplete gamma functions since {Tricomi}",
  crossref =     "Anonymous:1998:TIC",
  pages =        "203--237",
  year =         "1998",
  bibdate =      "Fri May 31 16:38:24 2024",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://web.archive.org/web/20070503103643/http://citeseer.ist.psu.edu/gautschi98incomplete.html",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Giordano:1998:UTG
author: C. Giordano and A. Laforgia and J. Pecaric
title: Unified treatment of Gautschi--Kershaw type inequalities for the gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 99
number: 1--2
pages: 167--175
day: 16
month: nov
monthnumber: 11
year: 1998
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:36:13 MST 2017
bibtimestamp: 2017.02.25 12:36:13 MST
URL: http://www.sciencedirect.com/science/article/pii/S037704279800154X
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: C. Giordano and A. Laforgia and J. Pecari{\'c}
rawtitle: Unified treatment of {Gautschi--Kershaw} type inequalities for the gamma function
entry:
@Article{Giordano:1998:UTG,
  author =       "C. Giordano and A. Laforgia and J. Pecari{\'c}",
  title =        "Unified treatment of {Gautschi--Kershaw} type
                 inequalities for the gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "99",
  number =       "1--2",
  pages =        "167--175",
  day =          "16",
  month =        nov,
  year =         "1998",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:13 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704279800154X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Harris:1998:MAL
author: Frank E. Harris
title: More About the Leaky Aquifer Function
journal: j-IJQC
volume: 70
number: 4--5
pages: 623--626
year: 1998
CODEN: IJQCB2
DOI: https://doi.org/10.1002/(SICI)1097-461X(1998)70:4/5<623::AID-QUA8>3.0.CO%3B2-X
ISSN: 0020-7608 (print), 1097-461X (electronic) OR 00207608 (print), 1097461X (electronic)
ISSNL: 0020-7608 OR 00207608
bibdate: Tue Oct 4 06:59:18 MDT 2011
bibtimestamp: 2011.10.04 06:59:18 MDT
fjournal: International Journal of Quantum Chemistry
acknowledgement: ack-nhfb
ajournal: Int. J. Quantum Chem.
journalURL: http://www.interscience.wiley.com/jpages/0020-7608/
onlinedate: 7 Dec 1998
rawauthor: Frank E. Harris
rawtitle: More About the Leaky Aquifer Function
bibsource:
http://www3.interscience.wiley.com/journalfinder.html; https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ijqc.bib; https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib

URL:
http://www3.interscience.wiley.com/cgi-bin/abstract?ID=75040; http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=75040&PLACEBO=IE.pdf

entry:
@Article{Harris:1998:MAL,
  author =       "Frank E. Harris",
  title =        "More About the Leaky Aquifer Function",
  journal =      j-IJQC,
  volume =       "70",
  number =       "4--5",
  pages =        "623--626",
  month =        "????",
  year =         "1998",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/(SICI)1097-461X(1998)70:4/5<623::AID-QUA8>3.0.CO%3B2-X",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Tue Oct 4 06:59:18 MDT 2011",
  bibsource =    "http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc1990.bib",
  URL =          "http://www3.interscience.wiley.com/cgi-bin/abstract?ID=75040;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=75040&PLACEBO=IE.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Quantum Chem.",
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
  onlinedate =   "7 Dec 1998",
}


bibtype: article
filename: elefunt.bib
label: Homeier:1998:AHC
author: Herbert H. H. Homeier
journal: j-NUMER-ALGORITHMS
volume: 18
number: 1
pages: 1--30
month: sep
monthnumber: 9
year: 1998
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Sep 29 08:36:54 MDT 2003
bibtimestamp: 2003.09.29 08:36:54 MDT
fjournal: Numerical Algorithms
keywords: convergence acceleration
ZMnumber: 914.65140
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Herbert H. H. Homeier
title:
An asymptotically hierarchy-consistent, iterative sequence transformation for convergence acceleration of Fourier series

bibsource:
http://www.kluweronline.com/issn/1017-1398; http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://ipsapp007.kluweronline.com/content/getfile/5058/13/2/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/13/2/fulltext.pdf; http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA972

rawtitle:
An asymptotically hierarchy-consistent, iterative sequence transformation for convergence acceleration of {Fourier} series

entry:
@Article{Homeier:1998:AHC,
  author =       "Herbert H. H. Homeier",
  title =        "An asymptotically hierarchy-consistent, iterative
                 sequence transformation for convergence acceleration of
                 {Fourier} series",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "18",
  number =       "1",
  pages =        "1--30",
  month =        sep,
  year =         "1998",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Sep 29 08:36:54 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/13/2/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/13/2/fulltext.pdf;
                 http://www.chemie.uni-regensburg.de/pub/preprint/preprint.html#TCNA972",
  ZMnumber =     "914.65140",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
  tech =         "Technical Report TC-NA-97-2, Institut f{\"u}r
                 {Physikalische} und {Theoretische Chemie,
                 Universit{\"a}t Regensburg, D-93040 Regensburg}, 1997",
}


bibtype: article
filename: elefunt.bib
label: Homeier:1998:CAM
author: H. H. H. Homeier
title: On Convergence Acceleration of Multipolar and Orthogonal Expansions
journal: j-INTERNET-J-CHEM
volume: 1
number: Article 28
year: 1998
CODEN: IJCHFJ
ISSN: 1099-8292 OR 10998292
note: Proceedings of the 4$^th$ Electronic Computational Chemistry Conference.
URL: http://www.ijc.com/articles/1998v1/28/
fjournal: Internet Journal of Chemistry
keywords: convergence acceleration
rawauthor: H. H. H. Homeier
rawnote: Proceedings of the {4$^{th}$ Electronic Computational Chemistry Conference}.
rawtitle: On Convergence Acceleration of Multipolar and Orthogonal Expansions
entry:
@Article{Homeier:1998:CAM,
  author =       "H. H. H. Homeier",
  title =        "On Convergence Acceleration of Multipolar and
                 Orthogonal Expansions",
  journal =      j-INTERNET-J-CHEM,
  volume =       "1",
  number =       "Article 28",
  pages =        "????",
  year =         "1998",
  CODEN =        "IJCHFJ",
  ISSN =         "1099-8292",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/homeier-herbert-h-h.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the {4$^{th}$ Electronic Computational
                 Chemistry Conference}.",
  URL =          "http://www.ijc.com/articles/1998v1/28/",
  fjournal =     "Internet Journal of Chemistry",
  keywords =     "convergence acceleration",
  tech =         "Technical Report TC-QM-97-5, Institut f{\"u}r
                 {Physikalische} und {Theoretische Chemie,
                 Universit{\"a}t Regensburg, D-93040 Regensburg}, 1997",
}


bibtype: article
filename: elefunt.bib
label: Jukic:1998:DTN
author: D. Jukic and T. Marossevic and R. Scitovski
title: Discrete total $ l_p $-norm approximation problem for the exponential function
journal: j-APPL-MATH-COMP
volume: 94
number: 2--3
pages: 137--143
day: 15
month: aug
monthnumber: 8
year: 1998
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/S0096-3003(97)10068-6
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Tue Nov 20 21:03:11 MST 2012
bibtimestamp: 2012.11.20 21:03:11 MST
URL: http://www.sciencedirect.com/science/article/pii/S0096300397100686
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: D. Juki{\'c} and T. Maros{\v{s}}evi{\'c} and R. Scitovski
rawtitle: Discrete total $ l_p $-norm approximation problem for the exponential function
bibsource:
http://www.sciencedirect.com/science/journal/00963003; https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Jukic:1998:DTN,
  author =       "D. Juki{\'c} and T. Maros{\v{s}}evi{\'c} and R.
                 Scitovski",
  title =        "Discrete total $ l_p $-norm approximation problem for
                 the exponential function",
  journal =      j-APPL-MATH-COMP,
  volume =       "94",
  number =       "2--3",
  pages =        "137--143",
  day =          "15",
  month =        aug,
  year =         "1998",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/S0096-3003(97)10068-6",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Tue Nov 20 21:03:11 MST 2012",
  bibsource =    "http://www.sciencedirect.com/science/journal/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput1995.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0096300397100686",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}


bibtype: article
filename: elefunt.bib
label: Kiranon:1998:SRV
author: W. Kiranon and N. Kumprasert
title: Square-rooting and vector summation circuits using current conveyors
volume: 145
number: 2
pages: 139
month: apr
monthnumber: 4
year: 1998
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
acknowledgement: ack-nhfb
rawauthor: W. Kiranon and N. Kumprasert
rawtitle: Square-rooting and vector summation circuits using current conveyors
journal:
IEE Proceedings on Circuits, Devices and Systems [see also IEE Proceedings G - Circuits, Devices and Systems]

entry:
@Article{Kiranon:1998:SRV,
  author =       "W. Kiranon and N. Kumprasert",
  title =        "Square-rooting and vector summation circuits using
                 current conveyors",
  journal =      "IEE Proceedings on Circuits, Devices and Systems [see
                 also IEE Proceedings G - Circuits, Devices and
                 Systems]",
  volume =       "145",
  number =       "2",
  pages =        "139",
  month =        apr,
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Recently, Lui [1995] presented a square-rooting
                 circuit using CCII, MOS transistors and a buffered
                 unity-gain inverting amplifier. It is interesting since
                 it finds various applications as described in his
                 paper. However, an error occurred in the \ldots{}",
}


bibtype: inbook
filename: elefunt.bib
label: Knuth:1998:EP
author: Donald E. Knuth
title: Evaluation of polynomials
crossref: Knuth:1998:SA
chapter: 4
pages: 485--524
year: 1998
bibdate: Fri Oct 20 11:29:58 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 11:29:58 ???
keywords: number of multiplications to evaluate a polynomial
acknowledgement: ack-nhfb
rawauthor: Donald E. Knuth
rawtitle: Evaluation of polynomials
remark:
This is the definitive treatment of the rearrangement of polynomial coefficients to reduce the multiplication count. See cite Todd:1955:MWN and references therein to early papers on the subject.

entry:
@InBook{Knuth:1998:EP,
  author =       "Donald E. Knuth",
  title =        "Evaluation of polynomials",
  crossref =     "Knuth:1998:SA",
  chapter =      "4",
  pages =        "485--524",
  year =         "1998",
  bibdate =      "Fri Oct 20 11:29:58 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  keywords =     "number of multiplications to evaluate a polynomial",
  remark =       "This is the definitive treatment of the rearrangement
                 of polynomial coefficients to reduce the multiplication
                 count. See \cite{Todd:1955:MWN} and references therein
                 to early papers on the subject.",
}


bibtype: article
filename: elefunt.bib
label: Kramer:1998:PWC
author: W. Kramer
title: A priori worst case error bounds for floating-point computations
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 7
pages: 750--756
month: jul
monthnumber: 7
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.709374
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Wed Jul 6 09:35:55 MDT 2011
bibtimestamp: 2011.07.06 09:35:55 MDT
note: See cite Tang:1992:TDI.
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709374
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
authordates: 1952--2014 (WK)
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: W. Kramer
rawnote: See \cite{Tang:1992:TDI}.
rawtitle: A priori worst case error bounds for floating-point computations
abstract:
A new technique for the a priori calculation of rigorous error bounds for floating-point computations is introduced. The theorems given in the paper combined with interval arithmetic lead to the implementation of reliable software routines, which enable the user to compute the desired error bounds automatically by a suitable computer program. As a prominent example, a table-lookup algorithm for calculating the function $ e x p(x) - 1 $ that has been published by P. T. P. Tang (1992) is analyzed using these new tools. The result shows the high quality of the new approach

rawabstract:
A new technique for the a priori calculation of rigorous error bounds for floating-point computations is introduced. The theorems given in the paper combined with interval arithmetic lead to the implementation of reliable software routines, which enable the user to compute the desired error bounds automatically by a suitable computer program. As a prominent example, a table-lookup algorithm for calculating the function $ e x p(x) - 1 $ that has been published by P. T. P. Tang (1992) is analyzed using these new tools. The result shows the high quality of the new approach

entry:
@Article{Kramer:1998:PWC,
  author =       "W. Kramer",
  title =        "A priori worst case error bounds for floating-point
                 computations",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "7",
  pages =        "750--756",
  month =        jul,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.709374",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Wed Jul 6 09:35:55 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput1990.bib",
  note =         "See \cite{Tang:1992:TDI}.",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=709374",
  abstract =     "A new technique for the a priori calculation of
                 rigorous error bounds for floating-point computations
                 is introduced. The theorems given in the paper combined
                 with interval arithmetic lead to the implementation of
                 reliable software routines, which enable the user to
                 compute the desired error bounds automatically by a
                 suitable computer program. As a prominent example, a
                 table-lookup algorithm for calculating the function $ e
                 x p(x) - 1 $ that has been published by P. T. P. Tang
                 (1992) is analyzed using these new tools. The result
                 shows the high quality of the new approach",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  author-dates = "1952--2014 (WK)",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: article
filename: elefunt.bib
label: Kravanja:1998:ZMS
author: P. Kravanja and O. Ragos and M. N. Vrahatis and F. A. Zafiropoulos
journal: j-COMP-PHYS-COMM
volume: 113
number: 2--3
pages: 220--238
month: oct
monthnumber: 10
year: 1998
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(98)00064-2
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:30:30 MST 2012
bibtimestamp: 2012.02.13 21:30:30 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465598000642
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: P. Kravanja and O. Ragos and M. N. Vrahatis and F. A. Zafiropoulos
title:
ZEBEC: a mathematical software package for computing simple zeros of Bessel functions of real order and complex argument

rawtitle:
{ZEBEC}: a mathematical software package for computing simple zeros of {Bessel} functions of real order and complex argument

entry:
@Article{Kravanja:1998:ZMS,
  author =       "P. Kravanja and O. Ragos and M. N. Vrahatis and F. A.
                 Zafiropoulos",
  title =        "{ZEBEC}: a mathematical software package for computing
                 simple zeros of {Bessel} functions of real order and
                 complex argument",
  journal =      j-COMP-PHYS-COMM,
  volume =       "113",
  number =       "2--3",
  pages =        "220--238",
  month =        oct,
  year =         "1998",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(98)00064-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:30 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465598000642",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: inproceedings
filename: elefunt.bib
label: Kuhlmann:1998:FLP
author: M. Kuhlmann and K. K. Parhi
title: Fast low-power shared division and square-root architecture
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 128--135
year: 1998
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: M. Kuhlmann and K. K. Parhi
rawtitle: Fast low-power shared division and square-root architecture
booktitle:
Proceedings of the 1998 International Conference on Computer Design: VLSI in Computers and Processors. ICCD '98

rawbooktitle:
{Proceedings of the 1998 International Conference on Computer Design: VLSI in Computers and Processors. ICCD '98}

entry:
@InProceedings{Kuhlmann:1998:FLP,
  author =       "M. Kuhlmann and K. K. Parhi",
  booktitle =    "{Proceedings of the 1998 International Conference on
                 Computer Design: VLSI in Computers and Processors. ICCD
                 '98}",
  title =        "Fast low-power shared division and square-root
                 architecture",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "128--135",
  year =         "1998",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper addresses a fast low-power implementation
                 of a shared division and square-root architecture. Two
                 approaches are considered in this paper; these include
                 the SRT (Sweeney, Robertson and Tocher) approach which
                 does not require prescaling and \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Lefevre:1998:TCR
author: V. Lefevre and J.-M. Muller and A. Tisserand
title: Toward correctly rounded transcendentals
journal: j-IEEE-TRANS-COMPUT
volume: 47
number: 11
pages: 1235--1243
month: nov
monthnumber: 11
year: 1998
CODEN: ITCOB4
DOI: https://doi.org/10.1109/12.736435
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 11:25:04 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 11:25:04 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: V. Lef{\`e}vre and J.-M. Muller and A. Tisserand
rawtitle: Toward correctly rounded transcendentals
entry:
@Article{Lefevre:1998:TCR,
  author =       "V. Lef{\`e}vre and J.-M. Muller and A. Tisserand",
  title =        "Toward correctly rounded transcendentals",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "47",
  number =       "11",
  pages =        "1235--1243",
  month =        nov,
  year =         "1998",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/12.736435",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 11:25:04 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "The Table Maker's Dilemma is the problem of always
                 getting correctly rounded results when computing the
                 elementary functions. After a brief presentation of
                 this problem, we present new developments that have
                 helped us to solve this problem for the \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Lopez:1998:SSC
author: JoseL. Lopez
title: Several series containing gamma and polygamma functions
journal: j-J-COMPUT-APPL-MATH
volume: 90
number: 1
pages: 15--23
day: 6
month: apr
monthnumber: 4
year: 1998
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:36:07 MST 2017
bibtimestamp: 2017.02.25 12:36:07 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042798000077
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Jos{\'e}L. L{\'o}pez
rawtitle: Several series containing gamma and polygamma functions
entry:
@Article{Lopez:1998:SSC,
  author =       "Jos{\'e}L. L{\'o}pez",
  title =        "Several series containing gamma and polygamma
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "90",
  number =       "1",
  pages =        "15--23",
  day =          "6",
  month =        apr,
  year =         "1998",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:07 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042798000077",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Miller:1998:CGI
author: Allen R. Miller and Ira S. Moskowitz
title: On certain generalized incomplete gamma functions
journal: j-J-COMPUT-APPL-MATH
volume: 91
number: 2
pages: 179--190
day: 4
month: may
monthnumber: 5
year: 1998
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:36:08 MST 2017
bibtimestamp: 2017.02.25 12:36:08 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042798000314
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Allen R. Miller and Ira S. Moskowitz
rawtitle: On certain generalized incomplete gamma functions
entry:
@Article{Miller:1998:CGI,
  author =       "Allen R. Miller and Ira S. Moskowitz",
  title =        "On certain generalized incomplete gamma functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "91",
  number =       "2",
  pages =        "179--190",
  day =          "4",
  month =        may,
  year =         "1998",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:08 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042798000314",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Morozov:1998:NWR
author: D. Kh. Morozov and V. V. Voitsekhovich
title: A new wide-range approximation of modified Bessel functions in terms of elementary functions
journal: Rev. Mexicana Fi s.
volume: 44
number: 3
pages: 231--234
year: 1998
CODEN: RMXFAT
ISSN: 0035-001X OR 0035001X
MRclass: 65D20
MRnumber: MR1629601
bibdate: Wed Apr 13 06:46:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.13 06:46:35 ???
fjournal: Revista Mexicana de Fi sica
acknowledgement: ack-nhfb
rawauthor: D. Kh. Morozov and V. V. Voitsekhovich
rawtitle: A new wide-range approximation of modified {Bessel} functions in terms of elementary functions
entry:
@Article{Morozov:1998:NWR,
  author =       "D. Kh. Morozov and V. V. Voitsekhovich",
  title =        "A new wide-range approximation of modified {Bessel}
                 functions in terms of elementary functions",
  journal =      "Rev. Mexicana F\'\i s.",
  volume =       "44",
  number =       "3",
  pages =        "231--234",
  year =         "1998",
  CODEN =        "RMXFAT",
  ISSN =         "0035-001X",
  MRclass =      "65D20",
  MRnumber =     "MR1629601",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Revista Mexicana de F\'\i sica",
}


bibtype: article
filename: elefunt.bib
label: Nguyen:1998:MLS
author: Phong Nguyen
title: A Montgomery-Like Square Root for the Number Field Sieve
journal: j-LECT-NOTES-COMP-SCI
volume: 1423
pages: 151--??
year: 1998
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Feb 5 11:52:18 MST 2002
bibtimestamp: 2002.02.05 11:52:18 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Phong Nguyen
rawtitle: A {Montgomery}-Like Square Root for the Number Field Sieve
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t1423.htm; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/1423/14230151.htm; http://link.springer-ny.com/link/service/series/0558/papers/1423/14230151.pdf

entry:
@Article{Nguyen:1998:MLS,
  author =       "Phong Nguyen",
  title =        "A {Montgomery}-Like Square Root for the Number Field
                 Sieve",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "1423",
  pages =        "151--??",
  year =         "1998",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Feb 5 11:52:18 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t1423.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/1423/14230151.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/1423/14230151.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: article
filename: elefunt.bib
label: Palumbo:1998:GSI
author: Biagio Palumbo
title: A generalization of some inequalities for the gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 88
number: 2
pages: 255--268
day: 2
month: mar
monthnumber: 3
year: 1998
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:36:06 MST 2017
bibtimestamp: 2017.02.25 12:36:06 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042797001878
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Biagio Palumbo
rawtitle: A generalization of some inequalities for the gamma function
entry:
@Article{Palumbo:1998:GSI,
  author =       "Biagio Palumbo",
  title =        "A generalization of some inequalities for the gamma
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "88",
  number =       "2",
  pages =        "255--268",
  day =          "2",
  month =        mar,
  year =         "1998",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:36:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042797001878",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Qiu:1998:SIG
author: S.-L. Qiu and M. K. Vamanamurthy and M. Vuorinen
title: Some Inequalities for the Growth of Elliptic Integrals
journal: j-SIAM-J-MATH-ANA
volume: 29
number: 5
pages: 1224--1237
month: sep
monthnumber: 9
year: 1998
CODEN: SJMAAH
DOI: https://doi.org/10.1137/S0036141096310491
ISSN: 0036-1410 (print), 1095-7154 (electronic) OR 00361410 (print), 10957154 (electronic)
ISSNL: 0036-1410 OR 00361410
bibdate: Sat Dec 5 14:39:16 MST 1998
bibsource: http://epubs.siam.org/sam-bin/dbq/toc/SIMA/29/5; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.12.05 14:39:16 MST
URL: http://epubs.siam.org/sam-bin/dbq/article/31049
fjournal: SIAM Journal on Mathematical Analysis
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sima
rawauthor: S.-L. Qiu and M. K. Vamanamurthy and M. Vuorinen
rawtitle: Some Inequalities for the Growth of Elliptic Integrals
entry:
@Article{Qiu:1998:SIG,
  author =       "S.-L. Qiu and M. K. Vamanamurthy and M. Vuorinen",
  title =        "Some Inequalities for the Growth of Elliptic
                 Integrals",
  journal =      j-SIAM-J-MATH-ANA,
  volume =       "29",
  number =       "5",
  pages =        "1224--1237",
  month =        sep,
  year =         "1998",
  CODEN =        "SJMAAH",
  DOI =          "https://doi.org/10.1137/S0036141096310491",
  ISSN =         "0036-1410 (print), 1095-7154 (electronic)",
  ISSN-L =       "0036-1410",
  bibdate =      "Sat Dec 5 14:39:16 MST 1998",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SIMA/29/5;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/31049",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Mathematical Analysis",
  journal-URL =  "http://epubs.siam.org/sima",
}


bibtype: article
filename: elefunt.bib
label: Rivolo:1998:CDR
author: M. T. Rivolo and A. Simi
journal: j-ARCH-HIST-EXACT-SCI
volume: 52
number: 2
pages: 161--193
month: feb
monthnumber: 2
year: 1998
CODEN: AHESAN
DOI: https://doi.org/10.1007/s004070050015
ISSN: 0003-9519 (print), 1432-0657 (electronic) OR 00039519 (print), 14320657 (electronic)
ISSNL: 0003-9519 OR 00039519
MRclass: 01A35 (01A40)
MRnumber: 1610136 (99d:01015)
MRreviewer: Massimo Galuzzi
bibdate: Fri Feb 4 21:50:33 MST 2011
bibtimestamp: 2011.02.04 21:50:33 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=52&issue=2&spage=161
fjournal: Archive for History of Exact Sciences
language: Italian
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/407
rawauthor: M. T. Rivolo and A. Simi
title:
Il Calcolo delle Radici Quadrate e Cubiche in Italia da Fibonacci a Bombelli. (Italian) [The calculation of square and cube roots in Italy from Fibonacci to Bombelli]

bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=52&issue=2; https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Il Calcolo delle Radici Quadrate e Cubiche in {Italia} da {Fibonacci} a {Bombelli}. ({Italian}) [{The} calculation of square and cube roots in {Italy} from {Fibonacci} to {Bombelli}]

entry:
@Article{Rivolo:1998:CDR,
  author =       "M. T. Rivolo and A. Simi",
  title =        "Il Calcolo delle Radici Quadrate e Cubiche in {Italia}
                 da {Fibonacci} a {Bombelli}. ({Italian}) [{The}
                 calculation of square and cube roots in {Italy} from
                 {Fibonacci} to {Bombelli}]",
  journal =      j-ARCH-HIST-EXACT-SCI,
  volume =       "52",
  number =       "2",
  pages =        "161--193",
  month =        feb,
  year =         "1998",
  CODEN =        "AHESAN",
  DOI =          "https://doi.org/10.1007/s004070050015",
  ISSN =         "0003-9519 (print), 1432-0657 (electronic)",
  ISSN-L =       "0003-9519",
  MRclass =      "01A35 (01A40)",
  MRnumber =     "1610136 (99d:01015)",
  MRreviewer =   "Massimo Galuzzi",
  bibdate =      "Fri Feb 4 21:50:33 MST 2011",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0003-9519&volume=52&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/archhistexactsci.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0003-9519&volume=52&issue=2&spage=161",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for History of Exact Sciences",
  journal-URL =  "http://link.springer.com/journal/407",
  language =     "Italian",
  MRtitle =      "The computation of square and cube roots in {Italy}
                 from {Fibonacci} to {Bombelli}",
}


bibtype: article
filename: elefunt.bib
label: Russinoff:1998:MCP
author: David M. Russinoff
journal: j-LMS-J-COMPUT-MATH
volume: 1
pages: 148--200
year: 1998
DOI: https://doi.org/10.1112/S1461157000000176
ISSN: 1461-1570 OR 14611570
ISSNL: 1461-1570 OR 14611570
MRclass: 68M07 (65Y99 68T15)
MRnumber: 99m:68015
MRreviewer: J. Michel Muller
bibdate: Fri Nov 29 08:13:48 2002
bibtimestamp: 2002.11.29 08:13:48 ???
URL: http://www.lms.ac.uk/jcm/1/lms1998-001/
fjournal: LMS Journal of Computation and Mathematics
acknowledgement: ack-nhfb
ajournal: LMS J. Comput. Math.
journalURL: http://journals.cambridge.org/action/displayJournal?jid=JCM
onlinedate: 01 February 2010
rawauthor: David M. Russinoff
title:
A Mechanically Checked Proof of IEEE Compliance of the Floating Point Multiplication, Division and Square Root Algorithms of the AMD-K7 Processor

bibsource:
http://journals.cambridge.org/action/displayJournal?jid=JCM; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib

note:
Appendices A and B available to subscribers electronically (http://www.lms.ac.uk/jcm/1/lms98001/appendix-a/ and http://www.lms.ac.uk/jcm/1/lms98001/appendix-b/)

rawnote:
Appendices A and B available to subscribers electronically (http://www.lms.ac.uk/jcm/1/lms98001/appendix-a/ and http://www.lms.ac.uk/jcm/1/lms98001/appendix-b/)

rawtitle:
A Mechanically Checked Proof of {IEEE} Compliance of the Floating Point Multiplication, Division and Square Root Algorithms of the {AMD-K7} Processor

entry:
@Article{Russinoff:1998:MCP,
  author =       "David M. Russinoff",
  title =        "A Mechanically Checked Proof of {IEEE} Compliance of
                 the Floating Point Multiplication, Division and Square
                 Root Algorithms of the {AMD-K7} Processor",
  journal =      j-LMS-J-COMPUT-MATH,
  volume =       "1",
  pages =        "148--200",
  year =         "1998",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1112/S1461157000000176",
  ISSN =         "1461-1570",
  ISSN-L =       "1461-1570",
  MRclass =      "68M07 (65Y99 68T15)",
  MRnumber =     "99m:68015",
  MRreviewer =   "J. Michel Muller",
  bibdate =      "Fri Nov 29 08:13:48 2002",
  bibsource =    "http://journals.cambridge.org/action/displayJournal?jid=JCM;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib",
  note =         "Appendices A and B available to subscribers
                 electronically
                 (http://www.lms.ac.uk/jcm/1/lms98001/appendix-a/ and
                 http://www.lms.ac.uk/jcm/1/lms98001/appendix-b/)",
  URL =          "http://www.lms.ac.uk/jcm/1/lms1998-001/",
  acknowledgement = ack-nhfb,
  ajournal =     "LMS J. Comput. Math.",
  fjournal =     "LMS Journal of Computation and Mathematics",
  journal-URL =  "http://journals.cambridge.org/action/displayJournal?jid=JCM",
  onlinedate =   "01 February 2010",
}


bibtype: article
filename: elefunt.bib
label: Segura:1998:PCF
author: J. Segura and A. Gil
title: Parabolic cylinder functions of integer and half-integer orders for nonnegative arguments
journal: j-COMP-PHYS-COMM
volume: 115
number: 1
pages: 69--86
day: 1
month: dec
monthnumber: 12
year: 1998
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(98)00097-6
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 21:30:32 MST 2012
bibtimestamp: 2012.02.13 21:30:32 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465598000976
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: J. Segura and A. Gil
rawtitle: Parabolic cylinder functions of integer and half-integer orders for nonnegative arguments
entry:
@Article{Segura:1998:PCF,
  author =       "J. Segura and A. Gil",
  title =        "Parabolic cylinder functions of integer and
                 half-integer orders for nonnegative arguments",
  journal =      j-COMP-PHYS-COMM,
  volume =       "115",
  number =       "1",
  pages =        "69--86",
  day =          "1",
  month =        dec,
  year =         "1998",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(98)00097-6",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 21:30:32 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465598000976",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: article
filename: elefunt.bib
label: Sidi:1998:UBC
author: Avram Sidi and Yair Shapira
title: Upper bounds for convergence rates of acceleration methods with initial iterations
journal: j-NUMER-ALGORITHMS
volume: 18
number: 2
pages: 113--132
month: sep
monthnumber: 9
year: 1998
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Sep 29 08:36:55 MDT 2003
bibtimestamp: 2003.09.29 08:36:55 MDT
fjournal: Numerical Algorithms
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Avram Sidi and Yair Shapira
rawtitle: Upper bounds for convergence rates of acceleration methods with initial iterations
bibsource:
http://www.kluweronline.com/issn/1017-1398; http://www.math.psu.edu/dna/contents/na.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://ipsapp007.kluweronline.com/content/getfile/5058/14/1/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/14/1/fulltext.pdf

entry:
@Article{Sidi:1998:UBC,
  author =       "Avram Sidi and Yair Shapira",
  title =        "Upper bounds for convergence rates of acceleration
                 methods with initial iterations",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "18",
  number =       "2",
  pages =        "113--132",
  month =        sep,
  year =         "1998",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Sep 29 08:36:55 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 http://www.math.psu.edu/dna/contents/na.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/14/1/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/14/1/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Wei:1998:NFS
author: Liqiang Wei
title: New formula for $9$--$j$ symbols and their direct calculation
journal: j-COMPUT-PHYS
volume: 12
number: 6
pages: 632--??
month: nov
monthnumber: 11
year: 1998
CODEN: CPHYE2
DOI: https://doi.org/10.1063/1.168745
ISSN: 0894-1866 (print), 1558-4208 (electronic) OR 08941866 (print), 15584208 (electronic)
ISSNL: 0894-1866 OR 08941866
bibdate: Wed Apr 10 08:46:17 MDT 2019
bibtimestamp: 2019.04.10 08:46:17 MDT
URL: https://aip.scitation.org/doi/10.1063/1.168745
fjournal: Computers in Physics
acknowledgement: ack-nhfb
ajournal: Comput. Phys
journalURL: https://aip.scitation.org/journal/cip
rawauthor: Liqiang Wei
rawtitle: New formula for $9$--$j$ symbols and their direct calculation
entry:
@Article{Wei:1998:NFS,
  author =       "Liqiang Wei",
  title =        "New formula for $9$--$j$ symbols and their direct
                 calculation",
  journal =      j-COMPUT-PHYS,
  volume =       "12",
  number =       "6",
  pages =        "632--??",
  month =        nov,
  year =         "1998",
  CODEN =        "CPHYE2",
  DOI =          "https://doi.org/10.1063/1.168745",
  ISSN =         "0894-1866 (print), 1558-4208 (electronic)",
  ISSN-L =       "0894-1866",
  bibdate =      "Wed Apr 10 08:46:17 MDT 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computphys.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "https://aip.scitation.org/doi/10.1063/1.168745",
  acknowledgement = ack-nhfb,
  ajournal =     "Comput. Phys",
  fjournal =     "Computers in Physics",
  journal-URL =  "https://aip.scitation.org/journal/cip",
}


bibtype: inproceedings
filename: elefunt.bib
label: Agarwal:1999:SAM
author: R. C. Agarwal and F. G. Gustavson and M. S. Schmookler
title: Series approximation methods for divide and square root in the Power3TM processor
crossref: Koren:1999:ISC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 116--123
year: 1999
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
keywords: ARITH; computer arithmetic; IEEE
acknowledgement: ack-nhfb
rawauthor: R. C. Agarwal and F. G. Gustavson and M. S. Schmookler
rawtitle: Series approximation methods for divide and square root in the {Power3{\TM}} processor
URL:
http://euler.ecs.umass.edu/paper/final/paper-144.pdf; http://euler.ecs.umass.edu/paper/final/paper-144.ps

entry:
@InProceedings{Agarwal:1999:SAM,
  author =       "R. C. Agarwal and F. G. Gustavson and M. S.
                 Schmookler",
  title =        "Series approximation methods for divide and square
                 root in the {Power3{\TM}} processor",
  crossref =     "Koren:1999:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "116--123",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://euler.ecs.umass.edu/paper/final/paper-144.pdf;
                 http://euler.ecs.umass.edu/paper/final/paper-144.ps",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH; computer arithmetic; IEEE",
  summary =      "The Power3 processor is a 64-bit implementation of the
                 PowerPC TM architecture and is the successor to the
                 Power2 TM processor for workstations and servers which
                 REQUIRE high performance floating point capability. The
                 previous \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Alzer:1999:SPP
author: Horst Alzer and O. G. Ruehr
title: A submultiplicative property of the psi function
journal: j-J-COMPUT-APPL-MATH
volume: 101
number: 1--2
pages: 53--60
day: 15
month: jan
monthnumber: 1
year: 1999
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:39:42 MST 2017
bibtimestamp: 2017.02.25 12:39:42 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042798001903
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Horst Alzer and O. G. Ruehr
rawtitle: A submultiplicative property of the psi function
entry:
@Article{Alzer:1999:SPP,
  author =       "Horst Alzer and O. G. Ruehr",
  title =        "A submultiplicative property of the psi function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "101",
  number =       "1--2",
  pages =        "53--60",
  day =          "15",
  month =        jan,
  year =         "1999",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:39:42 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath1990.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042798001903",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: book
filename: elefunt.bib
label: Andrews:1999:SF
author: George E. Andrews and Richard Askey and Ranjan Roy
title: Special Functions
volume: 71
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: xvi + 664
year: 1999
DOI: https://doi.org/10.1017/CBO9781107325937
LCCN: QA351 .A74 1999
bibdate: Mon Sep 17 18:52:30 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2001.09.17 18:52:30 ???
series: Encyclopedia of mathematics and its applications
subject: Functions, Special
acknowledgement: ack-nhfb
rawauthor: George E. Andrews and Richard Askey and Ranjan Roy
rawtitle: Special Functions
ISBN:
0-521-62321-9 (hardcover), 0-521-78988-5 (paperback), 1-107-32593-5 (e-book) OR 0521623219 (hardcover), 0521789885 (paperback), 1107325935 (ebook)

ISBN13:
978-0-521-62321-6 (hardcover), 978-0-521-78988-2 (paperback), 978-1-107-32593-7 (e-book) OR 9780521623216 (hardcover), 9780521789882 (paperback), 9781107325937 (ebook)

TOC:
Frontmatter / i--vi Contents / vii--xii Preface / xiii--xvi 1: The Gamma and Beta Functions / 1--60 2: The Hypergeometric Functions / 61--123 3: Hypergeometric Transformations and Identities / 124--186 4: Bessel Functions and Confluent Hypergeometric Functions / 187--239 5: Orthogonal Polynomials / 240--276 6: Special Orthogonal Polynomials / 277--354 7: Topics in Orthogonal Polynomials / 355--400 8: The Selberg Integral and Its Applications / 401--444 9: Spherical Harmonics / 445--480 10: Introduction to $q$-Series / 481--552 11: Partitions / 553--576 12: Bailey Chains / 577--594 A: Infinite Products / 595--598 B: Summability and Fractional Integration / 599--610 C: Asymptotic Expansions / 611--616 D: Euler--Maclaurin Summation Formula / 617--628 E: Lagrange Inversion Formula / 629--636 F: Series Solutions of Differential Equations / 637--640 Bibliography / 641--654 Index / 655--658 Subject Index / 659--662 Symbol Index / 663--664

rawTOC:
Frontmatter / i--vi \\ Contents / vii--xii \\ Preface / xiii--xvi \\ 1: The Gamma and Beta Functions / 1--60 \\ 2: The Hypergeometric Functions / 61--123 \\ 3: Hypergeometric Transformations and Identities / 124--186 \\ 4: Bessel Functions and Confluent Hypergeometric Functions / 187--239 \\ 5: Orthogonal Polynomials / 240--276 \\ 6: Special Orthogonal Polynomials / 277--354 \\ 7: Topics in Orthogonal Polynomials / 355--400 \\ 8: The Selberg Integral and Its Applications / 401--444 \\ 9: Spherical Harmonics / 445--480 \\ 10: Introduction to $q$-Series / 481--552 \\ 11: Partitions / 553--576 \\ 12: Bailey Chains / 577--594 \\ A: Infinite Products / 595--598 \\ B: Summability and Fractional Integration / 599--610 \\ C: Asymptotic Expansions / 611--616 \\ D: Euler--Maclaurin Summation Formula / 617--628 \\ E: Lagrange Inversion Formula / 629--636 \\ F: Series Solutions of Differential Equations / 637--640 \\ Bibliography / 641--654 \\ Index / 655--658 \\ Subject Index / 659--662 \\ Symbol Index / 663--664

entry:
@Book{Andrews:1999:SF,
  author =       "George E. Andrews and Richard Askey and Ranjan Roy",
  title =        "Special Functions",
  volume =       "71",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xvi + 664",
  year =         "1999",
  DOI =          "https://doi.org/10.1017/CBO9781107325937",
  ISBN =         "0-521-62321-9 (hardcover), 0-521-78988-5 (paperback),
                 1-107-32593-5 (e-book)",
  ISBN-13 =      "978-0-521-62321-6 (hardcover), 978-0-521-78988-2
                 (paperback), 978-1-107-32593-7 (e-book)",
  LCCN =         "QA351 .A74 1999",
  bibdate =      "Mon Sep 17 18:52:30 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  price =        "US\$90.00 (hardcover), US\$34.95 (paperback)",
  series =       "Encyclopedia of mathematics and its applications",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special",
  tableofcontents = "Frontmatter / i--vi \\
                 Contents / vii--xii \\
                 Preface / xiii--xvi \\
                 1: The Gamma and Beta Functions / 1--60 \\
                 2: The Hypergeometric Functions / 61--123 \\
                 3: Hypergeometric Transformations and Identities /
                 124--186 \\
                 4: Bessel Functions and Confluent Hypergeometric
                 Functions / 187--239 \\
                 5: Orthogonal Polynomials / 240--276 \\
                 6: Special Orthogonal Polynomials / 277--354 \\
                 7: Topics in Orthogonal Polynomials / 355--400 \\
                 8: The Selberg Integral and Its Applications / 401--444
                 \\
                 9: Spherical Harmonics / 445--480 \\
                 10: Introduction to $q$-Series / 481--552 \\
                 11: Partitions / 553--576 \\
                 12: Bailey Chains / 577--594 \\
                 A: Infinite Products / 595--598 \\
                 B: Summability and Fractional Integration / 599--610
                 \\
                 C: Asymptotic Expansions / 611--616 \\
                 D: Euler--Maclaurin Summation Formula / 617--628 \\
                 E: Lagrange Inversion Formula / 629--636 \\
                 F: Series Solutions of Differential Equations /
                 637--640 \\
                 Bibliography / 641--654 \\
                 Index / 655--658 \\
                 Subject Index / 659--662 \\
                 Symbol Index / 663--664",
  xxURL =        "http://www.loc.gov/catdir/toc/cam024/98025757.html;
                 http://www.loc.gov/catdir/description/cam029/98025757.html",
}


bibtype: article
filename: elefunt.bib
label: Bach:1999:NTS
author: E. Bach and K. Huber
title: Note on taking square-roots modulo $N$
journal: j-IEEE-TRANS-INF-THEORY
volume: 45
number: 2
pages: 807--809
month: mar
monthnumber: 3
year: 1999
CODEN: IETTAW
DOI: https://doi.org/10.1109/18.749034
ISSN: 0018-9448 (print), 1557-9654 (electronic) OR 00189448 (print), 15579654 (electronic)
ISSNL: 0018-9448 OR 00189448
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Information Theory
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18
rawauthor: E. Bach and K. Huber
rawtitle: Note on taking square-roots modulo {$N$}
entry:
@Article{Bach:1999:NTS,
  author =       "E. Bach and K. Huber",
  title =        "Note on taking square-roots modulo {$N$}",
  journal =      j-IEEE-TRANS-INF-THEORY,
  volume =       "45",
  number =       "2",
  pages =        "807--809",
  month =        mar,
  year =         "1999",
  CODEN =        "IETTAW",
  DOI =          "https://doi.org/10.1109/18.749034",
  ISSN =         "0018-9448 (print), 1557-9654 (electronic)",
  ISSN-L =       "0018-9448",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Information Theory",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18",
  summary =      "In this article it is shown how Gauss' (1981) famous
                 cyclotomic sum formula can be used for extracting
                 square-roots modulo \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Batten:1999:IBO
author: D. Batten and S. Jinturkar and J. Glossner and M. Schulte and R. Peri and P. D'arcy
title: Interactions Between Optimizations and a New Type of DSP Intrinsic Function
pages: 807--809
year: 1999
bibdate: Sun Mar 04 11:05:23 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.03.04 11:05:23 ???
note: Shortened version in cite Batten:1999:IFB.
URL: http://mesa.ece.wisc.edu/publications/cp_1999-09.pdf
acknowledgement: ack-nhfb
rawauthor: D. Batten and S. Jinturkar and J. Glossner and M. Schulte and R. Peri and P. D'arcy
rawnote: Shortened version in \cite{Batten:1999:IFB}.
rawtitle: Interactions Between Optimizations and a New Type of {DSP} Intrinsic Function
booktitle:
Proceedings of the International Conference on Signal Processing Applications and Technologies, Orlando, Florida, November, 1999

rawbooktitle:
Proceedings of the International Conference on Signal Processing Applications and Technologies, Orlando, Florida, November, 1999

entry:
@InProceedings{Batten:1999:IBO,
  author =       "D. Batten and S. Jinturkar and J. Glossner and M.
                 Schulte and R. Peri and P. D'arcy",
  editor =       "????",
  booktitle =    "Proceedings of the International Conference on Signal
                 Processing Applications and Technologies, Orlando,
                 Florida, November, 1999",
  title =        "Interactions Between Optimizations and a New Type of
                 {DSP} Intrinsic Function",
  publisher =    "????",
  address =      "????",
  year =         "1999",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sun Mar 04 11:05:23 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Shortened version in \cite{Batten:1999:IFB}.",
  URL =          "http://mesa.ece.wisc.edu/publications/cp_1999-09.pdf",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Batten:1999:IFB
author: D. Batten and P. D'arcy
title: Intrinsic Functions Boost Compilers
journal: Electrical Engineering Times
volume: 1085
pages: 104--104
month: nov
monthnumber: 11
year: 1999
bibdate: Sun Mar 04 11:06:22 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.03.04 11:06:22 ???
acknowledgement: ack-nhfb
rawauthor: D. Batten and P. D'arcy
rawtitle: Intrinsic Functions Boost Compilers
entry:
@Article{Batten:1999:IFB,
  author =       "D. Batten and P. D'arcy",
  title =        "Intrinsic Functions Boost Compilers",
  journal =      "Electrical Engineering Times",
  volume =       "1085",
  pages =        "104--104",
  month =        nov,
  year =         "1999",
  bibdate =      "Sun Mar 04 11:06:22 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: techreport
filename: elefunt.bib
label: Beebe:1999:FAE
author: Nelson H. F. Beebe
title: Fast Approximate Exponential Functions
type: Report
institution: inst-CSC
address: inst-CSC:adr
pages: 104--104
day: 7
month: dec
monthnumber: 12
year: 1999
bibdate: Sat Feb 02 15:08:59 2019
bibtimestamp: 2019.02.02 15:08:59 ???
acknowledgement: ack-nhfb
rawauthor: Nelson H. F. Beebe
rawtitle: Fast Approximate Exponential Functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
This package contains software conforming to 1989 ANSI/ISO Standard C (ANSI X3.159-1989, ISO/IEC 9899-1990) and 1998 ISO Standard C++ (ISO/IEC 14882:1998) for testing an interesting algorithm for fast approximate exp() functions, published in cite Schraudolph:1999:FCA. There is a font error in figure 2 of that paper: all carets should be replaced by underscore.

remark:
From the report: ``Schraudolph's formula for the approximate exponential function computes $ a times x + b - c $ in floating-point arithmetic, then converts it to a 32-bit integer which is stored in the appropriate integer word overlaying the floating-point representation. The entire cost is thus a floating-point multiply and add (one instruction on some RISC architectures), a conversion to an integer, and a storage to memory.''

rawabstract:
This package contains software conforming to 1989 ANSI/ISO Standard C (ANSI X3.159-1989, ISO/IEC 9899-1990) and 1998 ISO Standard C++ (ISO/IEC 14882:1998) for testing an interesting algorithm for fast approximate exp() functions, published in \cite{Schraudolph:1999:FCA}. There is a font error in figure 2 of that paper: all carets should be replaced by underscore.

entry:
@TechReport{Beebe:1999:FAE,
  author =       "Nelson H. F. Beebe",
  title =        "Fast Approximate Exponential Functions",
  type =         "Report",
  institution =  inst-CSC,
  address =      inst-CSC:adr,
  day =          "7",
  month =        dec,
  year =         "1999",
  bibdate =      "Sat Feb 02 15:08:59 2019",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/beebe-nelson-h-f.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This package contains software conforming to 1989
                 ANSI/ISO Standard C (ANSI X3.159-1989, ISO/IEC
                 9899-1990) and 1998 ISO Standard C++ (ISO/IEC
                 14882:1998) for testing an interesting algorithm for
                 fast approximate exp() functions, published in
                 \cite{Schraudolph:1999:FCA}. There is a font error in
                 figure 2 of that paper: all carets should be replaced
                 by underscore.",
  acknowledgement = ack-nhfb,
  remark =       "From the report: ``Schraudolph's formula for the
                 approximate exponential function computes $ a \times x
                 + b - c $ in floating-point arithmetic, then converts
                 it to a 32-bit integer which is stored in the
                 appropriate integer word overlaying the floating-point
                 representation. The entire cost is thus a
                 floating-point multiply and add (one instruction on
                 some RISC architectures), a conversion to an integer,
                 and a storage to memory.''",
}


bibtype: incollection
filename: elefunt.bib
label: Brezinski:1999:EEC
author: C. Brezinski
booktitle: Error control and adaptivity in scientific computing (Antalya, 1998)
title: Error estimates and convergence acceleration
volume: 536
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: 87--94
year: 1999
MRclass: 65B05 (65D15)
MRnumber: 1735125
bibdate: Thu Dec 1 17:36:45 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 17:36:45 ???
series: NATO Sci. Ser. C Math. Phys. Sci.
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawauthor: C. Brezinski
rawbooktitle: Error control and adaptivity in scientific computing ({Antalya}, 1998)
rawtitle: Error estimates and convergence acceleration
entry:
@InCollection{Brezinski:1999:EEC,
  author =       "C. Brezinski",
  booktitle =    "Error control and adaptivity in scientific computing
                 ({Antalya}, 1998)",
  title =        "Error estimates and convergence acceleration",
  volume =       "536",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "87--94",
  year =         "1999",
  MRclass =      "65B05 (65D15)",
  MRnumber =     "1735125",
  bibdate =      "Thu Dec 1 17:36:45 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "NATO Sci. Ser. C Math. Phys. Sci.",
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
}


bibtype: inproceedings
filename: elefunt.bib
label: Bui:1999:DSI
author: H. Bui and S. Tahar
booktitle: 1999 IEEE Canadian Conference on Electrical and Computer Engineering, 9--12 May 1999
title: Design and synthesis of an IEEE-754 exponential function
volume: 1
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 450--455
year: 1999
bibdate: Sat Jul 16 17:14:11 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 17:14:11 MDT
acknowledgement: ack-nhfb
rawauthor: H. Bui and S. Tahar
rawbooktitle: 1999 {IEEE} Canadian Conference on Electrical and Computer Engineering, 9--12 May 1999
rawtitle: Design and synthesis of an {IEEE-754} exponential function
entry:
@InProceedings{Bui:1999:DSI,
  author =       "H. Bui and S. Tahar",
  booktitle =    "1999 {IEEE} Canadian Conference on Electrical and
                 Computer Engineering, 9--12 May 1999",
  title =        "Design and synthesis of an {IEEE-754} exponential
                 function",
  volume =       "1",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "450--455",
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 17:14:11 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We have designed a floating-point exponential function
                 using the table-driven method. The algorithm was first
                 implemented using sequential VHDL and later translated
                 to Concurrent Verilog. The main part of the work
                 consisted of creating modules that \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Cappuccino:1999:HSS
author: G. Cappuccino and G. Cocorullo and P. Corsonello and S. Perri
title: High speed self-timed pipelined datapath for square rooting
volume: 146
number: 1
pages: 16--22
month: feb
monthnumber: 2
year: 1999
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
acknowledgement: ack-nhfb
rawauthor: G. Cappuccino and G. Cocorullo and P. Corsonello and S. Perri
rawtitle: High speed self-timed pipelined datapath for square rooting
journal:
IEE Proceedings on Circuits, Devices and Systems [see also IEE Proceedings G --- Circuits, Devices and Systems]

entry:
@Article{Cappuccino:1999:HSS,
  author =       "G. Cappuccino and G. Cocorullo and P. Corsonello and
                 S. Perri",
  title =        "High speed self-timed pipelined datapath for square
                 rooting",
  journal =      "IEE Proceedings on Circuits, Devices and Systems [see
                 also IEE Proceedings G --- Circuits, Devices and
                 Systems]",
  volume =       "146",
  number =       "1",
  pages =        "16--22",
  month =        feb,
  year =         "1999",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The authors describe a new high-performance self-timed
                 circuit for asynchronous square rooting. The new
                 architecture is based on a modified nonrestoring
                 algorithm. An asynchronous pipelined cellular array
                 without auxiliary system for the \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Carlson:1999:TSI
author: B. C. Carlson
title: Toward Symbolic Integration of Elliptic Integrals
journal: j-J-SYMBOLIC-COMP
volume: 28
number: 6
pages: 739--753
month: dec
monthnumber: 12
year: 1999
CODEN: JSYCEH
DOI: https://doi.org/10.1006/jsco.1999.0336
ISSN: 0747-7171 (print), 1095-855X (electronic) OR 07477171 (print), 1095855X (electronic)
ISSNL: 0747-7171 OR 07477171
bibdate: Tue Mar 7 11:48:04 MST 2000
bibsource: http://www.idealibrary.com/cgi-bin/links/toc/sy; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2000.03.07 11:48:04 MST
fjournal: Journal of Symbolic Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/07477171
rawauthor: B. C. Carlson
rawtitle: Toward Symbolic Integration of Elliptic Integrals
URL:
http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production; http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production/pdf; http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production/ref

entry:
@Article{Carlson:1999:TSI,
  author =       "B. C. Carlson",
  title =        "Toward Symbolic Integration of Elliptic Integrals",
  journal =      j-J-SYMBOLIC-COMP,
  volume =       "28",
  number =       "6",
  pages =        "739--753",
  month =        dec,
  year =         "1999",
  CODEN =        "JSYCEH",
  DOI =          "https://doi.org/10.1006/jsco.1999.0336",
  ISSN =         "0747-7171 (print), 1095-855X (electronic)",
  ISSN-L =       "0747-7171",
  bibdate =      "Tue Mar 7 11:48:04 MST 2000",
  bibsource =    "http://www.idealibrary.com/cgi-bin/links/toc/sy;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production;
                 http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production/pdf;
                 http://www.idealibrary.com/links/doi/10.1006/jsco.1999.0336/production/ref",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Symbolic Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/07477171",
}


