# bibtab

bibtype: article
filename: elefunt.bib
label: Sarafyan:1960:DCS
author: Diran Sarafyan
title: Divisionless computation of square roots through continued squaring
journal: j-CACM
volume: 3
number: 5
pages: 319--321
month: may
monthnumber: 5
year: 1960
CODEN: CACMA2
DOI: https://doi.org/10.1145/367236.367267
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.00
MRnumber: 22\#8639
bibdate: Fri Nov 25 18:19:26 MST 2005
bibtimestamp: 2005.11.25 18:19:26 MST
fjournal: Communications of the ACM
keywords: $sqrt (x)$; elementary functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Diran Sarafyan
rawtitle: Divisionless computation of square roots through continued squaring
bibsource:
http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Sarafyan:1960:DCS,
  author =       "Diran Sarafyan",
  title =        "Divisionless computation of square roots through
                 continued squaring",
  journal =      j-CACM,
  volume =       "3",
  number =       "5",
  pages =        "319--321",
  month =        may,
  year =         "1960",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/367236.367267",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.00",
  MRnumber =     "22\#8639",
  bibdate =      "Fri Nov 25 18:19:26 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions",
  ZMreviewer =   "M. Lotkin",
}


bibtype: article
filename: elefunt.bib
label: Sholander:1960:AEE
author: Marlow Sholander
title: Analytical expressions and elementary functions
journal: j-AMER-MATH-MONTHLY
volume: 67
number: 3
pages: 213--214
month: mar
monthnumber: 3
year: 1960
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
MRclass: 26.00
MRnumber: 22 \#9553
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
URL: http://www.jstor.org/stable/2309678
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Marlow Sholander
rawtitle: Analytical expressions and elementary functions
entry:
@Article{Sholander:1960:AEE,
  author =       "Marlow Sholander",
  title =        "Analytical expressions and elementary functions",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "67",
  number =       "3",
  pages =        "213--214",
  month =        mar,
  year =         "1960",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  MRclass =      "26.00",
  MRnumber =     "22 \#9553",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2309678",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: book
filename: elefunt.bib
label: Slater:1960:CHF
author: Lucy Joan Slater
title: Confluent hypergeometric functions
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: 247
year: 1960
LCCN: QA351 .S56
bibdate: Sat Oct 30 21:01:55 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 21:01:55 MDT
remark: Fullerton: Discussion of properties and 7 decimal place tables of $_1 F_1 (a; b; x)$.
subject: Hypergeometric functions
acknowledgement: ack-nhfb
rawauthor: Lucy Joan Slater
rawtitle: Confluent hypergeometric functions
entry:
@Book{Slater:1960:CHF,
  author =       "Lucy Joan Slater",
  title =        "Confluent hypergeometric functions",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "247",
  year =         "1960",
  LCCN =         "QA351 .S56",
  bibdate =      "Sat Oct 30 21:01:55 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  remark =       "Fullerton: Discussion of properties and 7 decimal
                 place tables of $_1 F_1 (a; b; x)$.",
  subject =      "Hypergeometric functions",
}


bibtype: article
filename: elefunt.bib
label: Traub:1960:CNM
author: J. F. Traub
title: Comments on a recent paper [``A New Method of Computation of Square Roots Without Using Division'']
journal: j-CACM
volume: 3
number: 2
pages: 86--86
month: feb
monthnumber: 2
year: 1960
CODEN: CACMA2
DOI: https://doi.org/10.1145/366959.366989
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:25 MST 2005
bibtimestamp: 2005.11.25 18:19:25 MST
note: See cite Sarafyan:1959:NMC.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: J. F. Traub
rawnote: See \cite{Sarafyan:1959:NMC}.
bibsource:
http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
Mr. Diran Sarafyan, in his paper booktitle A New Method of Computation of Square Roots Without Using Divisions (Communications, Nov. 1959) gave a way of computing square roots which converges faster than the standard Newton method. His technique can be generalized as follows.

rawabstract:
Mr. Diran Sarafyan, in his paper \booktitle{A New Method of Computation of Square Roots Without Using Divisions} (Communications, Nov. 1959) gave a way of computing square roots which converges faster than the standard Newton method. His technique can be generalized as follows.

rawtitle:
Comments on a recent paper [{``A New Method of Computation of Square Roots Without Using Division''}]

entry:
@Article{Traub:1960:CNM,
  author =       "J. F. Traub",
  title =        "Comments on a recent paper [{``A New Method of
                 Computation of Square Roots Without Using
                 Division''}]",
  journal =      j-CACM,
  volume =       "3",
  number =       "2",
  pages =        "86--86",
  month =        feb,
  year =         "1960",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/366959.366989",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:25 MST 2005",
  bibsource =    "http://dblp.uni-trier.de/db/journals/cacm/cacm3.html#Traub60;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Sarafyan:1959:NMC}.",
  abstract =     "Mr. Diran Sarafyan, in his paper \booktitle{A New
                 Method of Computation of Square Roots Without Using
                 Divisions} (Communications, Nov. 1959) gave a way of
                 computing square roots which converges faster than the
                 standard Newton method. His technique can be
                 generalized as follows.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  oldlabel =     "Traub60",
  XMLdata =      "ftp://ftp.informatik.uni-trier.de/pub/users/Ley/bib/records.tar.gz#journals/cacm/Traub60",
}


bibtype: article
filename: elefunt.bib
label: Ward:1960:CCE
author: Morgan Ward
title: The Calculation of the Complete Elliptic Integral of the Third Kind
journal: j-AMER-MATH-MONTHLY
volume: 67
number: 3
pages: 205--213
month: mar
monthnumber: 3
year: 1960
CODEN: AMMYAE
DOI: https://doi.org/10.2307/2309677
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Tue Feb 6 16:32:27 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2018.02.06 16:32:27 ???
URL: http://www.jstor.org/stable/2309677
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: http://www.jstor.org/journals/00029890.html
rawauthor: Morgan Ward
rawtitle: The Calculation of the Complete Elliptic Integral of the Third Kind
entry:
@Article{Ward:1960:CCE,
  author =       "Morgan Ward",
  title =        "The Calculation of the Complete Elliptic Integral of
                 the Third Kind",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "67",
  number =       "3",
  pages =        "205--213",
  month =        mar,
  year =         "1960",
  CODEN =        "AMMYAE",
  DOI =          "https://doi.org/10.2307/2309677",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Tue Feb 6 16:32:27 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2309677",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "http://www.jstor.org/journals/00029890.html",
}


bibtype: book
filename: elefunt.bib
label: Warmus:1960:TEF
author: Mieczyslaw Warmus
title: Tables of elementary functions
publisher: pub-PERGAMON
address: pub-PERGAMON:adr
pages: vii + 567
year: 1960
LCCN: QA55 .W3 1960
MRclass: 65.05
MRnumber: 23 \#B1141
MRreviewer: J. C. P. Miller
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
note: Panstwowe Wydawnictwo Naukowe, Warsaw. Separately bound table of proportional parts, 30 pp.
acknowledgement: ack-nhfb
rawauthor: Mieczys{\l}aw Warmus
rawnote: Pa{\'n}stwowe Wydawnictwo Naukowe, Warsaw. Separately bound table of proportional parts, 30 pp.
rawtitle: Tables of elementary functions
entry:
@Book{Warmus:1960:TEF,
  author =       "Mieczys{\l}aw Warmus",
  title =        "Tables of elementary functions",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "vii + 567",
  year =         "1960",
  LCCN =         "QA55 .W3 1960",
  MRclass =      "65.05",
  MRnumber =     "23 \#B1141",
  MRreviewer =   "J. C. P. Miller",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Pa{\'n}stwowe Wydawnictwo Naukowe, Warsaw. Separately
                 bound table of proportional parts, 30 pp.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Wynn:1960:RAF
author: Peter Wynn
title: The Rational Approximation of Functions which are Formally Defined by a Power Series Expansion
journal: j-MATH-COMPUT
volume: 14
number: 70
pages: 147--186
month: apr
monthnumber: 4
year: 1960
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Peter Wynn
rawtitle: The Rational Approximation of Functions which are Formally Defined by a Power Series Expansion
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; JSTOR database

entry:
@Article{Wynn:1960:RAF,
  author =       "Peter Wynn",
  title =        "The Rational Approximation of Functions which are
                 Formally Defined by a Power Series Expansion",
  journal =      j-MATH-COMPUT,
  volume =       "14",
  number =       "70",
  pages =        "147--186",
  month =        apr,
  year =         "1960",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Barakat:1961:EIG
author: Richard Barakat
title: Evaluation of the Incomplete Gamma Function of Imaginary Argument by Chebyshev Polynomials
journal: j-MATH-COMPUT
volume: 15
number: 73
pages: 7--11
month: jan
monthnumber: 1
year: 1961
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Richard Barakat
rawtitle: Evaluation of the Incomplete Gamma Function of Imaginary Argument by {Chebyshev} Polynomials
entry:
@Article{Barakat:1961:EIG,
  author =       "Richard Barakat",
  title =        "Evaluation of the Incomplete Gamma Function of
                 Imaginary Argument by {Chebyshev} Polynomials",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "73",
  pages =        "7--11",
  month =        jan,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Boersma:1961:TFR
author: J. Boersma
title: Two Formulas Relating to Elliptic Integrals of the Third Kind (in Technical Notes and Short Papers)
journal: j-MATH-COMPUT
volume: 15
number: 75
pages: 296--298
month: jul
monthnumber: 7
year: 1961
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: J. Boersma
rawtitle:
Two Formulas Relating to Elliptic Integrals of the Third Kind (in {Technical Notes and Short Papers})

entry:
@Article{Boersma:1961:TFR,
  author =       "J. Boersma",
  title =        "Two Formulas Relating to Elliptic Integrals of the
                 Third Kind (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "75",
  pages =        "296--298",
  month =        jul,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: book
filename: elefunt.bib
label: Bowman:1961:IEF
author: Frank Bowman
title: Introduction to Elliptic Functions with Applications
volume: 922
publisher: pub-DOVER
address: pub-DOVER:adr
pages: 115
year: 1961
LCCN: QA343 .B76 1961
bibdate: Wed Mar 15 06:50:49 MDT 2017
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.15 06:50:49 MDT
remark: Unabridged and corrected republication of cite Bowman:1953:IEF.
acknowledgement: ack-nhfb
rawauthor: Frank Bowman
rawtitle: Introduction to Elliptic Functions with Applications
entry:
@Book{Bowman:1961:IEF,
  author =       "Frank Bowman",
  title =        "Introduction to Elliptic Functions with Applications",
  volume =       "922",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "115",
  year =         "1961",
  LCCN =         "QA343 .B76 1961",
  bibdate =      "Wed Mar 15 06:50:49 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "Unabridged and corrected republication of
                 \cite{Bowman:1953:IEF}.",
}


bibtype: article
filename: elefunt.bib
label: Cheney:1961:TNA
author: E. W. Cheney and H. L. Loeb
title: Two new algorithms for rational approximation
journal: j-NUM-MATH
volume: 3
number: 1
pages: 72--75
month: dec
monthnumber: 12
year: 1961
CODEN: NUMMA7
DOI: https://doi.org/10.1007/BF01386002
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sun Oct 17 19:01:15 MDT 1999
bibtimestamp: 1999.10.17 19:01:15 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: E. W. Cheney and H. L. Loeb
rawtitle: Two new algorithms for rational approximation
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/nummath.bib

entry:
@Article{Cheney:1961:TNA,
  author =       "E. W. Cheney and H. L. Loeb",
  title =        "Two new algorithms for rational approximation",
  journal =      j-NUM-MATH,
  volume =       "3",
  number =       "1",
  pages =        "72--75",
  month =        dec,
  year =         "1961",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01386002",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 19:01:15 MDT 1999",
  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/nummath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Corrington:1961:ACE
author: Murlan S. Corrington
title: Applications of the Complex Exponential Integral
journal: j-MATH-COMPUT
volume: 15
number: 73
pages: 1--6
month: jan
monthnumber: 1
year: 1961
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Murlan S. Corrington
rawtitle: Applications of the Complex Exponential Integral
entry:
@Article{Corrington:1961:ACE,
  author =       "Murlan S. Corrington",
  title =        "Applications of the Complex Exponential Integral",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "73",
  pages =        "1--6",
  month =        jan,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Ehrling:1961:NCI
author: G. Ehrling
title: On the Numerical Computation of Incomplete Elliptic Integrals
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 1
number: 1
pages: 8--14
month: mar
monthnumber: 3
year: 1961
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01961946
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:06 MST 2006
bibtimestamp: 2006.01.04 18:52:06 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=1&spage=8
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: G. Ehrling
rawtitle: On the Numerical Computation of Incomplete Elliptic Integrals
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=1; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Ehrling:1961:NCI,
  author =       "G. Ehrling",
  title =        "On the Numerical Computation of Incomplete Elliptic
                 Integrals",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "1",
  number =       "1",
  pages =        "8--14",
  month =        mar,
  year =         "1961",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01961946",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:06 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=1&spage=8",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
}


bibtype: article
filename: elefunt.bib
label: Fields:1961:EHF
author: Jerry L. Fields and Jet Wimp
title: Expansions of Hypergeometric Functions in Hypergeometric Functions
journal: j-MATH-COMPUT
volume: 15
number: 76
pages: 390--395
month: oct
monthnumber: 10
year: 1961
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Jerry L. Fields and Jet Wimp
rawtitle: Expansions of Hypergeometric Functions in Hypergeometric Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; JSTOR database

entry:
@Article{Fields:1961:EHF,
  author =       "Jerry L. Fields and Jet Wimp",
  title =        "Expansions of Hypergeometric Functions in
                 Hypergeometric Functions",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "76",
  pages =        "390--395",
  month =        oct,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Floyd:1961:ACE
author: Robert W. Floyd
title: An algorithm for coding efficient arithmetic operations
journal: j-CACM
volume: 4
number: 1
pages: 42--51
month: jan
monthnumber: 1
year: 1961
CODEN: CACMA2
DOI: https://doi.org/10.1145/366062.366082
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:30 MST 2005
bibtimestamp: 2005.11.25 18:19:30 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
authordates: Robert W. Floyd (8 June 1936--25 September 2001)
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Robert W. Floyd
rawtitle: An algorithm for coding efficient arithmetic operations
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Compiler/Compiler.Lins.bib; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
Description of binary subdivision method for computing $n$-th powers in $ O(log _2 (n))$ operations, as referenced in cite Knuth:1962:EPC.

entry:
@Article{Floyd:1961:ACE,
  author =       "Robert W. Floyd",
  title =        "An algorithm for coding efficient arithmetic
                 operations",
  journal =      j-CACM,
  volume =       "4",
  number =       "1",
  pages =        "42--51",
  month =        jan,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/366062.366082",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:30 MST 2005",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Compiler/Compiler.Lins.bib;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Robert W. Floyd (8 June 1936--25 September 2001)",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Description of binary subdivision method for computing
                 $n$-th powers in $ O(\log_2 (n))$ operations, as
                 referenced in \cite{Knuth:1962:EPC}.",
}


bibtype: article
filename: elefunt.bib
label: Froberg:1961:RCA
author: Carl-Erik Froberg
title: Rational Chebyshev Approximations of Elementary Functions
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 1
number: 4
pages: 256--262
month: dec
monthnumber: 12
year: 1961
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01933243
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:07 MST 2006
bibtimestamp: 2006.01.04 18:52:07 MST
note: See erratum cite Froberg:1963:ERC.
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=4&spage=256
keywords: elementary functions
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Carl-Erik Fr{\"o}berg
rawnote: See erratum \cite{Froberg:1963:ERC}.
rawtitle: Rational {Chebyshev} Approximations of Elementary Functions
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Froberg:1961:RCA,
  author =       "Carl-Erik Fr{\"o}berg",
  title =        "Rational {Chebyshev} Approximations of Elementary
                 Functions",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "1",
  number =       "4",
  pages =        "256--262",
  month =        dec,
  year =         "1961",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01933243",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=1&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See erratum \cite{Froberg:1963:ERC}.",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=1&issue=4&spage=256",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elementary functions",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1961:RCR
author: Walter Gautschi
title: Recursive Computation of the Repeated Integrals of the Error Function
journal: j-MATH-COMPUT
volume: 15
number: 75
pages: 227--232
month: jul
monthnumber: 7
year: 1961
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Walter Gautschi
rawtitle: Recursive Computation of the Repeated Integrals of the Error Function
entry:
@Article{Gautschi:1961:RCR,
  author =       "Walter Gautschi",
  title =        "Recursive Computation of the Repeated Integrals of the
                 Error Function",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "75",
  pages =        "227--232",
  month =        jul,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Gray:1961:BFI
author: Marion C. Gray
title: Bessel functions of integral order and complex argument
journal: j-CACM
volume: 4
number: 4
pages: 169--169
month: apr
monthnumber: 4
year: 1961
CODEN: CACMA2
DOI: https://doi.org/10.1145/355578.366318
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 33.25
MRnumber: 27\#1636
bibdate: Fri Nov 25 18:19:32 MST 2005
bibtimestamp: 2005.11.25 18:19:32 MST
fjournal: Communications of the ACM
keywords: Bessel functions; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Marion C. Gray
rawtitle: {Bessel} functions of integral order and complex argument
bibsource:
http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
The FORTRAN II source language [1, 2] places rather severe restrictions on the form a subscript may take, primarily because of the manner in which indices are incremented in iterative loops. In the process of constructing a compiler for a medium-sized (8008-word memory) computer which will accept the FORTRAN II source language, it became clear that the ``recursive address calculation'' scheme, as used in the FORTRAN compilers to minimize object-program running time, was probably not the best one to use. This system, described in some detail by Samelson and Bauer [3], requires that the subscript expression be a linear function of the subscripting variable. The alternative, which requires complete evaluation of the ``storage mapping function'', is usually rejected because of the time required for the object program to perform the necessary address calculation.

rawabstract:
The FORTRAN II source language [1, 2] places rather severe restrictions on the form a subscript may take, primarily because of the manner in which indices are incremented in iterative loops. In the process of constructing a compiler for a medium-sized (8008-word memory) computer which will accept the FORTRAN II source language, it became clear that the ``recursive address calculation'' scheme, as used in the FORTRAN compilers to minimize object-program running time, was probably not the best one to use. This system, described in some detail by Samelson and Bauer [3], requires that the subscript expression be a linear function of the subscripting variable. The alternative, which requires complete evaluation of the ``storage mapping function'', is usually rejected because of the time required for the object program to perform the necessary address calculation.

entry:
@Article{Gray:1961:BFI,
  author =       "Marion C. Gray",
  title =        "{Bessel} functions of integral order and complex
                 argument",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "169--169",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.366318",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "33.25",
  MRnumber =     "27\#1636",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The FORTRAN II source language [1, 2] places rather
                 severe restrictions on the form a subscript may take,
                 primarily because of the manner in which indices are
                 incremented in iterative loops. In the process of
                 constructing a compiler for a medium-sized (8008-word
                 memory) computer which will accept the FORTRAN II
                 source language, it became clear that the ``recursive
                 address calculation'' scheme, as used in the FORTRAN
                 compilers to minimize object-program running time, was
                 probably not the best one to use. This system,
                 described in some detail by Samelson and Bauer [3],
                 requires that the subscript expression be a linear
                 function of the subscripting variable. The alternative,
                 which requires complete evaluation of the ``storage
                 mapping function'', is usually rejected because of the
                 time required for the object program to perform the
                 necessary address calculation.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Bessel functions; special functions",
}


bibtype: article
filename: elefunt.bib
label: Herndon:1961:ABF
author: John R. Herndon
title: Algorithm 57: Ber or Bei Function
journal: j-CACM
volume: 4
number: 4
pages: 181--181
month: apr
monthnumber: 4
year: 1961
CODEN: CACMA2
DOI: https://doi.org/10.1145/355578.366476
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:32 MST 2005
bibtimestamp: 2005.11.25 18:19:32 MST
fjournal: Communications of the ACM
keywords: bei functions; ber functions; special functions
remark: Fullerton: 20-line Algol procedure that only sums series.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: John R. Herndon
rawtitle: {Algorithm 57}: {Ber} or {Bei} Function
entry:
@Article{Herndon:1961:ABF,
  author =       "John R. Herndon",
  title =        "{Algorithm 57}: {Ber} or {Bei} Function",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "181--181",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.366476",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "bei functions; ber functions; special functions",
  remark =       "Fullerton: 20-line Algol procedure that only sums
                 series.",
}


bibtype: article
filename: elefunt.bib
label: Herndon:1961:ACEa
author: John R. Herndon
title: Algorithm 55: Complete elliptic integral of the first kind
journal: j-CACM
volume: 4
number: 4
pages: 180--180
month: apr
monthnumber: 4
year: 1961
CODEN: CACMA2
DOI: https://doi.org/10.1145/355578.366454
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:32 MST 2005
bibtimestamp: 2005.11.25 18:19:32 MST
fjournal: Communications of the ACM
keywords: special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: John R. Herndon
rawtitle: {Algorithm 55}: {Complete} elliptic integral of the first kind
entry:
@Article{Herndon:1961:ACEa,
  author =       "John R. Herndon",
  title =        "{Algorithm 55}: {Complete} elliptic integral of the
                 first kind",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "180--180",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.366454",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}


bibtype: article
filename: elefunt.bib
label: Herndon:1961:ACEb
author: John R. Herndon
title: Algorithm 56: Complete elliptic integral of the second kind
journal: j-CACM
volume: 4
number: 4
pages: 180--181
month: apr
monthnumber: 4
year: 1961
CODEN: CACMA2
DOI: https://doi.org/10.1145/355578.366474
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:32 MST 2005
bibtimestamp: 2005.11.25 18:19:32 MST
fjournal: Communications of the ACM
keywords: special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: John R. Herndon
rawtitle: {Algorithm 56}: {Complete} elliptic integral of the second kind
entry:
@Article{Herndon:1961:ACEb,
  author =       "John R. Herndon",
  title =        "{Algorithm 56}: {Complete} elliptic integral of the
                 second kind",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "180--181",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.366474",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}


bibtype: article
filename: elefunt.bib
label: Herndon:1961:AEC
author: John R. Herndon
title: Algorithm 46: Exponential of a Complex Number
journal: j-CACM
volume: 4
number: 4
pages: 178--178
month: apr
monthnumber: 4
year: 1961
CODEN: CACMA2
DOI: https://doi.org/10.1145/355578.366356
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:32 MST 2005
bibtimestamp: 2005.11.25 18:19:32 MST
fjournal: Communications of the ACM
keywords: $exp (z)$; $e^z$; elementary functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: John R. Herndon
rawtitle: {Algorithm 46}: {Exponential} of a Complex Number
entry:
@Article{Herndon:1961:AEC,
  author =       "John R. Herndon",
  title =        "{Algorithm 46}: {Exponential} of a Complex Number",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "178--178",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.366356",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\exp(z)$; $e^z$; elementary functions",
}


bibtype: article
filename: elefunt.bib
label: Herndon:1961:AGF
author: John R. Herndon
title: Algorithm 54: Gamma function for range $1$ to $2$
journal: j-CACM
volume: 4
number: 4
pages: 180--180
month: apr
monthnumber: 4
year: 1961
CODEN: CACMA2
DOI: https://doi.org/10.1145/355578.366453
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:32 MST 2005
bibtimestamp: 2005.11.25 18:19:32 MST
fjournal: Communications of the ACM
keywords: $Gamma (x)$; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: John R. Herndon
rawtitle: {Algorithm 54}: {Gamma} function for range $1$ to $2$
entry:
@Article{Herndon:1961:AGF,
  author =       "John R. Herndon",
  title =        "{Algorithm 54}: {Gamma} function for range $1$ to
                 $2$",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "180--180",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.366453",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\Gamma(x)$; special functions",
}


bibtype: article
filename: elefunt.bib
label: Herndon:1961:ASN
author: J. R. Herndon
title: Algorithm 49: Spherical Neumann Function
journal: j-CACM
volume: 4
number: 4
pages: 179--179
month: apr
monthnumber: 4
year: 1961
CODEN: CACMA2
DOI: https://doi.org/10.1145/355578.355579
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:32 MST 2005
bibtimestamp: 2005.11.25 18:19:32 MST
note: See also cite Coleman:1978:RSN.
fjournal: Communications of the ACM
keywords: Neumann functions; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: J. R. Herndon
rawnote: See also \cite{Coleman:1978:RSN}.
rawtitle: {Algorithm 49}: {Spherical} {Neumann} Function
entry:
@Article{Herndon:1961:ASN,
  author =       "J. R. Herndon",
  title =        "{Algorithm 49}: {Spherical} {Neumann} Function",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "179--179",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.355579",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Coleman:1978:RSN}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Neumann functions; special functions",
}


bibtype: book
filename: elefunt.bib
label: Hochstadt:1961:SFM
author: Harry Hochstadt
title: Special functions of mathematical physics
publisher: pub-HRW
address: pub-HRW:adr
pages: viii + 81
year: 1961
ISBN: 0-236-73011-8 OR 0236730118
ISBN13: 978-0-236-73011-7 OR 9780236730117
LCCN: QA351 H65 1961
bibdate: Sat Oct 30 18:01:08 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 18:01:08 ???
remark: Reprinted 1966.
acknowledgement: ack-nhfb
rawauthor: Harry Hochstadt
rawtitle: Special functions of mathematical physics
entry:
@Book{Hochstadt:1961:SFM,
  author =       "Harry Hochstadt",
  title =        "Special functions of mathematical physics",
  publisher =    pub-HRW,
  address =      pub-HRW:adr,
  pages =        "viii + 81",
  year =         "1961",
  ISBN =         "0-236-73011-8",
  ISBN-13 =      "978-0-236-73011-7",
  LCCN =         "QA351 H65 1961",
  bibdate =      "Sat Oct 30 18:01:08 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "Reprinted 1966.",
}


bibtype: article
filename: elefunt.bib
label: L:1961:BRF
author: Y. L. L.
journal: j-MATH-COMPUT
volume: 15
number: 75
pages: 310--311
month: jul
monthnumber: 7
year: 1961
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-61-99215-8
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Wed Nov 15 11:07:36 2023
bibtimestamp: 2023.11.15 11:07:36 ???
fjournal: Mathematics of Computation
remark: Y. L. L. == Yudell L. Luke
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
subjectdates: Leslie Fox (30 September 1918--1 August 1992)
rawauthor: Y. L. L.
title:
Book Review: L. Fox, booktitle Tables of Weber Parabolic Cylinder Functions and Other Functions for Large Arguments, National Physical Laboratory Mathematical Tables Volume 4, Her Majesty's Stationery Office, London, 1960, iii + 40 p., 28 cm. (Paperback)

URL:
http://www.jstor.org/stable/2002928; https://www.ams.org/journals/mcom/1961-15-075/S0025-5718-61-99215-8/S0025-5718-61-99215-8.pdf

rawtitle:
Book Review: {L. Fox, \booktitle{Tables of Weber Parabolic Cylinder Functions and Other Functions for Large Arguments}, National Physical Laboratory Mathematical Tables Volume 4, Her Majesty's Stationery Office, London, 1960, iii + 40 p., 28 cm. (Paperback)}

entry:
@Article{L:1961:BRF,
  author =       "Y. L. L.",
  title =        "Book Review: {L. Fox, \booktitle{Tables of Weber
                 Parabolic Cylinder Functions and Other Functions for
                 Large Arguments}, National Physical Laboratory
                 Mathematical Tables Volume 4, Her Majesty's Stationery
                 Office, London, 1960, iii + 40 p., 28 cm.
                 (Paperback)}",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "75",
  pages =        "310--311",
  month =        jul,
  year =         "1961",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-61-99215-8",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Wed Nov 15 11:07:36 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/f/fox-leslie.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2002928;
                 https://www.ams.org/journals/mcom/1961-15-075/S0025-5718-61-99215-8/S0025-5718-61-99215-8.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Y. L. L. == Yudell L. Luke",
  subject-dates = "Leslie Fox (30 September 1918--1 August 1992)",
}


bibtype: article
filename: elefunt.bib
label: Landau:1961:PSW
author: H. J. Landau and H. O. Pollak
title: Prolate spheroidal wave functions, Fourier analysis and uncertainty. II
journal: j-BELL-SYST-TECH-J
volume: 40
number: 1
pages: 65--84
month: jan
monthnumber: 1
year: 1961
CODEN: BSTJAN
ISSN: 0005-8580 OR 00058580
MRclass: 33.27
MRnumber: 0140733 (25 \#4147)
MRreviewer: I. Marx
bibdate: Tue Nov 9 11:15:54 MST 2010
bibtimestamp: 2010.11.09 11:15:54 MST
URL: http://bstj.bell-labs.com/BSTJ/images/Vol40/bstj40-1-65.pdf
fjournal: The Bell System Technical Journal
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: H. J. Landau and H. O. Pollak
rawtitle: Prolate spheroidal wave functions, {Fourier} analysis and uncertainty. {II}
bibsource:
http://bstj.bell-labs.com/oldfiles/year.1961/BSTJ.1961.4001.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Landau:1961:PSW,
  author =       "H. J. Landau and H. O. Pollak",
  title =        "Prolate spheroidal wave functions, {Fourier} analysis
                 and uncertainty. {II}",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "40",
  number =       "1",
  pages =        "65--84",
  month =        jan,
  year =         "1961",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  MRclass =      "33.27",
  MRnumber =     "0140733 (25 \#4147)",
  MRreviewer =   "I. Marx",
  bibdate =      "Tue Nov 9 11:15:54 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1961/BSTJ.1961.4001.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol40/bstj40-1-65.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}


bibtype: article
filename: elefunt.bib
label: Luke:1961:EHF
author: Yudell L. Luke and Richard L. Coleman
title: Expansion of Hypergeometric Functions in Series of Other Hypergeometric Functions
journal: j-MATH-COMPUT
volume: 15
number: 75
pages: 233--237
month: jul
monthnumber: 7
year: 1961
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Yudell L. Luke and Richard L. Coleman
rawtitle: Expansion of Hypergeometric Functions in Series of Other Hypergeometric Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; JSTOR database

entry:
@Article{Luke:1961:EHF,
  author =       "Yudell L. Luke and Richard L. Coleman",
  title =        "Expansion of Hypergeometric Functions in Series of
                 Other Hypergeometric Functions",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "75",
  pages =        "233--237",
  month =        jul,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Rader:1961:CAC
author: P. J. Rader and Henry C. Thacher, Jr.
title: Certification of Algorithm 14 [not 13]: Complex exponential integral
journal: j-CACM
volume: 4
number: 2
pages: 105--105
month: feb
monthnumber: 2
year: 1961
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:30 MST 2005
bibtimestamp: 2005.11.25 18:19:30 MST
fjournal: Communications of the ACM
keywords: $Ei (z)$; special functions
remark: Fullerton: It's accurate but sometimes slow.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: P. J. Rader and Henry C. {Thacher, Jr.}
rawtitle: Certification of {Algorithm 14 [not 13]}: {Complex} exponential integral
entry:
@Article{Rader:1961:CAC,
  author =       "P. J. Rader and Henry C. {Thacher, Jr.}",
  title =        "Certification of {Algorithm 14 [not 13]}: {Complex}
                 exponential integral",
  journal =      j-CACM,
  volume =       "4",
  number =       "2",
  pages =        "105--105",
  month =        feb,
  year =         "1961",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:30 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\Ei(z)$; special functions",
  remark =       "Fullerton: It's accurate but sometimes slow.",
}


bibtype: article
filename: elefunt.bib
label: Slepian:1961:PSW
author: D. Slepian and H. O. Pollak
title: Prolate spheroidal wave functions, Fourier analysis and uncertainty. I
journal: j-BELL-SYST-TECH-J
volume: 40
number: 1
pages: 43--63
month: jan
monthnumber: 1
year: 1961
CODEN: BSTJAN
ISSN: 0005-8580 OR 00058580
MRclass: 33.27
MRnumber: 0140732 (25 \#4146)
MRreviewer: I. Marx
bibdate: Tue Nov 9 11:15:54 MST 2010
bibtimestamp: 2010.11.09 11:15:54 MST
URL: http://bstj.bell-labs.com/BSTJ/images/Vol40/bstj40-1-43.pdf
fjournal: The Bell System Technical Journal
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: D. Slepian and H. O. Pollak
rawtitle: Prolate spheroidal wave functions, {Fourier} analysis and uncertainty. {I}
bibsource:
http://bstj.bell-labs.com/oldfiles/year.1961/BSTJ.1961.4001.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Slepian:1961:PSW,
  author =       "D. Slepian and H. O. Pollak",
  title =        "Prolate spheroidal wave functions, {Fourier} analysis
                 and uncertainty. {I}",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "40",
  number =       "1",
  pages =        "43--63",
  month =        jan,
  year =         "1961",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  MRclass =      "33.27",
  MRnumber =     "0140732 (25 \#4146)",
  MRreviewer =   "I. Marx",
  bibdate =      "Tue Nov 9 11:15:54 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1961/BSTJ.1961.4001.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol40/bstj40-1-43.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}


bibtype: book
filename: elefunt.bib
label: Sneddon:1961:SFM
author: Ian Naismith Sneddon
title: Special Functions of Mathematical Physics and Chemistry
publisher: Oliver and Boyd
address: Edinburgh, UK
edition: Ssecond
pages: 184
year: 1961
LCCN: QA331 .S65 1961
bibdate: Sat Oct 30 21:22:03 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 21:22:03 MDT
series: University mathematical texts
remark: See first edition cite Sneddon:1956:SFM and third edition Sneddon:1980:SFM
acknowledgement: ack-nhfb
rawauthor: Ian Naismith Sneddon
rawtitle: Special Functions of Mathematical Physics and Chemistry
entry:
@Book{Sneddon:1961:SFM,
  author =       "Ian Naismith Sneddon",
  title =        "Special Functions of Mathematical Physics and
                 Chemistry",
  publisher =    "Oliver and Boyd",
  address =      "Edinburgh, UK",
  edition =      "Ssecond",
  pages =        "184",
  year =         "1961",
  LCCN =         "QA331 .S65 1961",
  bibdate =      "Sat Oct 30 21:22:03 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "University mathematical texts",
  acknowledgement = ack-nhfb,
  remark =       "See first edition \cite{Sneddon:1956:SFM} and third
                 edition {Sneddon:1980:SFM}",
}


bibtype: article
filename: elefunt.bib
label: Spielberg:1961:ECF
author: Kurt Spielberg
title: Efficient Continued Fraction Approximations To Elementary Functions
journal: j-MATH-COMPUT
volume: 15
number: 76
pages: 409--417
month: oct
monthnumber: 10
year: 1961
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65.20
MRnumber: MR0134842 (24 \#B894)
MRreviewer: M. E. Rose
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nj
journalURL: http://www.ams.org/mcom/
rawauthor: Kurt Spielberg
rawtitle: Efficient Continued Fraction Approximations To Elementary Functions
bibsource:
garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database

entry:
@Article{Spielberg:1961:ECF,
  author =       "Kurt Spielberg",
  title =        "Efficient Continued Fraction Approximations To
                 Elementary Functions",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "76",
  pages =        "409--417",
  month =        oct,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.20",
  MRnumber =     "MR0134842 (24 \#B894)",
  MRreviewer =   "M. E. Rose",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Thacher:1961:ISR
author: Henry C. Thacher, Jr.
title: Iterated Square Root Expansions for the Inverse Cosine and Inverse Hyperbolic Cosine
journal: j-MATH-COMPUT
volume: 15
number: 76
pages: 399--403
month: oct
monthnumber: 10
year: 1961
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Henry C. {Thacher, Jr.}
rawtitle: Iterated Square Root Expansions for the Inverse Cosine and Inverse Hyperbolic Cosine
entry:
@Article{Thacher:1961:ISR,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Iterated Square Root Expansions for the Inverse Cosine
                 and Inverse Hyperbolic Cosine",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "76",
  pages =        "399--403",
  month =        oct,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Weingarten:1961:TGC
author: Harry Weingarten and A. R. Di Donato
title: A Table of Generalized Circular Error
journal: j-MATH-COMPUT
volume: 15
number: 74
pages: 169--173
month: apr
monthnumber: 4
year: 1961
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Harry Weingarten and A. R. {Di Donato}
rawtitle: A Table of Generalized Circular Error
entry:
@Article{Weingarten:1961:TGC,
  author =       "Harry Weingarten and A. R. {Di Donato}",
  title =        "A Table of Generalized Circular Error",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "74",
  pages =        "169--173",
  month =        apr,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Werner:1961:CAG
author: Helmut Werner and Robert Collinge
title: Chebyshev Approximations to the Gamma Function (in Technical Notes and Short Papers)
journal: j-MATH-COMPUT
volume: 15
number: 74
pages: 195--197
month: apr
monthnumber: 4
year: 1961
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Helmut Werner and Robert Collinge
rawtitle: {Chebyshev} Approximations to the Gamma Function (in {Technical Notes and Short Papers})
entry:
@Article{Werner:1961:CAG,
  author =       "Helmut Werner and Robert Collinge",
  title =        "{Chebyshev} Approximations to the Gamma Function (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "15",
  number =       "74",
  pages =        "195--197",
  month =        apr,
  year =         "1961",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Wojcicki:1961:ABF
author: Maria E. Wojcicki
title: Algorithm 44: Bessel Functions Computed Recursively
journal: j-CACM
volume: 4
number: 4
pages: 177--178
month: apr
monthnumber: 4
year: 1961
CODEN: CACMA2
DOI: https://doi.org/10.1145/355578.366341
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:32 MST 2005
bibtimestamp: 2005.11.25 18:19:32 MST
fjournal: Communications of the ACM
keywords: Bessel functions; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Maria E. Wojcicki
rawtitle: {Algorithm 44}: {Bessel} Functions Computed Recursively
entry:
@Article{Wojcicki:1961:ABF,
  author =       "Maria E. Wojcicki",
  title =        "{Algorithm 44}: {Bessel} Functions Computed
                 Recursively",
  journal =      j-CACM,
  volume =       "4",
  number =       "4",
  pages =        "177--178",
  month =        apr,
  year =         "1961",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355578.366341",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:32 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Bessel functions; special functions",
}


bibtype: article
filename: elefunt.bib
label: Albrecht:1962:FKM
author: J. Albrecht
journal: j-NUM-MATH
volume: 4
pages: 196--208
month: dec
monthnumber: 12
year: 1962
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon Oct 18 01:28:20 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.18 01:28:20 MDT
fjournal: Numerische Mathematik
keywords: convergence acceleration
language: German
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: J. Albrecht
title:
Fehlerschranken und Konvergenzbeschleunigung bei einer monotonen oder alternierenden Iterationsfolge. (German) [Error Bounds and Convergence Acceleration with a Monotone or Alternating Iteration Sequence]

rawtitle:
{Fehlerschranken und Konvergenzbeschleunigung bei einer monotonen oder alternierenden Iterationsfolge}. ({German}) [{Error} Bounds and Convergence Acceleration with a Monotone or Alternating Iteration Sequence]

entry:
@Article{Albrecht:1962:FKM,
  author =       "J. Albrecht",
  title =        "{Fehlerschranken und Konvergenzbeschleunigung bei
                 einer monotonen oder alternierenden Iterationsfolge}.
                 ({German}) [{Error} Bounds and Convergence Acceleration
                 with a Monotone or Alternating Iteration Sequence]",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "196--208",
  month =        dec,
  year =         "1962",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 01:28:20 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence acceleration",
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Arscott:1962:BRI
author: F. M. Arscott
title: Book Review: booktitle Introduction to Elliptic Functions with Applications (F. Bowman)
journal: j-SIAM-REVIEW
volume: 4
number: 4
pages: 408--408
year: 1962
CODEN: SIREAD
DOI: https://doi.org/10.1137/1004109
ISSN: 0036-1445 (print), 1095-7200 (electronic) OR 00361445 (print), 10957200 (electronic)
ISSNL: 0036-1445 OR 00361445
bibdate: Thu Mar 27 09:04:56 MDT 2014
bibtimestamp: 2014.03.27 09:04:56 MDT
fjournal: SIAM Review
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sirev
onlinedate: October 1962
rawauthor: F. M. Arscott
rawtitle: Book Review: {{\booktitle{Introduction to Elliptic Functions with Applications}} (F. Bowman)}
bibsource:
http://epubs.siam.org/toc/siread/4/4; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamreview.bib

entry:
@Article{Arscott:1962:BRI,
  author =       "F. M. Arscott",
  title =        "Book Review: {{\booktitle{Introduction to Elliptic
                 Functions with Applications}} (F. Bowman)}",
  journal =      j-SIAM-REVIEW,
  volume =       "4",
  number =       "4",
  pages =        "408--408",
  month =        "????",
  year =         "1962",
  CODEN =        "SIREAD",
  DOI =          "https://doi.org/10.1137/1004109",
  ISSN =         "0036-1445 (print), 1095-7200 (electronic)",
  ISSN-L =       "0036-1445",
  bibdate =      "Thu Mar 27 09:04:56 MDT 2014",
  bibsource =    "http://epubs.siam.org/toc/siread/4/4;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamreview.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Review",
  journal-URL =  "http://epubs.siam.org/sirev",
  onlinedate =   "October 1962",
}


bibtype: techreport
filename: elefunt.bib
label: Blanch:1962:TRR
author: Gertrude Blanch and Donald S. Clemm
title: Tables Relating to the Radial Mathieu Functions, Vols. 1 & 2
type: Report
institution: Aeronautical Research Labs. U. S. Government Printing Office
address: Washington, DC, USA
pages: 408--408
year: 1962
bibdate: Fri Oct 29 21:37:53 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.29 21:37:53 ???
remark: Fullerton: 7-place tables.
acknowledgement: ack-nhfb
authordates: Gertrude Blanch (1897--1996)
rawauthor: Gertrude Blanch and Donald S. Clemm
rawtitle: Tables Relating to the Radial {Mathieu} Functions, Vols. 1 \& 2
entry:
@TechReport{Blanch:1962:TRR,
  author =       "Gertrude Blanch and Donald S. Clemm",
  title =        "Tables Relating to the Radial {Mathieu} Functions,
                 Vols. 1 \& 2",
  type =         "Report",
  institution =  "Aeronautical Research Labs. U. S. Government Printing
                 Office",
  address =      "Washington, DC, USA",
  year =         "1962",
  bibdate =      "Fri Oct 29 21:37:53 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Gertrude Blanch (1897--1996)",
  citedby =      "Fullerton:1980:BEM",
  remark =       "Fullerton: 7-place tables.",
}


bibtype: article
filename: elefunt.bib
label: Boersma:1962:CLF
author: J. Boersma
title: On the Computation of Lommel's Functions of Two Variables (in Technical Notes and Short Papers)
journal: j-MATH-COMPUT
volume: 16
number: 78
pages: 232--238
month: apr
monthnumber: 4
year: 1962
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: Lommel's functions are infinite sums involving Bessel functions $ J_nu - 2m(x) $.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: J. Boersma
rawtitle: On the Computation of {Lommel}'s Functions of Two Variables (in {Technical Notes and Short Papers})
entry:
@Article{Boersma:1962:CLF,
  author =       "J. Boersma",
  title =        "On the Computation of {Lommel}'s Functions of Two
                 Variables (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "16",
  number =       "78",
  pages =        "232--238",
  month =        apr,
  year =         "1962",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Lommel's functions are infinite sums
                 involving Bessel functions $ J_{\nu - 2m}(x) $.",
}


bibtype: article
filename: elefunt.bib
label: Cantor:1962:LEF
author: D. Cantor and G. Estrin and R. Turn
title: Logarithmic and Exponential Function Evaluation in a Variable Structure Digital Computer
journal: j-IRE-TRANS-ELEC-COMPUT
volume: EC-11
number: 2
pages: 155--164
month: apr
monthnumber: 4
year: 1962
CODEN: IRELAO
DOI: https://doi.org/10.1109/TEC.1962.5219348
ISSN: 0367-9950 OR 03679950
bibdate: Thu Jul 14 09:11:49 MDT 2011
bibtimestamp: 2011.07.14 09:11:49 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348
fjournal: IRE Transactions on Electronic Computers
acknowledgement: ack-nj
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885
rawauthor: D. Cantor and G. Estrin and R. Turn
rawtitle: Logarithmic and Exponential Function Evaluation in a Variable Structure Digital Computer
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; 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/ieeetranscomput.bib

entry:
@Article{Cantor:1962:LEF,
  author =       "D. Cantor and G. Estrin and R. Turn",
  title =        "Logarithmic and Exponential Function Evaluation in a
                 Variable Structure Digital Computer",
  journal =      j-IRE-TRANS-ELEC-COMPUT,
  volume =       "EC-11",
  number =       "2",
  pages =        "155--164",
  month =        apr,
  year =         "1962",
  CODEN =        "IRELAO",
  DOI =          "https://doi.org/10.1109/TEC.1962.5219348",
  ISSN =         "0367-9950",
  bibdate =      "Thu Jul 14 09:11:49 MDT 2011",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 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/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5219348",
  acknowledgement = ack-nj # "\slash " # ack-nhfb,
  fjournal =     "IRE Transactions on Electronic Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5407885",
}


bibtype: article
filename: elefunt.bib
label: Christiansen:1962:APC
author: Soren Christiansen
title: Algol Programming: Contribution no. 3: Calculation of complementary Fresnel integrals
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 2
number: 3
pages: 192--194
year: 1962
CODEN: BITTEL, NBITAB
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Mon Nov 16 14:34:20 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.11.16 14:34:20 ???
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: S{\o}ren Christiansen
rawtitle: {Algol} Programming: Contribution no. 3: Calculation of complementary {Fresnel} integrals
remark:
Fullerton: A 50-line Algol procedure is given. It calculates $ int _x^infty cos (t) / sqrt 2 pi t d t $ and $ int _x^infty sin (t) / sqrt 2 pi t d t $.

entry:
@Article{Christiansen:1962:APC,
  author =       "S{\o}ren Christiansen",
  title =        "{Algol} Programming: Contribution no. 3: Calculation
                 of complementary {Fresnel} integrals",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "2",
  number =       "3",
  pages =        "192--194",
  year =         "1962",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon Nov 16 14:34:20 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  journal-URL =  "http://link.springer.com/journal/10543",
  remark =       "Fullerton: A 50-line Algol procedure is given. It
                 calculates $ \int_x^\infty \cos (t) / \sqrt {2 \pi t}
                 \, d t $ and $ \int_x^\infty \sin (t) / \sqrt {2 \pi t}
                 \, d t $.",
}


bibtype: article
filename: elefunt.bib
label: Cundiff:1962:AEA
author: John L. Cundiff
title: Algorithm 88: Evaluation of Asymptotic Expression for the Fresnel Sine and Cosine Integrals
journal: j-CACM
volume: 5
number: 5
pages: 280--280
month: may
monthnumber: 5
year: 1962
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:38 MST 2005
bibtimestamp: 2005.11.25 18:19:38 MST
fjournal: Communications of the ACM
keywords: C(x); S(x); special functions
remark: Fullerton: Can be used with algorithms 89 and 90. 30-line Algol procedure.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: John L. Cundiff
rawtitle: {Algorithm 88}: {Evaluation} of Asymptotic Expression for the {Fresnel} Sine and Cosine Integrals
entry:
@Article{Cundiff:1962:AEA,
  author =       "John L. Cundiff",
  title =        "{Algorithm 88}: {Evaluation} of Asymptotic Expression
                 for the {Fresnel} Sine and Cosine Integrals",
  journal =      j-CACM,
  volume =       "5",
  number =       "5",
  pages =        "280--280",
  month =        may,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:38 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "C(x); S(x); special functions",
  remark =       "Fullerton: Can be used with algorithms 89 and 90.
                 30-line Algol procedure.",
}


bibtype: article
filename: elefunt.bib
label: Cundiff:1962:AEFa
author: John L. Cundiff
title: Algorithm 89: Evaluation of the Fresnel Sine Integral
journal: j-CACM
volume: 5
number: 5
pages: 280--280
month: may
monthnumber: 5
year: 1962
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:38 MST 2005
bibtimestamp: 2005.11.25 18:19:38 MST
fjournal: Communications of the ACM
keywords: S(x); special functions
remark: Fullerton: 20-line Algol procedure that must be used with algorithm 88.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: John L. Cundiff
rawtitle: {Algorithm 89}: {Evaluation} of the {Fresnel} Sine Integral
entry:
@Article{Cundiff:1962:AEFa,
  author =       "John L. Cundiff",
  title =        "{Algorithm 89}: {Evaluation} of the {Fresnel} Sine
                 Integral",
  journal =      j-CACM,
  volume =       "5",
  number =       "5",
  pages =        "280--280",
  month =        may,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:38 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "S(x); special functions",
  remark =       "Fullerton: 20-line Algol procedure that must be used
                 with algorithm 88.",
}


bibtype: article
filename: elefunt.bib
label: Cundiff:1962:AEFb
author: John L. Cundiff
title: Algorithm 90: Evaluation of the Fresnel Cosine Integral
journal: j-CACM
volume: 5
number: 5
pages: 281--281
month: may
monthnumber: 5
year: 1962
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:38 MST 2005
bibtimestamp: 2005.11.25 18:19:38 MST
fjournal: Communications of the ACM
keywords: C(x); special functions
remark: Fullerton: 20-line Algol procedure that must be used with algorithm 88.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: John L. Cundiff
rawtitle: {Algorithm 90}: {Evaluation} of the {Fresnel} Cosine Integral
entry:
@Article{Cundiff:1962:AEFb,
  author =       "John L. Cundiff",
  title =        "{Algorithm 90}: {Evaluation} of the {Fresnel} Cosine
                 Integral",
  journal =      j-CACM,
  volume =       "5",
  number =       "5",
  pages =        "281--281",
  month =        may,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:38 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "C(x); special functions",
  remark =       "Fullerton: 20-line Algol procedure that must be used
                 with algorithm 88.",
}


bibtype: article
filename: elefunt.bib
label: DiDonato:1962:MCC
author: A. R. DiDonato and M. P. Jarnagin
title: A Method for Computing the Circular Coverage Function
journal: j-MATH-COMPUT
volume: 16
number: 79
pages: 347--355
month: jul
monthnumber: 7
year: 1962
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: A. R. DiDonato and M. P. Jarnagin
rawtitle: A Method for Computing the Circular Coverage Function
entry:
@Article{DiDonato:1962:MCC,
  author =       "A. R. DiDonato and M. P. Jarnagin",
  title =        "A Method for Computing the Circular Coverage
                 Function",
  journal =      j-MATH-COMPUT,
  volume =       "16",
  number =       "79",
  pages =        "347--355",
  month =        jul,
  year =         "1962",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: techreport
filename: elefunt.bib
label: DiDonato:1962:MCG
author: A. R. DiDonato and M. P. Jamagin
title: A Method for Computing the Generalized Circular Error Function and the Circular Coverage Function
type: NWL Report
number: 1768
institution: Naval Surface Weapons Center
address: Dahlgren, VA 22448, USA
pages: 347--355
day: 23
month: jan
monthnumber: 1
year: 1962
bibdate: Wed Nov 12 15:56:35 2014
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2014.11.12 15:56:35 ???
acknowledgement: ack-nhfb
rawauthor: A. R. DiDonato and M. P. Jamagin
rawtitle: A Method for Computing the Generalized Circular Error Function and the Circular Coverage Function
entry:
@TechReport{DiDonato:1962:MCG,
  author =       "A. R. DiDonato and M. P. Jamagin",
  title =        "A Method for Computing the Generalized Circular Error
                 Function and the Circular Coverage Function",
  type =         "NWL Report",
  number =       "1768",
  institution =  "Naval Surface Weapons Center",
  address =      "Dahlgren, VA 22448, USA",
  day =          "23",
  month =        jan,
  year =         "1962",
  bibdate =      "Wed Nov 12 15:56:35 2014",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Dorn:1962:GHR
author: William S. Dorn
title: Generalizations of Horner's rule for polynomial evaluation
journal: j-IBM-JRD
volume: 6
number: 2
pages: 239--245
month: apr
monthnumber: 4
year: 1962
CODEN: IBMJAE
DOI: https://doi.org/10.1147/rd.62.0239
ISSN: 0018-8646 (print), 2151-8556 (electronic) OR 00188646 (print), 21518556 (electronic)
ISSNL: 0018-8646 OR 00188646
MRclass: 65.50
MRnumber: 24 \#B2541
bibdate: Tue Sep 11 16:10:28 MDT 2012
bibtimestamp: 2012.09.11 16:10:28 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392358
fjournal: IBM Journal of Research and Development
ZMnumber: 128.37202
acknowledgement: ack-nhfb
bookURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520
reviewer: D. H. Lehmer
rawauthor: William S. Dorn
rawtitle: Generalizations of {Horner}'s rule for polynomial evaluation
bibsource:
http://www.research.ibm.com/journal/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib

entry:
@Article{Dorn:1962:GHR,
  author =       "William S. Dorn",
  title =        "Generalizations of {Horner}'s rule for polynomial
                 evaluation",
  journal =      j-IBM-JRD,
  volume =       "6",
  number =       "2",
  pages =        "239--245",
  month =        apr,
  year =         "1962",
  CODEN =        "IBMJAE",
  DOI =          "https://doi.org/10.1147/rd.62.0239",
  ISSN =         "0018-8646 (print), 2151-8556 (electronic)",
  ISSN-L =       "0018-8646",
  MRclass =      "65.50",
  MRnumber =     "24 \#B2541",
  bibdate =      "Tue Sep 11 16:10:28 MDT 2012",
  bibsource =    "http://www.research.ibm.com/journal/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ibmjrd.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5392358",
  ZMnumber =     "128.37202",
  acknowledgement = ack-nhfb,
  book-URL =     "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  fjournal =     "IBM Journal of Research and Development",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5288520",
  reviewer =     "D. H. Lehmer",
}


bibtype: article
filename: elefunt.bib
label: Fraser:1962:CRA
author: W. Fraser and J. F. Hart
title: On the computation of rational approximations to continuous functions
journal: j-CACM
volume: 5
number: 7
pages: 401--403
month: jul
monthnumber: 7
year: 1962
CODEN: CACMA2
DOI: https://doi.org/10.1145/368273.368578
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:39 MST 2005
bibtimestamp: 2005.11.25 18:19:39 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: W. Fraser and J. F. Hart
rawtitle: On the computation of rational approximations to continuous functions
bibsource:
http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

keywords:
$abs (x)$; $cos (x)$; $Gamma (1+x)$; $sin (x)$; elementary functions; Remes algorithm; special functions

remark:
This paper outlines the Remes algorithm for ``for finding polynomial approximations to the determination of `best' rational approximations.''. It also gives approximations for starting values of Newton--Raphson iterations for $ abs (x) $, $ cos (x) $, $ Gamma (1 + x) $, and $ sin (x) $.

entry:
@Article{Fraser:1962:CRA,
  author =       "W. Fraser and J. F. Hart",
  title =        "On the computation of rational approximations to
                 continuous functions",
  journal =      j-CACM,
  volume =       "5",
  number =       "7",
  pages =        "401--403",
  month =        jul,
  year =         "1962",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/368273.368578",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:39 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\abs(x)$; $\cos(x)$; $\Gamma(1+x)$; $\sin(x)$;
                 elementary functions; Remes algorithm; special
                 functions",
  remark =       "This paper outlines the Remes algorithm for ``for
                 finding polynomial approximations to the determination
                 of `best' rational approximations.''. It also gives
                 approximations for starting values of Newton--Raphson
                 iterations for $ \abs (x) $, $ \cos (x) $, $ \Gamma (1
                 + x) $, and $ \sin (x) $.",
}


bibtype: article
filename: elefunt.bib
label: Hansen:1962:SRV
author: Eldon R. Hansen and Merrell L. Patrick
title: Some Relations and Values for the Generalized Riemann Zeta Function
journal: j-MATH-COMPUT
volume: 16
number: 79
pages: 265--274
month: jul
monthnumber: 7
year: 1962
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Eldon R. Hansen and Merrell L. Patrick
rawtitle: Some Relations and Values for the Generalized {Riemann} Zeta Function
entry:
@Article{Hansen:1962:SRV,
  author =       "Eldon R. Hansen and Merrell L. Patrick",
  title =        "Some Relations and Values for the Generalized
                 {Riemann} Zeta Function",
  journal =      j-MATH-COMPUT,
  volume =       "16",
  number =       "79",
  pages =        "265--274",
  month =        jul,
  year =         "1962",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Jefferson:1962:RAI
author: David K. Jefferson
title: Remark on Algorithm 73: Incomplete elliptic integrals
journal: j-CACM
volume: 5
number: 10
pages: 514--514
month: oct
monthnumber: 10
year: 1962
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:41 MST 2005
bibtimestamp: 2005.11.25 18:19:41 MST
fjournal: Communications of the ACM
keywords: special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: David K. Jefferson
rawtitle: Remark on {Algorithm 73}: {Incomplete} elliptic integrals
entry:
@Article{Jefferson:1962:RAI,
  author =       "David K. Jefferson",
  title =        "Remark on {Algorithm 73}: {Incomplete} elliptic
                 integrals",
  journal =      j-CACM,
  volume =       "5",
  number =       "10",
  pages =        "514--514",
  month =        oct,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:41 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}


bibtype: article
filename: elefunt.bib
label: Knuth:1962:ECP
author: Donald E. Knuth
title: Euler's Constant to $ 1271 $ Places
journal: j-MATH-COMPUT
volume: 16
number: 79
pages: 275--281
month: jul
monthnumber: 7
year: 1962
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-1962-0148255-X
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 10.41
MRnumber: 26 #5763
bibdate: Fri Mar 22 18:03:29 MST 2002
bibtimestamp: 2002.03.22 18:03:29 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Donald E. Knuth
rawtitle: {Euler}'s Constant to $ 1271 $ Places
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; JSTOR database; MathSciNet database

entry:
@Article{Knuth:1962:ECP,
  author =       "Donald E. Knuth",
  title =        "{Euler}'s Constant to $ 1271 $ Places",
  journal =      j-MATH-COMPUT,
  volume =       "16",
  number =       "79",
  pages =        "275--281",
  month =        jul,
  year =         "1962",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1962-0148255-X",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "10.41",
  MRnumber =     "26 #5763",
  bibdate =      "Fri Mar 22 18:03:29 MST 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database; MathSciNet database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Knuth:1962:EPC
author: Donald E. Knuth
title: Evaluation of polynomials by computer
journal: j-CACM
volume: 5
number: 12
pages: 595--599
month: dec
monthnumber: 12
year: 1962
CODEN: CACMA2
DOI: https://doi.org/10.1145/355580.369074
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 68.00 (12.00)
MRnumber: 27 #970
bibdate: Thu Dec 08 11:11:03 2005
bibtimestamp: 2005.12.08 11:11:03 ???
note: See letter cite Knuth:1963:LEE.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Donald E. Knuth
rawnote: See letter \cite{Knuth:1963:LEE}.
rawtitle: Evaluation of polynomials by computer
bibsource:
http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; MathSciNet database

remark:
The author reports that Motzkin (1962) showed that Horner's rule for polynomial evaluation may not be optimal, and develops the idea further for arbitrary polynomials, but also observes that the coefficients of the revised polynomials may be difficult to find. He also asks about, but does not answer, the question of error analysis of the various methods.

entry:
@Article{Knuth:1962:EPC,
  author =       "Donald E. Knuth",
  title =        "Evaluation of polynomials by computer",
  journal =      j-CACM,
  volume =       "5",
  number =       "12",
  pages =        "595--599",
  month =        dec,
  year =         "1962",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355580.369074",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "68.00 (12.00)",
  MRnumber =     "27 #970",
  bibdate =      "Thu Dec 08 11:11:03 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 MathSciNet database",
  note =         "See letter \cite{Knuth:1963:LEE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "The author reports that Motzkin (1962) showed that
                 Horner's rule for polynomial evaluation may not be
                 optimal, and develops the idea further for arbitrary
                 polynomials, but also observes that the coefficients of
                 the revised polynomials may be difficult to find. He
                 also asks about, but does not answer, the question of
                 error analysis of the various methods.",
}


bibtype: article
filename: elefunt.bib
label: Landau:1962:PSW
author: H. J. Landau and H. O. Pollak
journal: j-BELL-SYST-TECH-J
volume: 41
number: 4
pages: 1295--1336
month: jul
monthnumber: 7
year: 1962
CODEN: BSTJAN
ISSN: 0005-8580 OR 00058580
MRclass: 33.28 (94.10)
MRnumber: 0147686 (26 \#5200)
MRreviewer: I. Marx
bibdate: Tue Nov 9 11:15:54 MST 2010
bibtimestamp: 2010.11.09 11:15:54 MST
URL: http://bstj.bell-labs.com/BSTJ/images/Vol41/bstj41-4-1295.pdf
fjournal: The Bell System Technical Journal
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: H. J. Landau and H. O. Pollak
title:
Prolate spheroidal wave functions, Fourier analysis and uncertainty. III. The dimension of the space of essentially time- and band-limited signals

bibsource:
http://bstj.bell-labs.com/oldfiles/year.1962/BSTJ.1962.4104.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Prolate spheroidal wave functions, {Fourier} analysis and uncertainty. {III}. {The} dimension of the space of essentially time- and band-limited signals

entry:
@Article{Landau:1962:PSW,
  author =       "H. J. Landau and H. O. Pollak",
  title =        "Prolate spheroidal wave functions, {Fourier} analysis
                 and uncertainty. {III}. {The} dimension of the space of
                 essentially time- and band-limited signals",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "41",
  number =       "4",
  pages =        "1295--1336",
  month =        jul,
  year =         "1962",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  MRclass =      "33.28 (94.10)",
  MRnumber =     "0147686 (26 \#5200)",
  MRreviewer =   "I. Marx",
  bibdate =      "Tue Nov 9 11:15:54 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1962/BSTJ.1962.4104.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol41/bstj41-4-1295.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}


bibtype: article
filename: elefunt.bib
label: Merner:1962:AAC
author: J. N. Merner
title: ACM Algorithm 149: Complete Elliptic Integral
journal: j-CACM
volume: 5
number: 12
pages: 605
month: dec
monthnumber: 12
year: 1962
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 08 09:47:50 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.08 09:47:50 ???
note: See also cite Skovgaard:1978:RCE.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: J. N. Merner
rawnote: See also \cite{Skovgaard:1978:RCE}.
rawtitle: {ACM Algorithm 149}: Complete Elliptic Integral
entry:
@Article{Merner:1962:AAC,
  author =       "J. N. Merner",
  title =        "{ACM Algorithm 149}: Complete Elliptic Integral",
  journal =      j-CACM,
  volume =       "5",
  number =       "12",
  pages =        "605",
  month =        dec,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:47:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Skovgaard:1978:RCE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: elefunt.bib
label: Thacher:1962:CAB
author: Henry C. Thacher, Jr.
title: Certification of Algorithm 57: $ operatorname ber $ or $ operatorname bei $ function
journal: j-CACM
volume: 5
number: 8
pages: 438--438
month: aug
monthnumber: 8
year: 1962
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:40 MST 2005
bibtimestamp: 2005.11.25 18:19:40 MST
fjournal: Communications of the ACM
keywords: bei functions; ber functions; special functions
remark: Fullerton: The algorithm is inaccurate for large $x$.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Henry C. {Thacher, Jr.}
rawtitle: Certification of {Algorithm 57}: {$ \operatorname {ber} $} or {$ \operatorname {bei} $} function
entry:
@Article{Thacher:1962:CAB,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Certification of {Algorithm 57}: {$ \operatorname
                 {ber} $} or {$ \operatorname {bei} $} function",
  journal =      j-CACM,
  volume =       "5",
  number =       "8",
  pages =        "438--438",
  month =        aug,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:40 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "bei functions; ber functions; special functions",
  remark =       "Fullerton: The algorithm is inaccurate for large
                 $x$.",
}


bibtype: article
filename: elefunt.bib
label: Thacher:1962:CAH
author: Henry C. Thacher, Jr.
title: Certification of Algorithms 191 and 192, Hypergeometric and Confluent Hypergeometric Functions
journal: j-CACM
volume: 7
number: 4
pages: 244--244
month: apr
monthnumber: 4
year: 1962
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Sat Oct 30 11:27:28 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 11:27:28 ???
fjournal: Communications of the ACM
remark: Fullerton: An error in a comment is noted.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Henry C. {Thacher, Jr.}
rawtitle: Certification of {Algorithms 191 and 192, Hypergeometric and Confluent Hypergeometric Functions}
entry:
@Article{Thacher:1962:CAH,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Certification of {Algorithms 191 and 192,
                 Hypergeometric and Confluent Hypergeometric
                 Functions}",
  journal =      j-CACM,
  volume =       "7",
  number =       "4",
  pages =        "244--244",
  month =        apr,
  year =         "1962",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Sat Oct 30 11:27:28 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: An error in a comment is noted.",
}


bibtype: article
filename: elefunt.bib
label: Wimp:1962:PEB
author: Jet Wimp
title: Polynomial Expansions of Bessel Functions and Some Associated Functions
journal: j-MATH-COMPUT
volume: 16
number: 80
pages: 446--458
month: oct
monthnumber: 10
year: 1962
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
note: See corrigendum cite Wimp:1972:CPE.
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Jet Wimp
rawnote: See corrigendum \cite{Wimp:1972:CPE}.
rawtitle: Polynomial Expansions of {Bessel} Functions and Some Associated Functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; JSTOR database

entry:
@Article{Wimp:1962:PEB,
  author =       "Jet Wimp",
  title =        "Polynomial Expansions of {Bessel} Functions and Some
                 Associated Functions",
  journal =      j-MATH-COMPUT,
  volume =       "16",
  number =       "80",
  pages =        "446--458",
  month =        oct,
  year =         "1962",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 JSTOR database",
  note =         "See corrigendum \cite{Wimp:1972:CPE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Wynn:1962:AAP
author: P. Wynn
title: An Arsenal of ALGOL Procedures for Complex Arithmetic
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 2
number: 4
pages: 232--255
month: dec
monthnumber: 12
year: 1962
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01940171
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:07 MST 2006
bibtimestamp: 2006.01.04 18:52:07 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=232
remark: Cited in cite Sterbenz:1974:FPC.
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: P. Wynn
rawtitle: An Arsenal of {ALGOL} Procedures for Complex Arithmetic
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4; 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

keywords:
ALGOL; complex arithmetic; confluence hypergeometric function; continued fractions; incomplete beta function; incomplete gamma function; Stieltjes $S$-fractions; Weber parabolic cylinder function

entry:
@Article{Wynn:1962:AAP,
  author =       "P. Wynn",
  title =        "An Arsenal of {ALGOL} Procedures for Complex
                 Arithmetic",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "2",
  number =       "4",
  pages =        "232--255",
  month =        dec,
  year =         "1962",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01940171",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=2&issue=4;
                 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.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=2&issue=4&spage=232",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "ALGOL; complex arithmetic; confluence hypergeometric
                 function; continued fractions; incomplete beta
                 function; incomplete gamma function; Stieltjes
                 $S$-fractions; Weber parabolic cylinder function",
  remark =       "Cited in \cite{Sterbenz:1974:FPC}.",
}


bibtype: article
filename: elefunt.bib
label: Barakat:1963:CES
author: Richard Barakat and Agnes Houston
title: Chebyschev Expansion of the Sine and Cosine Integrals
journal: j-J-MATH-PHYS-MIT
volume: 42
number: 1--4
pages: 331--333
month: apr
monthnumber: 4
year: 1963
CODEN: JMPHA9
DOI: https://doi.org/10.1002/sapm1963421331
ISSN: 0097-1421 OR 00971421
ISSNL: 0097-1421 OR 00971421
bibdate: Sat Aug 19 13:36:07 MDT 2023
bibtimestamp: 2023.08.19 13:36:07 MDT
URL: https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1963421331
fjournal: Journal of Mathematics and Physics (MIT)
acknowledgement: ack-nhfb
ajournal: J. Math. Phys. (MIT)
journalURL: http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590
onlinedate: April 1963
rawauthor: Richard Barakat and Agnes Houston
rawtitle: {Chebyschev} Expansion of the Sine and Cosine Integrals
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib

entry:
@Article{Barakat:1963:CES,
  author =       "Richard Barakat and Agnes Houston",
  title =        "{Chebyschev} Expansion of the Sine and Cosine
                 Integrals",
  journal =      j-J-MATH-PHYS-MIT,
  volume =       "42",
  number =       "1--4",
  pages =        "331--333",
  month =        apr,
  year =         "1963",
  CODEN =        "JMPHA9",
  DOI =          "https://doi.org/10.1002/sapm1963421331",
  ISSN =         "0097-1421",
  ISSN-L =       "0097-1421",
  bibdate =      "Sat Aug 19 13:36:07 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphysmit.bib",
  URL =          "https://onlinelibrary.wiley.com/doi/epdf/10.1002/sapm1963421331",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Math. Phys. (MIT)",
  fjournal =     "Journal of Mathematics and Physics (MIT)",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590",
  onlinedate =   "April 1963",
}


bibtype: article
filename: elefunt.bib
label: Burgoyne:1963:AKF
author: F. D. Burgoyne
title: Approximations to Kelvin Functions (in Technical Notes and Short Papers)
journal: j-MATH-COMPUT
volume: 17
number: 83
pages: 295--298
month: jul
monthnumber: 7
year: 1963
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: 9-digit approximations.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: F. D. Burgoyne
rawtitle: Approximations to {Kelvin} Functions (in {Technical Notes and Short Papers})
entry:
@Article{Burgoyne:1963:AKF,
  author =       "F. D. Burgoyne",
  title =        "Approximations to {Kelvin} Functions (in {Technical
                 Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "17",
  number =       "83",
  pages =        "295--298",
  month =        jul,
  year =         "1963",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 9-digit approximations.",
}


bibtype: article
filename: elefunt.bib
label: Carlitz:1963:IEF
author: L. Carlitz
title: The Inverse of the Error Function
journal: j-PAC-J-MATH
volume: 13
number: 2
pages: 459--470
year: 1963
CODEN: PJMAAI
ISSN: 0030-8730 (print), 1945-5844 (electronic) OR 00308730 (print), 19455844 (electronic)
ISSNL: 0030-8730 OR 00308730
bibdate: Thu Sep 13 21:30:05 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.09.13 21:30:05 ???
fjournal: Pacific Journal of Mathematics
acknowledgement: ack-nhfb
journalURL: http://msp.org/pjm
rawauthor: L. Carlitz
rawtitle: The Inverse of the Error Function
URL:
http://pjm.math.berkeley.edu/pjm; http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.pjm/1103035736&view=body&content-type=pdf_1

entry:
@Article{Carlitz:1963:IEF,
  author =       "L. Carlitz",
  title =        "The Inverse of the Error Function",
  journal =      j-PAC-J-MATH,
  volume =       "13",
  number =       "2",
  pages =        "459--470",
  year =         "1963",
  CODEN =        "PJMAAI",
  ISSN =         "0030-8730 (print), 1945-5844 (electronic)",
  ISSN-L =       "0030-8730",
  bibdate =      "Thu Sep 13 21:30:05 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://pjm.math.berkeley.edu/pjm;
                 http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?handle=euclid.pjm/1103035736&view=body&content-type=pdf_1",
  acknowledgement = ack-nhfb,
  fjournal =     "Pacific Journal of Mathematics",
  journal-URL =  "http://msp.org/pjm",
}


bibtype: article
filename: elefunt.bib
label: Clenshaw:1963:ASF
author: C. W. Clenshaw and G. F. Miller and M. Woodger
title: Algorithms for Special Functions I
journal: j-NUM-MATH
volume: 4
pages: 403--419
month: dec
monthnumber: 12
year: 1963
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Fri Sep 16 10:21:31 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.16 10:21:31 ???
fjournal: Numerische Mathematik
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/211
rawauthor: C. W. Clenshaw and G. F. Miller and M. Woodger
rawtitle: Algorithms for Special Functions {I}
remark:
Fullerton: ALGOL 60 procedures with accuracy $ approx 10^-15 $ for $ exp $, $ ln $, $ sin $, $ cos $, $ tan $, $ arcsin $, $ arctan $, $ gamma $, $ Ei $ and $ erf $. See G. F. Miller (1965) for corrections.

entry:
@Article{Clenshaw:1963:ASF,
  author =       "C. W. Clenshaw and G. F. Miller and M. Woodger",
  title =        "Algorithms for Special Functions {I}",
  journal =      j-NUM-MATH,
  volume =       "4",
  pages =        "403--419",
  month =        dec,
  year =         "1963",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Sep 16 10:21:31 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  remark =       "Fullerton: ALGOL 60 procedures with accuracy $ \approx
                 10^{-15} $ for $ \exp $, $ \ln $, $ \sin $, $ \cos $, $
                 \tan $, $ \arcsin $, $ \arctan $, $ \gamma $, $ \Ei $
                 and $ \erf $. See G. F. Miller (1965) for
                 corrections.",
}


bibtype: article
filename: elefunt.bib
label: Eisman:1963:PER
author: S. H. Eisman
title: Polynomial Evaluation Revisited
journal: j-CACM
volume: 6
number: 7
pages: 384--385
month: jul
monthnumber: 7
year: 1963
CODEN: CACMA2
DOI: https://doi.org/10.1145/366663.366668
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:47 MST 2005
bibtimestamp: 2005.11.25 18:19:47 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: S. H. Eisman
rawtitle: Polynomial Evaluation Revisited
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Eisman:1963:PER,
  author =       "S. H. Eisman",
  title =        "Polynomial Evaluation Revisited",
  journal =      j-CACM,
  volume =       "6",
  number =       "7",
  pages =        "384--385",
  month =        jul,
  year =         "1963",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/366663.366668",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:47 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: elefunt.bib
label: Erdelyi:1963:AEC
author: A. Erdelyi and M. Wyman
title: The asymptotic evaluation of certain integrals
journal: j-ARCH-RAT-MECH-ANAL
volume: 14
number: 1
pages: 217--260
month: jan
monthnumber: 1
year: 1963
CODEN: AVRMAW
DOI: https://doi.org/10.1007/BF00250704
ISSN: 0003-9527 (print), 1432-0673 (electronic) OR 00039527 (print), 14320673 (electronic)
ISSNL: 0003-9527 OR 00039527
bibdate: Sat Feb 18 14:53:08 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 14:53:08 ???
URL: http://link.springer.com/article/10.1007/BF00250704
fjournal: Archive for rational mechanics and analysis
keywords: incomplete gamma function
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/205
rawauthor: A. Erd{\'e}lyi and M. Wyman
rawtitle: The asymptotic evaluation of certain integrals
entry:
@Article{Erdelyi:1963:AEC,
  author =       "A. Erd{\'e}lyi and M. Wyman",
  title =        "The asymptotic evaluation of certain integrals",
  journal =      j-ARCH-RAT-MECH-ANAL,
  volume =       "14",
  number =       "1",
  pages =        "217--260",
  month =        jan,
  year =         "1963",
  CODEN =        "AVRMAW",
  DOI =          "https://doi.org/10.1007/BF00250704",
  ISSN =         "0003-9527 (print), 1432-0673 (electronic)",
  ISSN-L =       "0003-9527",
  bibdate =      "Sat Feb 18 14:53:08 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.com/article/10.1007/BF00250704",
  acknowledgement = ack-nhfb,
  fjournal =     "Archive for rational mechanics and analysis",
  journal-URL =  "http://link.springer.com/journal/205",
  keywords =     "incomplete gamma function",
}


bibtype: article
filename: elefunt.bib
label: Eve:1963:SAI
author: J. Eve
title: Starting Approximations for the Iterative Calculation of Square Roots
journal: j-COMP-J
volume: 6
number: 3
pages: 274--276
month: nov
monthnumber: 11
year: 1963
CODEN: CMPJA6
DOI: https://doi.org/10.1093/comjnl/6.3.274
ISSN: 0010-4620 (print), 1460-2067 (electronic) OR 00104620 (print), 14602067 (electronic)
ISSNL: 0010-4620 OR 00104620
bibdate: Tue Dec 4 14:47:30 MST 2012
bibtimestamp: 2012.12.04 14:47:30 MST
fjournal: The Computer Journal
acknowledgement: ack-nhfb
journalURL: http://comjnl.oxfordjournals.org/
rawauthor: J. Eve
rawtitle: Starting Approximations for the Iterative Calculation of Square Roots
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://comjnl.oxfordjournals.org/content/6/3.toc; http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/; https://www.math.utah.edu/pub/tex/bib/compj1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Several starting approximations are given which, in conjunction with a well-known iterative process, lead to square root approximations, with a relative error in the range $ (2^-55, 2^-45) $, at the expense of three divisions. More accurate approximations are given which require in addition a single multiplication.

rawabstract:
Several starting approximations are given which, in conjunction with a well-known iterative process, lead to square root approximations, with a relative error in the range $ (2^{-55}, 2^{-45}) $, at the expense of three divisions. More accurate approximations are given which require in addition a single multiplication.

entry:
@Article{Eve:1963:SAI,
  author =       "J. Eve",
  title =        "Starting Approximations for the Iterative Calculation
                 of Square Roots",
  journal =      j-COMP-J,
  volume =       "6",
  number =       "3",
  pages =        "274--276",
  month =        nov,
  year =         "1963",
  CODEN =        "CMPJA6",
  DOI =          "https://doi.org/10.1093/comjnl/6.3.274",
  ISSN =         "0010-4620 (print), 1460-2067 (electronic)",
  ISSN-L =       "0010-4620",
  bibdate =      "Tue Dec 4 14:47:30 MST 2012",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://comjnl.oxfordjournals.org/content/6/3.toc;
                 http://www3.oup.co.uk/computer_journal/hdb/Volume_06/Issue_03/;
                 https://www.math.utah.edu/pub/tex/bib/compj1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "Several starting approximations are given which, in
                 conjunction with a well-known iterative process, lead
                 to square root approximations, with a relative error in
                 the range $ (2^{-55}, 2^{-45}) $, at the expense of
                 three divisions. More accurate approximations are given
                 which require in addition a single multiplication.",
  acknowledgement = ack-nhfb # " and " # ack-nj,
  fjournal =     "The Computer Journal",
  journal-URL =  "http://comjnl.oxfordjournals.org/",
}


bibtype: article
filename: elefunt.bib
label: Fettis:1963:AMH
author: Henry E. Fettis
title: Algorithm 163: Modified Hankel function
journal: j-CACM
volume: 6
number: 4
pages: 161--162
month: apr
monthnumber: 4
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:46 MST 2005
bibtimestamp: 2005.11.25 18:19:46 MST
fjournal: Communications of the ACM
keywords: Hankel functions; special functions
remark: Fullerton: A 25-line Algol procedure for $ e^x K_p(x) $.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Henry E. Fettis
rawtitle: {Algorithm 163}: {Modified} {Hankel} function
entry:
@Article{Fettis:1963:AMH,
  author =       "Henry E. Fettis",
  title =        "{Algorithm 163}: {Modified} {Hankel} function",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "161--162",
  month =        apr,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:46 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Hankel functions; special functions",
  remark =       "Fullerton: A 25-line Algol procedure for $ e^x K_p(x)
                 $.",
}


bibtype: article
filename: elefunt.bib
label: Froberg:1963:APC
author: Carl-Erik Froberg
title: Algol Programming: Contribution no. 5: Computation of the Fermi function
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 3
number: 2
pages: 141--142
year: 1963
CODEN: BITTEL, NBITAB
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Mon Nov 16 14:36:22 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.11.16 14:36:22 ???
remark: Fullerton: The Fermi function depends on several physical parameters of the atomic nucleus.
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Carl-Erik Fr{\"o}berg
rawtitle: {Algol} Programming: Contribution no. 5: Computation of the {Fermi} function
entry:
@Article{Froberg:1963:APC,
  author =       "Carl-Erik Fr{\"o}berg",
  title =        "{Algol} Programming: Contribution no. 5: Computation
                 of the {Fermi} function",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "3",
  number =       "2",
  pages =        "141--142",
  year =         "1963",
  CODEN =        "BITTEL, NBITAB",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Mon Nov 16 14:36:22 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  journal-URL =  "http://link.springer.com/journal/10543",
  remark =       "Fullerton: The Fermi function depends on several
                 physical parameters of the atomic nucleus.",
}


bibtype: article
filename: elefunt.bib
label: Froberg:1963:ERC
author: C.-E. Froberg
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 3
number: 1
pages: 68--68
month: mar
monthnumber: 3
year: 1963
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01963538
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:07 MST 2006
bibtimestamp: 2006.01.04 18:52:07 MST
note: See cite Froberg:1961:RCA.
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=3&issue=1&spage=68
keywords: elementary functions
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: C.-E. Fr{\"o}berg
rawnote: See \cite{Froberg:1961:RCA}.
title:
Erratum: ``Rational Chebyshev Approximations of Elementary Functions'' [BIT bf 1(4), 1961, p. 261, line 12]

bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=3&issue=1; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Erratum: {``Rational Chebyshev Approximations of Elementary Functions'' [BIT {\bf 1}(4), 1961, p. 261, line 12]}

entry:
@Article{Froberg:1963:ERC,
  author =       "C.-E. Fr{\"o}berg",
  title =        "Erratum: {``Rational Chebyshev Approximations of
                 Elementary Functions'' [BIT {\bf 1}(4), 1961, p. 261,
                 line 12]}",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "3",
  number =       "1",
  pages =        "68--68",
  month =        mar,
  year =         "1963",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01963538",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:07 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=3&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Froberg:1961:RCA}.",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=3&issue=1&spage=68",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elementary functions",
}


bibtype: inproceedings
filename: elefunt.bib
label: Gautschi:1963:RCS
author: Walter Gautschi
booktitle: The University of Michigan Engineering Summer Conferences, Numerical Analysis, Summer 1963
title: Recursive computation of special functions
pages: ??--??
year: 1963
bibdate: Fri Aug 21 11:08:35 2020
bibtimestamp: 2020.08.21 11:08:35 ???
acknowledgement: ack-nhfb
rawauthor: Walter Gautschi
rawbooktitle: {The University of Michigan Engineering Summer Conferences, Numerical Analysis, Summer 1963}
rawtitle: Recursive computation of special functions
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:1963:RCS,
  author =       "Walter Gautschi",
  editor =       "????",
  booktitle =    "{The University of Michigan Engineering Summer
                 Conferences, Numerical Analysis, Summer 1963}",
  title =        "Recursive computation of special functions",
  publisher =    "????",
  address =      "????",
  pages =        "??--??",
  year =         "1963",
  bibdate =      "Fri Aug 21 11:08:35 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Gray:1963:AFI
author: Malcolm D. Gray
title: Algorithm 213: Fresnel Integrals
journal: j-CACM
volume: 6
number: 10
pages: 617--617
month: oct
monthnumber: 10
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:49 MST 2005
bibtimestamp: 2005.11.25 18:19:49 MST
note: See certification cite Gray:1964:CAF and related remark cite Gray:1963:RAE.
fjournal: Communications of the ACM
keywords: C(x); S(x); special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Malcolm D. Gray
rawnote: See certification \cite{Gray:1964:CAF} and related remark \cite{Gray:1963:RAE}.
rawtitle: {Algorithm 213}: {Fresnel} Integrals
entry:
@Article{Gray:1963:AFI,
  author =       "Malcolm D. Gray",
  title =        "{Algorithm 213}: {Fresnel} Integrals",
  journal =      j-CACM,
  volume =       "6",
  number =       "10",
  pages =        "617--617",
  month =        oct,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:49 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See certification \cite{Gray:1964:CAF} and related
                 remark \cite{Gray:1963:RAE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "C(x); S(x); special functions",
}


bibtype: article
filename: elefunt.bib
label: Gray:1963:RAE
author: Malcolm D. Gray
title: Remark on Algorithms 88, 89, and 90 evaluation of the Fresnel integrals
journal: j-CACM
volume: 6
number: 10
pages: 618--618
month: oct
monthnumber: 10
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:49 MST 2005
bibtimestamp: 2005.11.25 18:19:49 MST
fjournal: Communications of the ACM
keywords: C(x); S(x); special functions
remark: Fullerton: An error is noted.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Malcolm D. Gray
rawtitle: Remark on Algorithms 88, 89, and 90 evaluation of the {Fresnel} integrals
entry:
@Article{Gray:1963:RAE,
  author =       "Malcolm D. Gray",
  title =        "Remark on Algorithms 88, 89, and 90 evaluation of the
                 {Fresnel} integrals",
  journal =      j-CACM,
  volume =       "6",
  number =       "10",
  pages =        "618--618",
  month =        oct,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:49 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "C(x); S(x); special functions",
  remark =       "Fullerton: An error is noted.",
}


bibtype: article
filename: elefunt.bib
label: Hofsommer:1963:NCE
author: D. J. Hofsommer and R. van de Riet
journal: j-NUM-MATH
volume: 5
pages: 291--302
month: dec
monthnumber: 12
year: 1963
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon Oct 18 01:28:20 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.18 01:28:20 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: D. J. Hofsommer and R. van de Riet
title:
On the numerical calculation of elliptic integrals of the first and second kind and the elliptic functions of Jacobi

rawtitle:
On the numerical calculation of elliptic integrals of the first and second kind and the elliptic functions of {Jacobi}

entry:
@Article{Hofsommer:1963:NCE,
  author =       "D. J. Hofsommer and R. van de Riet",
  title =        "On the numerical calculation of elliptic integrals of
                 the first and second kind and the elliptic functions of
                 {Jacobi}",
  journal =      j-NUM-MATH,
  volume =       "5",
  pages =        "291--302",
  month =        dec,
  year =         "1963",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 01:28:20 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Ibbetson:1963:AG
author: D. Ibbetson
title: Algorithm 209: Gauss
journal: j-CACM
volume: 6
number: 10
pages: 616--616
month: oct
monthnumber: 10
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:49 MST 2005
bibtimestamp: 2005.11.25 18:19:49 MST
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: D. Ibbetson
rawtitle: {Algorithm 209}: {Gauss}
entry:
@Article{Ibbetson:1963:AG,
  author =       "D. Ibbetson",
  title =        "{Algorithm 209}: {Gauss}",
  journal =      j-CACM,
  volume =       "6",
  number =       "10",
  pages =        "616--616",
  month =        oct,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:49 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: elefunt.bib
label: Knuth:1963:LEE
author: Donald E. Knuth
title: Letter to the Editor: Evaluation of polynomials by computer
journal: j-CACM
volume: 6
number: 2
pages: 51--51
month: feb
monthnumber: 2
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Tue Dec 26 16:31:38 1995
bibtimestamp: 1995.12.26 16:31:38 ???
note: See cite Knuth:1962:EPC.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Donald E. Knuth
rawnote: See \cite{Knuth:1962:EPC}.
rawtitle: Letter to the {Editor}: {Evaluation} of polynomials by computer
bibsource:
https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Knuth:1963:LEE,
  author =       "Donald E. Knuth",
  title =        "Letter to the {Editor}: {Evaluation} of polynomials by
                 computer",
  journal =      j-CACM,
  volume =       "6",
  number =       "2",
  pages =        "51--51",
  month =        feb,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Tue Dec 26 16:31:38 1995",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Knuth:1962:EPC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: elefunt.bib
label: Lee-Whiting:1963:EFC
author: G. E. Lee-Whiting
title: Erratum: ``Formulas for Computing Incomplete Elliptic Integrals of the First and Second Kinds''
journal: j-J-ACM
volume: 10
pages: 412--412
year: 1963
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Sat Dec 10 15:59:26 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.12.10 15:59:26 ???
note: See cite Lee-Whiting:1963:FCI.
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
ajournal: J. Assoc. Comput. Mach.
journalURL: https://dl.acm.org/loi/jacm
rawauthor: G. E. Lee-Whiting
rawnote: See \cite{Lee-Whiting:1963:FCI}.
rawtitle: Erratum: ``{Formulas} for Computing Incomplete Elliptic Integrals of the First and Second Kinds''
entry:
@Article{Lee-Whiting:1963:EFC,
  author =       "G. E. Lee-Whiting",
  title =        "Erratum: ``{Formulas} for Computing Incomplete
                 Elliptic Integrals of the First and Second Kinds''",
  journal =      j-J-ACM,
  volume =       "10",
  pages =        "412--412",
  year =         "1963",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Sat Dec 10 15:59:26 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Lee-Whiting:1963:FCI}.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
  xxmonth =      "none",
  xxnumber =     "none",
}


bibtype: article
filename: elefunt.bib
label: Lee-Whiting:1963:FCI
author: G. E. Lee-Whiting
title: Formulas for Computing Incomplete Elliptic Integrals of the First and Second Kinds
journal: j-J-ACM
volume: 10
number: 2
pages: 126--130
month: apr
monthnumber: 4
year: 1963
CODEN: JACOAH
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Sat Nov 05 22:55:28 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.11.05 22:55:28 ???
note: See also cite Lee-Whiting:1963:EFC.
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
ajournal: J. Assoc. Comput. Mach.
journalURL: https://dl.acm.org/loi/jacm
rawauthor: G. E. Lee-Whiting
rawnote: See also \cite{Lee-Whiting:1963:EFC}.
rawtitle: Formulas for Computing Incomplete Elliptic Integrals of the First and Second Kinds
entry:
@Article{Lee-Whiting:1963:FCI,
  author =       "G. E. Lee-Whiting",
  title =        "Formulas for Computing Incomplete Elliptic Integrals
                 of the First and Second Kinds",
  journal =      j-J-ACM,
  volume =       "10",
  number =       "2",
  pages =        "126--130",
  month =        apr,
  year =         "1963",
  CODEN =        "JACOAH",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Sat Nov 05 22:55:28 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Lee-Whiting:1963:EFC}.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}


bibtype: book
filename: elefunt.bib
label: Ljusternik:1963:MVF
author: L. A. Ljusternik and O. A. Cervonenkis and A. R. Janpolskii
publisher: Gosudarstv. Izdat. Fiz-Mat. Lit.
address: Moscow, USSR
pages: 247
year: 1963
MRclass: 65.25
MRnumber: 28 \#1733
MRreviewer: John Todd
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: L. A. Ljusternik and O. A. {\v{C}}ervonenkis and A. R. Janpol{\'s}ki{{\u{\i}}}
title:
cyr Matematicheskiianaliz. Vychislenie elementarnykh funktsii. [Mathematical analysis. Computation of the elementary functions]

rawtitle:
{{\cyr Matematicheski{\u{\i}}analiz. Vychislenie {\`e}lementarnykh funktsi{\u{\i}}}}. [Mathematical analysis. {Computation} of the elementary functions]

entry:
@Book{Ljusternik:1963:MVF,
  author =       "L. A. Ljusternik and O. A. {\v{C}}ervonenkis and A. R.
                 Janpol{\'s}ki{{\u{\i}}}",
  title =        "{{\cyr Matematicheski{\u{\i}}analiz. Vychislenie
                 {\`e}lementarnykh funktsi{\u{\i}}}}. [Mathematical
                 analysis. {Computation} of the elementary functions]",
  publisher =    "Gosudarstv. Izdat. Fiz-Mat. Lit.",
  address =      "Moscow, USSR",
  pages =        "247",
  year =         "1963",
  MRclass =      "65.25",
  MRnumber =     "28 \#1733",
  MRreviewer =   "John Todd",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Ludwig:1963:AIB
author: Oliver G. Ludwig
title: Algorithm 179: Incomplete beta ratio
journal: j-CACM
volume: 6
number: 6
pages: 314--314
month: jun
monthnumber: 6
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:47 MST 2005
bibtimestamp: 2005.11.25 18:19:47 MST
note: See remark cite Pike:1976:RIB,Bosten:1974:RAI.
fjournal: Communications of the ACM
remark: Fullerton: This algorithm is the basis for a modern treatment by Bosten and Battiste.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Oliver G. Ludwig
rawnote: See remark \cite{Pike:1976:RIB,Bosten:1974:RAI}.
rawtitle: {Algorithm 179}: {Incomplete} beta ratio
entry:
@Article{Ludwig:1963:AIB,
  author =       "Oliver G. Ludwig",
  title =        "{Algorithm 179}: {Incomplete} beta ratio",
  journal =      j-CACM,
  volume =       "6",
  number =       "6",
  pages =        "314--314",
  month =        jun,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:47 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Pike:1976:RIB,Bosten:1974:RAI}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: This algorithm is the basis for a modern
                 treatment by Bosten and Battiste.",
}


bibtype: article
filename: elefunt.bib
label: Meyer:1963:CAI
author: Noelle A. Meyer
title: Certification of Algorithm 73: Incomplete elliptic integrals
journal: j-CACM
volume: 6
number: 2
pages: 69--69
month: feb
monthnumber: 2
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:44 MST 2005
bibtimestamp: 2005.11.25 18:19:44 MST
fjournal: Communications of the ACM
keywords: special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Noelle A. Meyer
rawtitle: Certification of {Algorithm 73}: {Incomplete} elliptic integrals
entry:
@Article{Meyer:1963:CAI,
  author =       "Noelle A. Meyer",
  title =        "Certification of {Algorithm 73}: {Incomplete} elliptic
                 integrals",
  journal =      j-CACM,
  volume =       "6",
  number =       "2",
  pages =        "69--69",
  month =        feb,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:44 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}


bibtype: article
filename: elefunt.bib
label: Newman:1963:ICS
author: J. N. Newman and W. Frank
title: An Integral Containing the Square of a Bessel Function
journal: j-MATH-COMPUT
volume: 17
number: 81
pages: 64--70
month: jan
monthnumber: 1
year: 1963
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: J. N. Newman and W. Frank
rawtitle: An Integral Containing the Square of a {Bessel} Function
remark:
Fullerton: The integral $ I_n^m(x) = int _0^pi / 2 frac J_n^2(x cos (theta ))(x cos (theta ))^2m d theta $, where $m$ and $n$ are either integers or half integers, is considered.

entry:
@Article{Newman:1963:ICS,
  author =       "J. N. Newman and W. Frank",
  title =        "An Integral Containing the Square of a {Bessel}
                 Function",
  journal =      j-MATH-COMPUT,
  volume =       "17",
  number =       "81",
  pages =        "64--70",
  month =        jan,
  year =         "1963",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: The integral $ I_n^m(x) = \int_0^{\pi / 2}
                 \frac {J_n^2(x \cos (\theta))}{(x \cos (\theta))^{2m}}
                 \, d \theta $, where $m$ and $n$ are either integers or
                 half integers, is considered.",
}


bibtype: article
filename: elefunt.bib
label: Peuizulaev:1963:AEF
author: S. I. Peizulaev
title: An approximation by elementary functions. (Russian)
journal: Z. Vycisl. Mat. i Mat. Fiz.
volume: 3
pages: 769--770
year: 1963
MRclass: 41.30
MRnumber: 28 \#398
MRreviewer: D. D. Stancu
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: {\v{S}}. I. Pe{\u{\i}}zulaev
rawtitle: An approximation by elementary functions. ({Russian})
entry:
@Article{Peuizulaev:1963:AEF,
  author =       "{\v{S}}. I. Pe{\u{\i}}zulaev",
  title =        "An approximation by elementary functions.
                 ({Russian})",
  journal =      "{\v{Z}}. Vy{\v{c}}isl. Mat. i Mat. Fiz.",
  volume =       "3",
  pages =        "769--770",
  year =         "1963",
  MRclass =      "41.30",
  MRnumber =     "28 \#398",
  MRreviewer =   "D. D. Stancu",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: Relph:1963:AAH
author: A. P. Relph
title: ACM Algorithm 191: Hypergeometric
journal: j-CACM
volume: 6
number: 7
pages: 388--389
month: jul
monthnumber: 7
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 08 09:32:02 1994
bibtimestamp: 1994.09.08 09:32:02 ???
note: See certification cite Koppelaar:1974:CRA.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: A. P. Relph
rawnote: See certification \cite{Koppelaar:1974:CRA}.
rawtitle: {ACM Algorithm 191}: Hypergeometric
bibsource:
https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Relph:1963:AAH,
  author =       "A. P. Relph",
  title =        "{ACM Algorithm 191}: Hypergeometric",
  journal =      j-CACM,
  volume =       "6",
  number =       "7",
  pages =        "388--389",
  month =        jul,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:32:02 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See certification \cite{Koppelaar:1974:CRA}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: article
filename: elefunt.bib
label: Relph:1963:ACH
author: A. P. Relph
title: Algorithm 192: Confluent hypergeometric
journal: j-CACM
volume: 6
number: 7
pages: 388--388
month: jul
monthnumber: 7
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:47 MST 2005
bibtimestamp: 2005.11.25 18:19:47 MST
fjournal: Communications of the ACM
remark: Fullerton: 30-line Algol procedure for complex args. The work of Luke supersedes this.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: A. P. Relph
rawtitle: {Algorithm 192}: {Confluent} hypergeometric
entry:
@Article{Relph:1963:ACH,
  author =       "A. P. Relph",
  title =        "{Algorithm 192}: {Confluent} hypergeometric",
  journal =      j-CACM,
  volume =       "6",
  number =       "7",
  pages =        "388--388",
  month =        jul,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:47 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: 30-line Algol procedure for complex args.
                 The work of Luke supersedes this.",
}


bibtype: article
filename: elefunt.bib
label: Relph:1963:AH
author: A. P. Relph
title: Algorithm 191: Hypergeometric
journal: j-CACM
volume: 6
number: 7
pages: 388--388
month: jul
monthnumber: 7
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:47 MST 2005
bibtimestamp: 2005.11.25 18:19:47 MST
note: See certification cite Koppelaar:1974:CRA.
fjournal: Communications of the ACM
remark: Fullerton: 30-line Algol procedure. The work of Luke is better.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: A. P. Relph
rawnote: See certification \cite{Koppelaar:1974:CRA}.
rawtitle: {Algorithm 191}: {Hypergeometric}
entry:
@Article{Relph:1963:AH,
  author =       "A. P. Relph",
  title =        "{Algorithm 191}: {Hypergeometric}",
  journal =      j-CACM,
  volume =       "6",
  number =       "7",
  pages =        "388--388",
  month =        jul,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:47 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See certification \cite{Koppelaar:1974:CRA}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: 30-line Algol procedure. The work of Luke
                 is better.",
}


bibtype: article
filename: elefunt.bib
label: Rutishauser:1963:BQG
author: H. Rutishauser
title: Betrachtungen zur Quadratwurzeliteration. (German) [Considerations on square root iteration]
journal: j-MONAT-MATH
volume: 67
pages: 452--464
year: 1963
CODEN: MNMTA2
DOI: https://doi.org/10.1007/BF01295091
ISSN: 0026-9255 (print), 1436-5081 (electronic) OR 00269255 (print), 14365081 (electronic)
ISSNL: 0026-9255 OR 00269255
MRclass: 65.50
MRnumber: 158532
MRreviewer: A. S. Householder
bibdate: Mon Aug 24 21:56:15 2020
bibtimestamp: 2020.08.24 21:56:15 ???
fjournal: Monatshefte fur Mathematik
language: German
acknowledgement: ack-nhfb
authordates: Heinz Rutishauser (30 January 1918--10 November 1970)
journalURL: http://link.springer.com/journal/605
rawauthor: H. Rutishauser
rawtitle: {Betrachtungen zur Quadratwurzeliteration}. ({German}) [{Considerations} on square root iteration]
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Rutishauser:1963:BQG,
  author =       "H. Rutishauser",
  title =        "{Betrachtungen zur Quadratwurzeliteration}. ({German})
                 [{Considerations} on square root iteration]",
  journal =      j-MONAT-MATH,
  volume =       "67",
  pages =        "452--464",
  year =         "1963",
  CODEN =        "MNMTA2",
  DOI =          "https://doi.org/10.1007/BF01295091",
  ISSN =         "0026-9255 (print), 1436-5081 (electronic)",
  ISSN-L =       "0026-9255",
  MRclass =      "65.50",
  MRnumber =     "158532",
  MRreviewer =   "A. S. Householder",
  bibdate =      "Mon Aug 24 21:56:15 2020",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rutishauser-heinz.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Heinz Rutishauser (30 January 1918--10 November
                 1970)",
  fjournal =     "Monatshefte f{\"u}r Mathematik",
  journal-URL =  "http://link.springer.com/journal/605",
  language =     "German",
}


bibtype: book
filename: elefunt.bib
label: Sneddon:1963:SFM
author: Ian Naismith Sneddon
volume: 54
publisher: pub-BIBLIO-INST
address: pub-BIBLIO-INST:adr
pages: 166
year: 1963
LCCN: QA351 .S6415
bibdate: Sat Oct 30 21:22:03 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 21:22:03 MDT
series: B. I.-Hochschultaschenbucher
language: German
remark: German translation of cite Sneddon:1961:SFM.
subject: Functions; Mathematical physics
acknowledgement: ack-nhfb
rawauthor: Ian Naismith Sneddon
title:
Spezielle Funktionen der mathematischen Physik und Chemie. Mathematische Formelsammlung II. (German) [Special functions of mathematical physics and chemistry. Mathematical formula collection II]

rawtitle:
{Spezielle Funktionen der mathematischen Physik und Chemie. Mathematische Formelsammlung II}. ({German}) [Special {functions} of mathematical physics and chemistry. {Mathematical} formula collection {II}]

entry:
@Book{Sneddon:1963:SFM,
  author =       "Ian Naismith Sneddon",
  title =        "{Spezielle Funktionen der mathematischen Physik und
                 Chemie. Mathematische Formelsammlung II}. ({German})
                 [Special {functions} of mathematical physics and
                 chemistry. {Mathematical} formula collection {II}]",
  volume =       "54",
  publisher =    pub-BIBLIO-INST,
  address =      pub-BIBLIO-INST:adr,
  pages =        "166",
  year =         "1963",
  LCCN =         "QA351 .S6415",
  bibdate =      "Sat Oct 30 21:22:03 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "B. I.-Hochschultaschenb{\"u}cher",
  acknowledgement = ack-nhfb,
  language =     "German",
  remark =       "German translation of \cite{Sneddon:1961:SFM}.",
  subject =      "Functions; Mathematical physics",
}


bibtype: article
filename: elefunt.bib
label: Stern:1963:CSR
author: T. E. Stern and R. M. Lerner
title: A circuit for the square root of the sum of the squares
journal: j-PROC-IEEE
volume: 51
number: 4
pages: 593--596
month: apr
monthnumber: 4
year: 1963
CODEN: IEEPAD
ISSN: 0018-9219 (print), 1558-2256 (electronic) OR 00189219 (print), 15582256 (electronic)
ISSNL: 0018-9219 OR 00189219
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: Proceedings of the IEEE
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5
rawauthor: T. E. Stern and R. M. Lerner
rawtitle: A circuit for the square root of the sum of the squares
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Stern:1963:CSR,
  author =       "T. E. Stern and R. M. Lerner",
  title =        "A circuit for the square root of the sum of the
                 squares",
  journal =      j-PROC-IEEE,
  volume =       "51",
  number =       "4",
  pages =        "593--596",
  month =        apr,
  year =         "1963",
  CODEN =        "IEEPAD",
  ISSN =         "0018-9219 (print), 1558-2256 (electronic)",
  ISSN-L =       "0018-9219",
  bibdate =      "Sat Jul 16 15:28:13 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,
  fjournal =     "Proceedings of the IEEE",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=5",
  summary =      "A piecewise-linear network can produce an output
                 proportional to the square root of the sum of the
                 squares of a set of input voltages, using resistors and
                 diodes alone. The required relationship between
                 voltages can be represented by a multi- \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Sweeney:1963:CEC
author: Dura W. Sweeney
title: On the Computation of Euler's Constant
journal: j-MATH-COMPUT
volume: 17
number: 82
pages: 170--178
month: apr
monthnumber: 4
year: 1963
CODEN: MCMPAF
DOI: https://doi.org/10.1090/S0025-5718-1963-0160308-X
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: 3566 digits should be enough.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Dura W. Sweeney
rawtitle: On the Computation of {Euler}'s Constant
entry:
@Article{Sweeney:1963:CEC,
  author =       "Dura W. Sweeney",
  title =        "On the Computation of {Euler}'s Constant",
  journal =      j-MATH-COMPUT,
  volume =       "17",
  number =       "82",
  pages =        "170--178",
  month =        apr,
  year =         "1963",
  CODEN =        "MCMPAF",
  DOI =          "https://doi.org/10.1090/S0025-5718-1963-0160308-X",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 3566 digits should be enough.",
}


bibtype: article
filename: elefunt.bib
label: Thacher:1963:ACEa
author: Henry C. Thacher, Jr.
title: Algorithm 165: Complete elliptic integrals
journal: j-CACM
volume: 6
number: 4
pages: 163--164
month: apr
monthnumber: 4
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:46 MST 2005
bibtimestamp: 2005.11.25 18:19:46 MST
fjournal: Communications of the ACM
keywords: special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Henry C. {Thacher, Jr.}
rawtitle: {Algorithm 165}: {Complete} elliptic integrals
entry:
@Article{Thacher:1963:ACEa,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "{Algorithm 165}: {Complete} elliptic integrals",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "163--164",
  month =        apr,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:46 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}


bibtype: article
filename: elefunt.bib
label: Thacher:1963:CACa
author: Henry C. Thacher, Jr.
title: Certification of Algorithm 55: Complete elliptic integral of the first kind
journal: j-CACM
volume: 6
number: 4
pages: 166--167
month: apr
monthnumber: 4
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:46 MST 2005
bibtimestamp: 2005.11.25 18:19:46 MST
fjournal: Communications of the ACM
keywords: special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Henry C. {Thacher, Jr.}
rawtitle: Certification of {Algorithm 55}: {Complete} elliptic integral of the first kind
entry:
@Article{Thacher:1963:CACa,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Certification of {Algorithm 55}: {Complete} elliptic
                 integral of the first kind",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "166--167",
  month =        apr,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:46 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}


bibtype: article
filename: elefunt.bib
label: Thacher:1963:CACb
author: Henry C. Thacher, Jr.
title: Certification of Algorithm 149: Complete elliptic integral
journal: j-CACM
volume: 6
number: 4
pages: 166--167
month: apr
monthnumber: 4
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:46 MST 2005
bibtimestamp: 2005.11.25 18:19:46 MST
fjournal: Communications of the ACM
keywords: special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Henry C. {Thacher, Jr.}
rawtitle: Certification of {Algorithm 149}: {Complete} elliptic integral
entry:
@Article{Thacher:1963:CACb,
  author =       "Henry C. {Thacher, Jr.}",
  title =        "Certification of {Algorithm 149}: {Complete} elliptic
                 integral",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "166--167",
  month =        apr,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:46 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}


bibtype: book
filename: elefunt.bib
label: Tocher:1963:AS
author: K. D. Tocher
title: The Art of Simulation
publisher: Van Nostrand
address: Princeton, NJ, USA
pages: viii + 184
year: 1963
LCCN: TA177 .T6
bibdate: Sat Dec 16 17:47:12 MST 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.12.16 17:47:12 MST
subject: Simulation methods
acknowledgement: ack-nhfb
rawauthor: K. D. Tocher
rawtitle: The Art of Simulation
entry:
@Book{Tocher:1963:AS,
  author =       "K. D. Tocher",
  title =        "The Art of Simulation",
  publisher =    "Van Nostrand",
  address =      "Princeton, NJ, USA",
  pages =        "viii + 184",
  year =         "1963",
  LCCN =         "TA177 .T6",
  bibdate =      "Sat Dec 16 17:47:12 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Simulation methods",
}


bibtype: article
filename: elefunt.bib
label: vandeRiet:1963:CAI
author: R. P. van de Riet
title: Certification of Algorithm 73: Incomplete elliptic integrals
journal: j-CACM
volume: 6
number: 4
pages: 167--167
month: apr
monthnumber: 4
year: 1963
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:46 MST 2005
bibtimestamp: 2005.11.25 18:19:46 MST
fjournal: Communications of the ACM
keywords: special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: R. P. van de Riet
rawtitle: Certification of {Algorithm 73}: {Incomplete} elliptic integrals
entry:
@Article{vandeRiet:1963:CAI,
  author =       "R. P. van de Riet",
  title =        "Certification of {Algorithm 73}: {Incomplete} elliptic
                 integrals",
  journal =      j-CACM,
  volume =       "6",
  number =       "4",
  pages =        "167--167",
  month =        apr,
  year =         "1963",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:46 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}


bibtype: article
filename: elefunt.bib
label: Werner:1963:AFI
author: H. Werner and G. Raymann
title: An Approximation to the Fermi Integral $ F_1 / 2(x) $
journal: j-MATH-COMPUT
volume: 17
number: 82
pages: 193--194
month: apr
monthnumber: 4
year: 1963
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
URL: http://www.jstor.org/stable/2003641
fjournal: Mathematics of Computation
remark: Fullerton: Relative errors of $ 5 times 10^-4 $.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: H. Werner and G. Raymann
rawtitle: An Approximation to the {Fermi} Integral {$ F_{1 / 2}(x) $}
entry:
@Article{Werner:1963:AFI,
  author =       "H. Werner and G. Raymann",
  title =        "An Approximation to the {Fermi} Integral {$ F_{1 /
                 2}(x) $}",
  journal =      j-MATH-COMPUT,
  volume =       "17",
  number =       "82",
  pages =        "193--194",
  month =        apr,
  year =         "1963",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2003641",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Relative errors of $ 5 \times 10^{-4} $.",
}


bibtype: article
filename: elefunt.bib
label: Whittlesey:1963:IGF
author: John R. B. Whittlesey
title: Incomplete Gamma Functions for Evaluating Erlang Process Probabilities
journal: j-MATH-COMPUT
volume: 17
number: 81
pages: 11--17
month: jan
monthnumber: 1
year: 1963
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: John R. B. Whittlesey
rawtitle: Incomplete Gamma Functions for Evaluating {Erlang} Process Probabilities
entry:
@Article{Whittlesey:1963:IGF,
  author =       "John R. B. Whittlesey",
  title =        "Incomplete Gamma Functions for Evaluating {Erlang}
                 Process Probabilities",
  journal =      j-MATH-COMPUT,
  volume =       "17",
  number =       "81",
  pages =        "11--17",
  month =        jan,
  year =         "1963",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: incollection
filename: elefunt.bib
label: Abramowitz:1964:CWF
author: Milton Abramowitz
title: Coulomb Wave Functions
crossref: Abramowitz:1964:HMF
pages: 537--554
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Milton Abramowitz
rawtitle: {Coulomb} Wave Functions
entry:
@InCollection{Abramowitz:1964:CWF,
  author =       "Milton Abramowitz",
  title =        "{Coulomb} Wave Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "537--554",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: incollection
filename: elefunt.bib
label: Abramowitz:1964:SFR
author: Milton Abramowitz
title: Struve Functions and Related Functions
crossref: Abramowitz:1964:HMF
pages: 495--502
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Milton Abramowitz
rawtitle: {Struve} Functions and Related Functions
entry:
@InCollection{Abramowitz:1964:SFR,
  author =       "Milton Abramowitz",
  title =        "{Struve} Functions and Related Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "495--502",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: article
filename: elefunt.bib
label: Aiken:1964:PAC
author: H. H. Aiken and A. G. Oettinger and T. C. Bartee
title: Proposed automatic calculating machine
journal: j-IEEE-SPECTRUM
volume: 1
number: 8
pages: 62--69
month: aug
monthnumber: 8
year: 1964
CODEN: IEESAM
DOI: https://doi.org/10.1109/MSPEC.1964.6500770
ISSN: 0018-9235 (print), 1939-9340 (electronic) OR 00189235 (print), 19399340 (electronic)
ISSNL: 0018-9235 OR 00189235
bibdate: Tue Jan 14 11:14:17 2020
bibtimestamp: 2020.01.14 11:14:17 ???
fjournal: IEEE Spectrum
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6
rawauthor: H. H. Aiken and A. G. Oettinger and T. C. Bartee
rawtitle: Proposed automatic calculating machine
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/ieeespectrum1960.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

abstract:
Here presented is the memorandum that 20 years ago initiated a series of events whose revolutionary implications are only beginning to manifest themselves a description of the first large-scale general-purpose automatic digital computer. Twenty years ago, on August 7, 1944, Mark I, the first large-scale general-purpose automatic digital computer ever to be put in operation was dedicated at Harvard University by James B. Conant, then president of Harvard, and the late Thomas J. Watson, founder of IBM.

remark:
Pages 66--69 discuss computation of the elementary functions with minimal intermediate storage: recipes are given for integral and fractional power, log, exponential, trigonometric, inverse trigonometric, hyperbolic, and inverse hyperbolic. Mention is also made of the probability integral, elliptic functions, and Bessel functions, but the text says they will be discussed later (meaning, in a future publication). The methods involve recurrences and series summations, and thus, can be regarded as precision independent.

rawabstract:
Here presented is the memorandum that 20 years ago initiated a series of events whose revolutionary implications are only beginning to manifest themselves a description of the first large-scale general-purpose automatic digital computer. Twenty years ago, on August 7, 1944, Mark I, the first large-scale general-purpose automatic digital computer ever to be put in operation was dedicated at Harvard University by James B. Conant, then president of Harvard, and the late Thomas J. Watson, founder of IBM.

entry:
@Article{Aiken:1964:PAC,
  author =       "H. H. Aiken and A. G. Oettinger and T. C. Bartee",
  title =        "Proposed automatic calculating machine",
  journal =      j-IEEE-SPECTRUM,
  volume =       "1",
  number =       "8",
  pages =        "62--69",
  month =        aug,
  year =         "1964",
  CODEN =        "IEESAM",
  DOI =          "https://doi.org/10.1109/MSPEC.1964.6500770",
  ISSN =         "0018-9235 (print), 1939-9340 (electronic)",
  ISSN-L =       "0018-9235",
  bibdate =      "Tue Jan 14 11:14:17 2020",
  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/ieeespectrum1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  abstract =     "Here presented is the memorandum that 20 years ago
                 initiated a series of events whose revolutionary
                 implications are only beginning to manifest themselves
                 a description of the first large-scale general-purpose
                 automatic digital computer. Twenty years ago, on August
                 7, 1944, Mark I, the first large-scale general-purpose
                 automatic digital computer ever to be put in operation
                 was dedicated at Harvard University by James B. Conant,
                 then president of Harvard, and the late Thomas J.
                 Watson, founder of IBM.",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Spectrum",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=6",
  remark =       "Pages 66--69 discuss computation of the elementary
                 functions with minimal intermediate storage: recipes
                 are given for integral and fractional power, log,
                 exponential, trigonometric, inverse trigonometric,
                 hyperbolic, and inverse hyperbolic. Mention is also
                 made of the probability integral, elliptic functions,
                 and Bessel functions, but the text says they will be
                 discussed later (meaning, in a future publication). The
                 methods involve recurrences and series summations, and
                 thus, can be regarded as precision independent.",
  xxnote =       "Previously unpublished memorandum written by Aiken and
                 dated by an unknown recipient as 4 November 1937.
                 Reprinted in \cite[\S 5.1]{Randell:1982:ODC}.",
}


bibtype: incollection
filename: elefunt.bib
label: Antosiewicz:1964:BFF
author: H. A. Antosiewicz
title: Bessel Functions of Fractional Order
crossref: Abramowitz:1964:HMF
pages: 435--478
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: H. A. Antosiewicz
rawtitle: {Bessel} Functions of Fractional Order
entry:
@InCollection{Antosiewicz:1964:BFF,
  author =       "H. A. Antosiewicz",
  title =        "{Bessel} Functions of Fractional Order",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "435--478",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: incollection
filename: elefunt.bib
label: Blanch:1964:MF
author: Gertrude Blanch
title: Mathieu Functions
crossref: Abramowitz:1964:HMF
pages: 721--750
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
authordates: 1897--1996
rawauthor: Gertrude Blanch
rawtitle: {Mathieu} Functions
entry:
@InCollection{Blanch:1964:MF,
  author =       "Gertrude Blanch",
  title =        "{Mathieu} Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "721--750",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  author-dates = "1897--1996",
  citedby =      "Fullerton:1980:BEM",
}


bibtype: article
filename: elefunt.bib
label: Bray:1964:CAGa
author: T. A. Bray
title: Certification of Algorithm 225: Gamma function with controlled accuracy
journal: j-CACM
volume: 7
number: 10
pages: 586--586
month: oct
monthnumber: 10
year: 1964
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:56 MST 2005
bibtimestamp: 2005.11.25 18:19:56 MST
fjournal: Communications of the ACM
keywords: $Gamma (x)$; special functions
remark: Fullerton: No corrections were necessary.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: T. A. Bray
rawtitle: Certification of {Algorithm 225}: {Gamma} function with controlled accuracy
bibsource:
http://portal.acm.org/; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Bray:1964:CAGa,
  author =       "T. A. Bray",
  title =        "Certification of {Algorithm 225}: {Gamma} function
                 with controlled accuracy",
  journal =      j-CACM,
  volume =       "7",
  number =       "10",
  pages =        "586--586",
  month =        oct,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:56 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\Gamma(x)$; special functions",
  remark =       "Fullerton: No corrections were necessary.",
}


bibtype: article
filename: elefunt.bib
label: Burgoyne:1964:GTF
author: F. D. Burgoyne
title: Generalized Trigonometric Functions (in Technical Notes and Short Papers)
journal: j-MATH-COMPUT
volume: 18
number: 86
pages: 314--316
month: apr
monthnumber: 4
year: 1964
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: F. D. Burgoyne
rawtitle: Generalized Trigonometric Functions (in {Technical Notes and Short Papers})
entry:
@Article{Burgoyne:1964:GTF,
  author =       "F. D. Burgoyne",
  title =        "Generalized Trigonometric Functions (in {Technical
                 Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "18",
  number =       "86",
  pages =        "314--316",
  month =        apr,
  year =         "1964",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Cody:1964:DPS
author: William J. Cody, Jr.
title: Double-Precision Square Root for the CDC-3600
journal: j-CACM
volume: 7
number: 12
pages: 715--718
month: dec
monthnumber: 12
year: 1964
CODEN: CACMA2
DOI: https://doi.org/10.1145/355588.365122
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:57 MST 2005
bibtimestamp: 2005.11.25 18:19:57 MST
fjournal: Communications of the ACM
keywords: $sqrt(x)$; CDC 3600; elementary functions; floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: William J. {Cody, Jr.}
rawtitle: Double-Precision Square Root for the {CDC-3600}
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
In January of 1960, the late Hans J. Maehly completed a summary of approximations to the elementary functions for the CDC-1604 computer. The approximations and techniques suggested by Maehly are equally applicable to the second large computer in the CDC line, the 3600. Unlike the 1604, however, the 3600 has built-in double-precision floating-point arithmetic. The present work, largely inspired by the successes of Maehly and his associates, concerns the extension of one of Maehly's ideas to a double-precision subroutine for the 3600.

rawabstract:
In January of 1960, the late Hans J. Maehly completed a summary of approximations to the elementary functions for the CDC-1604 computer. The approximations and techniques suggested by Maehly are equally applicable to the second large computer in the CDC line, the 3600. Unlike the 1604, however, the 3600 has built-in double-precision floating-point arithmetic. The present work, largely inspired by the successes of Maehly and his associates, concerns the extension of one of Maehly's ideas to a double-precision subroutine for the 3600.

entry:
@Article{Cody:1964:DPS,
  author =       "William J. {Cody, Jr.}",
  title =        "Double-Precision Square Root for the {CDC-3600}",
  journal =      j-CACM,
  volume =       "7",
  number =       "12",
  pages =        "715--718",
  month =        dec,
  year =         "1964",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355588.365122",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:57 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  abstract =     "In January of 1960, the late Hans J. Maehly completed
                 a summary of approximations to the elementary functions
                 for the CDC-1604 computer. The approximations and
                 techniques suggested by Maehly are equally applicable
                 to the second large computer in the CDC line, the 3600.
                 Unlike the 1604, however, the 3600 has built-in
                 double-precision floating-point arithmetic. The present
                 work, largely inspired by the successes of Maehly and
                 his associates, concerns the extension of one of
                 Maehly's ideas to a double-precision subroutine for the
                 3600.",
  acknowledgement = ack-nhfb # "\slash " # ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$sqrt(x)$; CDC 3600; elementary functions;
                 floating-point arithmetic",
}


bibtype: article
filename: elefunt.bib
label: Cowgill:1964:LEB
author: D. Cowgill
title: Logic Equations for a Built-In Square Root Method
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-13
number: 2
pages: 156--157
month: apr
monthnumber: 4
year: 1964
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1964.263791
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:56:59 MDT 2011
bibtimestamp: 2011.07.14 06:56:59 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038119
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: D. Cowgill
rawtitle: Logic Equations for a Built-In Square Root Method
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/ieeetranscomput.bib

entry:
@Article{Cowgill:1964:LEB,
  author =       "D. Cowgill",
  title =        "Logic Equations for a Built-In Square Root Method",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-13",
  number =       "2",
  pages =        "156--157",
  month =        apr,
  year =         "1964",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1964.263791",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:56:59 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/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038119",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: elefunt.bib
label: Curtiss:1964:EIB
author: C. F. Curtiss
title: Expansions of Integrals of Bessel Functions of Large Order
journal: j-J-MATH-PHYS
volume: 5
number: 4
pages: 561--564
month: apr
monthnumber: 4
year: 1964
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.1704149
ISSNL: 0022-2488 OR 00222488
bibdate: Fri Oct 28 08:40:12 MDT 2011
bibtimestamp: 2011.10.28 08:40:12 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v5/i4/p561_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
onlinedate: 22 December 2004
rawauthor: C. F. Curtiss
rawtitle: Expansions of Integrals of {Bessel} Functions of Large Order
ISSN:
0022-2488 (print), 1089-7658 (electronic), 1527-2427 OR 00222488 (print), 10897658 (electronic), 15272427

bibsource:
http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1960.bib

entry:
@Article{Curtiss:1964:EIB,
  author =       "C. F. Curtiss",
  title =        "Expansions of Integrals of {Bessel} Functions of Large
                 Order",
  journal =      j-J-MATH-PHYS,
  volume =       "5",
  number =       "4",
  pages =        "561--564",
  month =        apr,
  year =         "1964",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1704149",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Oct 28 08:40:12 MDT 2011",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1960.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v5/i4/p561_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  onlinedate =   "22 December 2004",
  pagecount =    "4",
}


bibtype: article
filename: elefunt.bib
label: Cyvin:1964:AGF
author: S. J. Cyvin and B. N. Cyvin
title: Algorithm 225: Gamma function with controlled accuracy
journal: j-CACM
volume: 7
number: 5
pages: 295--295
month: may
monthnumber: 5
year: 1964
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:53 MST 2005
bibtimestamp: 2005.11.25 18:19:53 MST
fjournal: Communications of the ACM
keywords: $Gamma (x)$; special functions
remark: Fullerton: 30-line Algol procedure based on out-of-date method.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: S. J. Cyvin and B. N. Cyvin
rawtitle: {Algorithm 225}: {Gamma} function with controlled accuracy
bibsource:
http://portal.acm.org/; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Cyvin:1964:AGF,
  author =       "S. J. Cyvin and B. N. Cyvin",
  title =        "{Algorithm 225}: {Gamma} function with controlled
                 accuracy",
  journal =      j-CACM,
  volume =       "7",
  number =       "5",
  pages =        "295--295",
  month =        may,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:53 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\Gamma(x)$; special functions",
  remark =       "Fullerton: 30-line Algol procedure based on
                 out-of-date method.",
}


bibtype: article
filename: elefunt.bib
label: Cyvin:1964:AND
author: S. J. Cyvin
title: Algorithm 226: Normal distribution function
journal: j-CACM
volume: 7
number: 5
pages: 295--295
month: may
monthnumber: 5
year: 1964
CODEN: CACMA2
DOI: https://doi.org/10.1145/364099.364315
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:53 MST 2005
bibtimestamp: 2005.11.25 18:19:53 MST
fjournal: Communications of the ACM
keywords: probability functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: S. J. Cyvin
rawtitle: {Algorithm 226}: {Normal} distribution function
bibsource:
http://portal.acm.org/; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Cyvin:1964:AND,
  author =       "S. J. Cyvin",
  title =        "{Algorithm 226}: {Normal} distribution function",
  journal =      j-CACM,
  volume =       "7",
  number =       "5",
  pages =        "295--295",
  month =        may,
  year =         "1964",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/364099.364315",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:53 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "probability functions",
}


bibtype: incollection
filename: elefunt.bib
label: Davis:1964:GFR
author: Philip J. Davis
title: Gamma Function and Related Functions
crossref: Abramowitz:1964:HMF
pages: 253--294
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Philip J. Davis
rawtitle: Gamma Function and Related Functions
entry:
@InCollection{Davis:1964:GFR,
  author =       "Philip J. Davis",
  title =        "Gamma Function and Related Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "253--294",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: article
filename: elefunt.bib
label: Eve:1964:EP
author: J. Eve
title: The evaluation of polynomials
journal: j-NUM-MATH
volume: 6
number: 1
pages: 17--21
month: dec
monthnumber: 12
year: 1964
CODEN: NUMMA7
DOI: https://doi.org/10.1007/BF01386049
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon Oct 18 20:10:40 MDT 1999
bibtimestamp: 1999.10.18 20:10:40 MDT
fjournal: Numerische Mathematik
keywords: number of multiplications to evaluate a polynomial
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: J. Eve
rawtitle: The evaluation of polynomials
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib

remark:
From the first two paragraphs: ``Ostrowski [5] has shown that the $ 2 n $ operations required by this algorithm [Horner's] are minimal for $ n leq 4 $. Motzkin [4] (see also Todd [8]) and Knuth [3] have given methods whereby polynomials with $ 4 leq n leq 6 $ can be evaluated in $ [(1 / 2)(n + 3)] $ multiplications and not more than $ n + 1 $ additions. Similar methods effecting a reduction in the number of multiplications have been described by Pan [6] for $ n leq 12 $. Each of these methods is valid only for a particular value of $n$.par A general method due to Pan [7] applicable to all polynomials with $ n geq 5 $ results in an evaluation involving $ [(1 / 2) (n + 4)] $ multiplications and $ n + 1 $ additions. Knuth has also given a method applicable to all polynomials with $ n geq 3 $ in which $ n + 1 $ additions are required while the number of multiplications varies between $ [(1 / 2) (n + 3)] $ and approximately $ (3 / 4)n $.''

entry:
@Article{Eve:1964:EP,
  author =       "J. Eve",
  title =        "The evaluation of polynomials",
  journal =      j-NUM-MATH,
  volume =       "6",
  number =       "1",
  pages =        "17--21",
  month =        dec,
  year =         "1964",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01386049",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 20:10:40 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "number of multiplications to evaluate a polynomial",
  remark =       "From the first two paragraphs: ``Ostrowski [5] has
                 shown that the $ 2 n $ operations required by this
                 algorithm [Horner's] are minimal for $ n \leq 4 $.
                 Motzkin [4] (see also Todd [8]) and Knuth [3] have
                 given methods whereby polynomials with $ 4 \leq n \leq
                 6 $ can be evaluated in $ [(1 / 2)(n + 3)] $
                 multiplications and not more than $ n + 1 $ additions.
                 Similar methods effecting a reduction in the number of
                 multiplications have been described by Pan [6] for $ n
                 \leq 12 $. Each of these methods is valid only for a
                 particular value of $n$.\par A general method due to
                 Pan [7] applicable to all polynomials with $ n \geq 5 $
                 results in an evaluation involving $ [(1 / 2) (n + 4)]
                 $ multiplications and $ n + 1 $ additions. Knuth has
                 also given a method applicable to all polynomials with
                 $ n \geq 3 $ in which $ n + 1 $ additions are required
                 while the number of multiplications varies between $
                 [(1 / 2) (n + 3)] $ and approximately $ (3 / 4)n $.''",
}


bibtype: techreport
filename: elefunt.bib
label: Fisherkeller:1964:TCE
author: M. A. Fisherkeller and W. J. Cody, Jr.
title: Tables of the Complete Elliptic Integrals $ K $, $ K' $, $ E $, and $ E' $
type: Technical Memo
number: ANL AMD 71
institution: inst-ANL
address: inst-ANL:adr
pages: 14
year: 1964
bibdate: Thu Nov 17 10:44:21 1994
bibtimestamp: 1994.11.17 10:44:21 ???
note: See review by John W. Wrench in Mathematics of Computation, bf 19(89--92), 342, 1965.
acknowledgement: ack-nhfb
rawauthor: M. A. Fisherkeller and W. J. {Cody, Jr.}
rawnote: See review by John W. Wrench in Mathematics of Computation, {\bf 19}(89--92), 342, 1965.
rawtitle: Tables of the Complete Elliptic Integrals $ {K} $, $ {K}' $, $ {E} $, and $ {E}' $
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@TechReport{Fisherkeller:1964:TCE,
  author =       "M. A. Fisherkeller and W. J. {Cody, Jr.}",
  title =        "Tables of the Complete Elliptic Integrals $ {K} $, $
                 {K}' $, $ {E} $, and $ {E}' $",
  type =         "Technical Memo",
  number =       "ANL AMD 71",
  institution =  inst-ANL,
  address =      inst-ANL:adr,
  pages =        "14",
  year =         "1964",
  bibdate =      "Thu Nov 17 10:44:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See review by John W. Wrench in Mathematics of
                 Computation, {\bf 19}(89--92), 342, 1965.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Gargantini:1964:RCA
author: I. Gargantini and T. Pomentale
title: Rational Chebyshev approximations to the Bessel function integrals $ K i_s(x) $
journal: j-CACM
volume: 7
number: 12
pages: 727--730
month: dec
monthnumber: 12
year: 1964
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
MRclass: 65.25
MRnumber: 31\#863
bibdate: Fri Nov 25 18:19:57 MST 2005
bibtimestamp: 2005.11.25 18:19:57 MST
fjournal: Communications of the ACM
keywords: Bessel functions; Kis(x); special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: I. Gargantini and T. Pomentale
rawtitle: Rational {Chebyshev} approximations to the {Bessel} function integrals {$ K i_s(x) $}
abstract:
The second Remes algorithm is used to approximate the integrals $ K i_s $ by rational functions. The related coefficients for the approximations of $ K i_1, K i_2, K i_3 $ are given for different precisions.

remark:
Fullerton: Approximations for repeated integrals $ operatorname Ki_s(x) $ of $ K(x) $ for $ s = 1, 2, 3 $ are given for accuracies down to $ 10^-5 $ for $ s = 1 $ and to $ 10^-7 $ for $ s = 2, 3 $.

rawabstract:
The second Remes algorithm is used to approximate the integrals $ K i_s $ by rational functions. The related coefficients for the approximations of $ K i_1, K i_2, K i_3 $ are given for different precisions.

entry:
@Article{Gargantini:1964:RCA,
  author =       "I. Gargantini and T. Pomentale",
  title =        "Rational {Chebyshev} approximations to the {Bessel}
                 function integrals {$ K i_s(x) $}",
  journal =      j-CACM,
  volume =       "7",
  number =       "12",
  pages =        "727--730",
  month =        dec,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  MRclass =      "65.25",
  MRnumber =     "31\#863",
  bibdate =      "Fri Nov 25 18:19:57 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "The second Remes algorithm is used to approximate the
                 integrals $ K i_s $ by rational functions. The related
                 coefficients for the approximations of $ K i_1, K i_2,
                 K i_3 $ are given for different precisions.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Bessel functions; Kis(x); special functions",
  remark =       "Fullerton: Approximations for repeated integrals $
                 \operatorname {Ki}_s(x) $ of $ K(x) $ for $ s = 1, 2, 3
                 $ are given for accuracies down to $ 10^{-5} $ for $ s
                 = 1 $ and to $ 10^{-7} $ for $ s = 2, 3 $.",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1964:AAB
author: W. Gautschi
title: ACM Algorithm 236: Bessel Functions of the First Kind [S17]
journal: j-CACM
volume: 7
number: 8
pages: 479--480
month: aug
monthnumber: 8
year: 1964
CODEN: CACMA2
DOI: https://doi.org/10.1145/355586.355587
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:55 MST 2005
bibtimestamp: 2005.11.25 18:19:55 MST
note: See remark cite Skovgaard:1975:RBF.
fjournal: Communications of the ACM
keywords: $J_n(x)$; Bessel functions of the first kind; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: W. Gautschi
rawnote: See remark \cite{Skovgaard:1975:RBF}.
rawtitle: {ACM Algorithm 236}: {Bessel} Functions of the First Kind [{S17}]
bibsource:
http://portal.acm.org/; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/cacm1970.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

entry:
@Article{Gautschi:1964:AAB,
  author =       "W. Gautschi",
  title =        "{ACM Algorithm 236}: {Bessel} Functions of the First
                 Kind [{S17}]",
  journal =      j-CACM,
  volume =       "7",
  number =       "8",
  pages =        "479--480",
  month =        aug,
  year =         "1964",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/355586.355587",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:55 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  note =         "See remark \cite{Skovgaard:1975:RBF}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$J_n(x)$; Bessel functions of the first kind; special
                 functions",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1964:AGF
author: Walter Gautschi
title: Algorithm 221: Gamma functions
journal: j-CACM
volume: 7
number: 3
pages: 143--143
month: mar
monthnumber: 3
year: 1964
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:52 MST 2005
bibtimestamp: 2005.11.25 18:19:52 MST
fjournal: Communications of the ACM
keywords: $Gamma (x)$; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Walter Gautschi
rawtitle: {Algorithm 221}: {Gamma} functions
entry:
@Article{Gautschi:1964:AGF,
  author =       "Walter Gautschi",
  title =        "{Algorithm 221}: {Gamma} functions",
  journal =      j-CACM,
  volume =       "7",
  number =       "3",
  pages =        "143--143",
  month =        mar,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:52 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\Gamma(x)$; special functions",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1964:AIB
author: Walter Gautschi
title: Algorithm 222: Incomplete beta functions ratios
journal: j-CACM
volume: 7
number: 3
pages: 143--143
month: mar
monthnumber: 3
year: 1964
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:52 MST 2005
bibtimestamp: 2005.11.25 18:19:52 MST
fjournal: Communications of the ACM
keywords: beta functions; special functions
remark: Fullerton: 200-line Algol procedure.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Walter Gautschi
rawtitle: {Algorithm 222}: {Incomplete} beta functions ratios
entry:
@Article{Gautschi:1964:AIB,
  author =       "Walter Gautschi",
  title =        "{Algorithm 222}: {Incomplete} beta functions ratios",
  journal =      j-CACM,
  volume =       "7",
  number =       "3",
  pages =        "143--143",
  month =        mar,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:52 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "beta functions; special functions",
  remark =       "Fullerton: 200-line Algol procedure.",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1964:CAI
author: Walter Gautschi
title: Certification of Algorithm 222: Incomplete beta function ratios
journal: j-CACM
volume: 7
number: 4
pages: 244--244
month: apr
monthnumber: 4
year: 1964
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:53 MST 2005
bibtimestamp: 2005.11.25 18:19:53 MST
fjournal: Communications of the ACM
keywords: beta functions; special functions
remark: Fullerton: A typographical error is noted.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Walter Gautschi
rawtitle: Certification of {Algorithm 222}: {Incomplete} beta function ratios
entry:
@Article{Gautschi:1964:CAI,
  author =       "Walter Gautschi",
  title =        "Certification of {Algorithm 222}: {Incomplete} beta
                 function ratios",
  journal =      j-CACM,
  volume =       "7",
  number =       "4",
  pages =        "244--244",
  month =        apr,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:53 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "beta functions; special functions",
  remark =       "Fullerton: A typographical error is noted.",
}


bibtype: incollection
filename: elefunt.bib
label: Gautschi:1964:EFF
author: Walter Gautschi
title: Error Function and Fresnel Integrals
crossref: Abramowitz:1964:HMF
pages: 295--330
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Walter Gautschi
rawtitle: Error Function and {Fresnel} Integrals
entry:
@InCollection{Gautschi:1964:EFF,
  author =       "Walter Gautschi",
  title =        "Error Function and {Fresnel} Integrals",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "295--330",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: incollection
filename: elefunt.bib
label: Gautschi:1964:EIR
author: Walter Gautschi and William F. Cahill
title: Exponential Integral and Related Functions
crossref: Abramowitz:1964:HMF
pages: 227--252
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Walter Gautschi and William F. Cahill
rawtitle: Exponential Integral and Related Functions
entry:
@InCollection{Gautschi:1964:EIR,
  author =       "Walter Gautschi and William F. Cahill",
  title =        "Exponential Integral and Related Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "227--252",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: article
filename: elefunt.bib
label: Gray:1964:CAF
author: Malcolm Gray
title: Certification of Algorithm 213: Fresnel integrals
journal: j-CACM
volume: 7
number: 11
pages: 661--661
month: nov
monthnumber: 11
year: 1964
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:56 MST 2005
bibtimestamp: 2005.11.25 18:19:56 MST
note: See cite Gray:1963:AFI,Gray:1963:RAE.
fjournal: Communications of the ACM
keywords: C(x); S(x); special functions
remark: Fullerton: Several corrections are given.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Malcolm Gray
rawnote: See \cite{Gray:1963:AFI,Gray:1963:RAE}.
rawtitle: Certification of {Algorithm 213}: {Fresnel} integrals
entry:
@Article{Gray:1964:CAF,
  author =       "Malcolm Gray",
  title =        "Certification of {Algorithm 213}: {Fresnel}
                 integrals",
  journal =      j-CACM,
  volume =       "7",
  number =       "11",
  pages =        "661--661",
  month =        nov,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:56 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Gray:1963:AFI,Gray:1963:RAE}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "C(x); S(x); special functions",
  remark =       "Fullerton: Several corrections are given.",
}


bibtype: incollection
filename: elefunt.bib
label: Haynsworth:1964:BEP
author: Emilie V. Haynsworth and Karl Goldberg
title: Bernoulli and Euler Polynomials, Riemann Zeta Function
crossref: Abramowitz:1964:HMF
pages: 803--820
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Emilie V. Haynsworth and Karl Goldberg
rawtitle: {Bernoulli} and {Euler} Polynomials, {Riemann Zeta} Function
entry:
@InCollection{Haynsworth:1964:BEP,
  author =       "Emilie V. Haynsworth and Karl Goldberg",
  title =        "{Bernoulli} and {Euler} Polynomials, {Riemann Zeta}
                 Function",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "803--820",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: incollection
filename: elefunt.bib
label: Hochstrasser:1964:OP
author: Urs W. Hochstrasser
title: Orthogonal Polynomials
crossref: Abramowitz:1964:HMF
pages: 771--802
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Urs W. Hochstrasser
rawtitle: Orthogonal Polynomials
entry:
@InCollection{Hochstrasser:1964:OP,
  author =       "Urs W. Hochstrasser",
  title =        "Orthogonal Polynomials",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "771--802",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: article
filename: elefunt.bib
label: Hummer:1964:EDF
author: David G. Hummer
journal: j-MATH-COMPUT
volume: 18
number: 86
pages: 317--319
month: apr
monthnumber: 4
year: 1964
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: Almost l5-digit approximations.
acknowledgement: ack-nhfb
ajournal: Math. Comput.
journalURL: http://www.ams.org/mcom/
rawauthor: David G. Hummer
title:
Expansions of Dawson's Function in a Series of Chebyshev Polynomials (in Technical Notes and Short Papers)

rawtitle:
Expansions of {Dawson}'s Function in a Series of {Chebyshev} Polynomials (in {Technical Notes and Short Papers})

entry:
@Article{Hummer:1964:EDF,
  author =       "David G. Hummer",
  title =        "Expansions of {Dawson}'s Function in a Series of
                 {Chebyshev} Polynomials (in {Technical Notes and Short
                 Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "18",
  number =       "86",
  pages =        "317--319",
  month =        apr,
  year =         "1964",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  ajournal =     "Math. Comput.",
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Almost l5-digit approximations.",
}


bibtype: article
filename: elefunt.bib
label: Lanczos:1964:PAG
author: Cornelius Lanczos
title: A Precision Approximation of the Gamma Function
journal: j-SIAM-J-NUM-ANALYSIS-B
volume: 1
number: 1
pages: 86--96
year: 1964
DOI: https://doi.org/10.1137/0701008
ISSN: 0887-459X (print), 1095-7170 (electronic) OR 0887459X (print), 10957170 (electronic)
ISSNL: 0887-459X OR 0887459X
MRclass: 33.15
MRnumber: 0176115 (31 \#390)
MRreviewer: S. C. van Veen
bibdate: Fri Oct 16 06:57:22 MDT 1998
bibtimestamp: 1998.10.16 06:57:22 MDT
URL: http://www.jstor.org/stable/2949767
fjournal: Journal of the Society for Industrial and Applied Mathematics: Series B, Numerical Analysis
ZMnumber: Zbl 0136.05201
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/loi/sjnaam.1
rawauthor: Cornelius Lanczos
rawtitle: A Precision Approximation of the Gamma Function
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib; JSTOR database

entry:
@Article{Lanczos:1964:PAG,
  author =       "Cornelius Lanczos",
  title =        "A Precision Approximation of the Gamma Function",
  journal =      j-SIAM-J-NUM-ANALYSIS-B,
  volume =       "1",
  number =       "1",
  pages =        "86--96",
  month =        "????",
  year =         "1964",
  DOI =          "https://doi.org/10.1137/0701008",
  ISSN =         "0887-459X (print), 1095-7170 (electronic)",
  ISSN-L =       "0887-459X",
  MRclass =      "33.15",
  MRnumber =     "0176115 (31 \#390)",
  MRreviewer =   "S. C. van Veen",
  bibdate =      "Fri Oct 16 06:57:22 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/siamjnumeranal.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2949767",
  ZMnumber =     "Zbl 0136.05201",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Society for Industrial and Applied
                 Mathematics: Series B, Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/loi/sjnaam.1",
}


bibtype: article
filename: elefunt.bib
label: Lotsch:1964:AFI
author: Helmut Lotsch and Malcolm Gray
title: Algorithm 244: Fresnel Integrals [S20]
journal: j-CACM
volume: 7
number: 11
pages: 660--661
month: nov
monthnumber: 11
year: 1964
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:56 MST 2005
bibtimestamp: 2005.11.25 18:19:56 MST
fjournal: Communications of the ACM
keywords: C(x); Fresnel integrals; S(x); special functions
remark: Fullerton: 100-line Algol procedure.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Helmut Lotsch and Malcolm Gray
rawtitle: {Algorithm 244}: {Fresnel} Integrals [{S20}]
abstract:
This procedure computes the Fresnel sine and cosine integrals $ C(w) = int _0^infty cos [(pi / 2)t^2] d t $ and $ S(w) = int _0^w sin [(pi / 2)t^2] d t $. It is a modification of Algorithm 213 (Comm. ACM, 6 (Oct. 1963), 617) such that the accuracy, expressed by textit eps, is improved. eps can arbitrarily be chosen up to $ textit eps = 10^-6 $ for a computer with sufficient word length as, for example, the Burroughs B5000 which has 11--12 significant digits. Referring to the formulas of Algorithm 213: if $ |w| < sqrt (26.20 / pi ) $ the series expansions $ C(w) $ and $ S(w) $ are terminated when the absolute value of the relative change in two successive terms is $ leq textit eps $. If $ |w| geq sqrt (26.20 / pi ) $ the series $ Q(x) $ and $ P(x) $ are terminated when the absolute value of the terms is $ leq textit eps / 2 $. However, this truncation point is not necessarily valid for the range $ sqrt (26.20 / pi ) leq |w| < sqrt (28.50 / pi ) $ when $ textit eps = 10^-6 $, since the asymptotic series must be terminated before arriving at the minimum. In this range the ignored terms of the series expansions are $ < 3 times 10^6 $, and for larger arguments $ < 10^-6 $. This accuracy may be improved if desired: the switch-over point from the regular to the asymptotic series expansions has to be displaced to larger arguments.

rawabstract:
This procedure computes the Fresnel sine and cosine integrals $ C(w) = \int_0^\infty \cos [(\pi / 2)t^2] \, d t $ and $ S(w) = \int_0^w \sin [(\pi / 2)t^2] \, d t $. It is a modification of Algorithm 213 (Comm. ACM, 6 (Oct. 1963), 617) such that the accuracy, expressed by \textit{eps}, is improved. eps can arbitrarily be chosen up to $ \textit {eps} = 10^{-6} $ for a computer with sufficient word length as, for example, the Burroughs B5000 which has 11--12 significant digits. Referring to the formulas of Algorithm 213: if $ |w| < \sqrt {(26.20 / \pi)} $ the series expansions $ C(w) $ and $ S(w) $ are terminated when the absolute value of the relative change in two successive terms is $ \leq \textit {eps} $. If $ |w| \geq \sqrt {(26.20 / \pi)} $ the series $ Q(x) $ and $ P(x) $ are terminated when the absolute value of the terms is $ \leq \textit {eps} / 2 $. However, this truncation point is not necessarily valid for the range $ \sqrt {(26.20 / \pi)} \leq |w| < \sqrt {(28.50 / \pi)} $ when $ \textit {eps} = 10^{-6} $, since the asymptotic series must be terminated before arriving at the minimum. In this range the ignored terms of the series expansions are $ < 3 \times 10^6 $, and for larger arguments $ < 10^{-6} $. This accuracy may be improved if desired: the switch-over point from the regular to the asymptotic series expansions has to be displaced to larger arguments.

entry:
@Article{Lotsch:1964:AFI,
  author =       "Helmut Lotsch and Malcolm Gray",
  title =        "{Algorithm 244}: {Fresnel} Integrals [{S20}]",
  journal =      j-CACM,
  volume =       "7",
  number =       "11",
  pages =        "660--661",
  month =        nov,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:56 MST 2005",
  bibsource =    "http://portal.acm.org/;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This procedure computes the Fresnel sine and cosine
                 integrals $ C(w) = \int_0^\infty \cos [(\pi / 2)t^2] \,
                 d t $ and $ S(w) = \int_0^w \sin [(\pi / 2)t^2] \, d t
                 $. It is a modification of Algorithm 213 (Comm. ACM, 6
                 (Oct. 1963), 617) such that the accuracy, expressed by
                 \textit{eps}, is improved. eps can arbitrarily be
                 chosen up to $ \textit {eps} = 10^{-6} $ for a computer
                 with sufficient word length as, for example, the
                 Burroughs B5000 which has 11--12 significant digits.
                 Referring to the formulas of Algorithm 213: if $ |w| <
                 \sqrt {(26.20 / \pi)} $ the series expansions $ C(w) $
                 and $ S(w) $ are terminated when the absolute value of
                 the relative change in two successive terms is $ \leq
                 \textit {eps} $. If $ |w| \geq \sqrt {(26.20 / \pi)} $
                 the series $ Q(x) $ and $ P(x) $ are terminated when
                 the absolute value of the terms is $ \leq \textit {eps}
                 / 2 $. However, this truncation point is not
                 necessarily valid for the range $ \sqrt {(26.20 / \pi)}
                 \leq |w| < \sqrt {(28.50 / \pi)} $ when $ \textit {eps}
                 = 10^{-6} $, since the asymptotic series must be
                 terminated before arriving at the minimum. In this
                 range the ignored terms of the series expansions are $
                 < 3 \times 10^6 $, and for larger arguments $ < 10^{-6}
                 $. This accuracy may be improved if desired: the
                 switch-over point from the regular to the asymptotic
                 series expansions has to be displaced to larger
                 arguments.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "C(x); Fresnel integrals; S(x); special functions",
  remark =       "Fullerton: 100-line Algol procedure.",
}


bibtype: incollection
filename: elefunt.bib
label: Lowan:1964:SWF
author: Arnold N. Lowan
title: Spheroidal Wave Functions
crossref: Abramowitz:1964:HMF
pages: 751--770
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Arnold N. Lowan
rawtitle: Spheroidal Wave Functions
entry:
@InCollection{Lowan:1964:SWF,
  author =       "Arnold N. Lowan",
  title =        "Spheroidal Wave Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "751--770",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: incollection
filename: elefunt.bib
label: Luke:1964:IBF
author: Yudell L. Luke
title: Integrals of Bessel Functions
crossref: Abramowitz:1964:HMF
pages: 479--494
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Yudell L. Luke
rawtitle: Integrals of {Bessel} Functions
entry:
@InCollection{Luke:1964:IBF,
  author =       "Yudell L. Luke",
  title =        "Integrals of {Bessel} Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "479--494",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: book
filename: elefunt.bib
label: Meinardus:1964:AFI
author: Gunter Meinardus
volume: 4
publisher: pub-SV
address: pub-SV:adr
pages: viii + 180
year: 1964
DOI: https://doi.org/10.1007/978-3-642-85646-4
ISBN: 3-540-03219-3, 3-642-85646-2, 3-642-85647-0 (print) OR 3540032193, 3642856462, 3642856470 (print)
LCCN: QA320 .M4
bibdate: Thu Oct 19 17:00:27 MDT 2023
bibtimestamp: 2023.10.19 17:00:27 MDT
series: Springer tracts in natural philosophy
language: German
subject: Aproximaciones
acknowledgement: ack-nhfb
authordates: 1926--
rawauthor: Gunter Meinardus
title:
Approximation von Funktionen und ihre numerische Behandlung. (German) [Approximation of functions and their numerical treatment]

ISBN13:
978-3-540-03219-9, 978-3-642-85646-4, 978-3-642-85647-1 (print) OR 9783540032199, 9783642856464, 9783642856471 (print)

bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
[numerous OCR errors to be corrected] Erst in den letzten Jahren hat sich derjenige Tell der Approximations theorie, der sich auf numerische Fragestellungen anwenden lass t, starker entwickelt. Das Prinzip der in einem gewissen Sinne besten Annaherung von Funktionen gewann insbesondere durch die Verwendung elektronischer Rechenmaschinen an Bedeutung. Einige der theoretischen Grundlagen, die zur Behandlung der auftretenden Probleme herange zogen werden mussen, finden sich verstreut in wenigen Buchern. Der weitaus gross te Teil der theoretischen und praktischen Untersuchungen ist jedoch nur in den Originalarbeiten nachzulesen. Hieraus ergab sich die Zielsetzung des vorliegenden Buches: Es sollte eine Zusammen stellung der wesentlichen Ergebnisse der Approximationstheorie gegeben werden, die einerseits ein rasches Eindringen in die modernen Entwicklungen dieses Gebietes ermoglicht und andererseits eine gewisse Vollstandigkeit auf dem Problemkreis der Tschebyscheff-Approximationen bietet, womit keineswegs gemeint ist, dass eine vollstandige Literatur ubersicht angestrebt wurde. Die Auswahl erfolgte stets nach dem immer noch subjektiven Gesichtspunkt der Bedeutung fur die Anwendungen. Dies gilt z. B. auch fur die asymptotischen Untersuchungen des 3, denn ich bin der Meinung, dass man sich auch beinumerischen Approximationen uber die, wenigstens asymptotisch zu erwartende Genauigkeit Gedanken machen sollte. Fast ausschliess lich habe ich mich auf die Theorie der gleich mass igen Approximation beschrankt, da diese die weitaus gross te praktische Bedeutung besitzt. Das erste Kapitel behandelt lineare Approximationen. Der 3 enthalt wohl den heute kurzesten Zugang zur linearen Theorie.

TOC:
I Lineare Approximationen I.1. Das allgemeine lineare Approximationsproblem I.2. Dichte Systeme I.3. Allgemeine Theorie linearer Tschebyscheff-Approximationen I.4. Spezielle Tschebyscheff-Approximationen I.5. Abschatzungen der Gross enordnung des Fehlers bei trigonometrischer und bei polynomialer Approximation I.6. Polynomapproximationen I.7. Numerische Verfahren bei linearen Tschebyscheff-Approximationen II Nicht-lineare Approximationen II.8. Allgemeine Theorie nicht-linearer Tschebyscheff-Approximationen II.9. Rationale Approximationen II.10. Exponentialapproximationen

rawabstract:
[numerous OCR errors to be corrected] Erst in den letzten Jahren hat sich derjenige Tell der Approximations theorie, der sich auf numerische Fragestellungen anwenden l{\"a}{\ss}t, starker entwickelt. Das Prinzip der in einem gewissen Sinne besten Ann{\"a}herung von Funktionen gewann insbesondere durch die Verwendung elektronischer Rechenmaschinen an Bedeutung. Einige der theoretischen Grundlagen, die zur Behandlung der auftretenden Probleme herange zogen werden mussen, finden sich verstreut in wenigen Buchern. Der weitaus gro{\ss}te Teil der theoretischen und praktischen Untersuchungen ist jedoch nur in den Originalarbeiten nachzulesen. Hieraus ergab sich die Zielsetzung des vorliegenden Buches: Es sollte eine Zusammen stellung der wesentlichen Ergebnisse der Approximationstheorie gegeben werden, die einerseits ein rasches Eindringen in die modernen Entwicklungen dieses Gebietes ermoglicht und andererseits eine gewisse Vollst{\"a}ndigkeit auf dem Problemkreis der Tschebyscheff-Approximationen bietet, womit keineswegs gemeint ist, da{\ss} eine vollst{\"a}ndige Literatur {\"u}bersicht angestrebt wurde. Die Auswahl erfolgte stets nach dem immer noch subjektiven Gesichtspunkt der Bedeutung f{\"u}r die Anwendungen. Dies gilt z. B. auch f{\"u}r die asymptotischen Untersuchungen des {\S} 3, denn ich bin der Meinung, da{\ss} man sich auch beinumerischen Approximationen {\"u}ber die, wenigstens asymptotisch zu erwartende Genauigkeit Gedanken machen sollte. Fast ausschlie{\ss}lich habe ich mich auf die Theorie der gleich m{\"a}{\ss}igen Approximation beschr{\"a}nkt, da diese die weitaus gro{\ss}te praktische Bedeutung besitzt. Das erste Kapitel behandelt lineare Approximationen. Der {\S} 3 enth{\"a}lt wohl den heute k{\"u}rzesten Zugang zur linearen Theorie.

rawtitle:
{Approximation von Funktionen und ihre numerische Behandlung}. ({German}) [{Approximation} of functions and their numerical treatment]

rawTOC:
I Lineare Approximationen \\ I.1. Das allgemeine lineare Approximationsproblem \\ I.2. Dichte Systeme \\ I.3. Allgemeine Theorie linearer Tschebyscheff-Approximationen \\ I.4. Spezielle Tschebyscheff-Approximationen \\ I.5. Absch{\"a}tzungen der Gr{\"o}{\ss}enordnung des Fehlers bei trigonometrischer und bei polynomialer Approximation \\ I.6. Polynomapproximationen \\ I.7. Numerische Verfahren bei linearen Tschebyscheff-Approximationen \\ II Nicht-lineare Approximationen \\ II.8. Allgemeine Theorie nicht-linearer Tschebyscheff-Approximationen \\ II.9. Rationale Approximationen \\ II.10. Exponentialapproximationen

entry:
@Book{Meinardus:1964:AFI,
  author =       "Gunter Meinardus",
  title =        "{Approximation von Funktionen und ihre numerische
                 Behandlung}. ({German}) [{Approximation} of functions
                 and their numerical treatment]",
  volume =       "4",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 180",
  year =         "1964",
  DOI =          "https://doi.org/10.1007/978-3-642-85646-4",
  ISBN =         "3-540-03219-3, 3-642-85646-2, 3-642-85647-0 (print)",
  ISBN-13 =      "978-3-540-03219-9, 978-3-642-85646-4,
                 978-3-642-85647-1 (print)",
  LCCN =         "QA320 .M4",
  bibdate =      "Thu Oct 19 17:00:27 MDT 2023",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Springer tracts in natural philosophy",
  abstract =     "[numerous OCR errors to be corrected] Erst in den
                 letzten Jahren hat sich derjenige Tell der
                 Approximations theorie, der sich auf numerische
                 Fragestellungen anwenden l{\"a}{\ss}t, starker
                 entwickelt. Das Prinzip der in einem gewissen Sinne
                 besten Ann{\"a}herung von Funktionen gewann
                 insbesondere durch die Verwendung elektronischer
                 Rechenmaschinen an Bedeutung. Einige der theoretischen
                 Grundlagen, die zur Behandlung der auftretenden
                 Probleme herange zogen werden mussen, finden sich
                 verstreut in wenigen Buchern. Der weitaus gro{\ss}te
                 Teil der theoretischen und praktischen Untersuchungen
                 ist jedoch nur in den Originalarbeiten nachzulesen.
                 Hieraus ergab sich die Zielsetzung des vorliegenden
                 Buches: Es sollte eine Zusammen stellung der
                 wesentlichen Ergebnisse der Approximationstheorie
                 gegeben werden, die einerseits ein rasches Eindringen
                 in die modernen Entwicklungen dieses Gebietes
                 ermoglicht und andererseits eine gewisse
                 Vollst{\"a}ndigkeit auf dem Problemkreis der
                 Tschebyscheff-Approximationen bietet, womit keineswegs
                 gemeint ist, da{\ss} eine vollst{\"a}ndige Literatur
                 {\"u}bersicht angestrebt wurde. Die Auswahl erfolgte
                 stets nach dem immer noch subjektiven Gesichtspunkt der
                 Bedeutung f{\"u}r die Anwendungen. Dies gilt z. B. auch
                 f{\"u}r die asymptotischen Untersuchungen des {\S} 3,
                 denn ich bin der Meinung, da{\ss} man sich auch
                 beinumerischen Approximationen {\"u}ber die, wenigstens
                 asymptotisch zu erwartende Genauigkeit Gedanken machen
                 sollte. Fast ausschlie{\ss}lich habe ich mich auf die
                 Theorie der gleich m{\"a}{\ss}igen Approximation
                 beschr{\"a}nkt, da diese die weitaus gro{\ss}te
                 praktische Bedeutung besitzt. Das erste Kapitel
                 behandelt lineare Approximationen. Der {\S} 3
                 enth{\"a}lt wohl den heute k{\"u}rzesten Zugang zur
                 linearen Theorie.",
  acknowledgement = ack-nhfb,
  author-dates = "1926--",
  language =     "German",
  subject =      "Aproximaciones",
  tableofcontents = "I Lineare Approximationen \\
                 I.1. Das allgemeine lineare Approximationsproblem \\
                 I.2. Dichte Systeme \\
                 I.3. Allgemeine Theorie linearer
                 Tschebyscheff-Approximationen \\
                 I.4. Spezielle Tschebyscheff-Approximationen \\
                 I.5. Absch{\"a}tzungen der Gr{\"o}{\ss}enordnung des
                 Fehlers bei trigonometrischer und bei polynomialer
                 Approximation \\
                 I.6. Polynomapproximationen \\
                 I.7. Numerische Verfahren bei linearen
                 Tschebyscheff-Approximationen \\
                 II Nicht-lineare Approximationen \\
                 II.8. Allgemeine Theorie nicht-linearer
                 Tschebyscheff-Approximationen \\
                 II.9. Rationale Approximationen \\
                 II.10. Exponentialapproximationen",
}


bibtype: incollection
filename: elefunt.bib
label: Miller:1964:PCF
author: J. C. P. Miller
title: Parabolic Cylinder Functions
crossref: Abramowitz:1964:HMF
pages: 685--720
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: J. C. P. Miller
rawtitle: Parabolic Cylinder Functions
entry:
@InCollection{Miller:1964:PCF,
  author =       "J. C. P. Miller",
  title =        "Parabolic Cylinder Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "685--720",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: incollection
filename: elefunt.bib
label: Milne-Thomson:1964:EI
author: L. M. Milne-Thomson
title: Elliptic Integrals
crossref: Abramowitz:1964:HMF
pages: 587--626
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: L. M. Milne-Thomson
rawtitle: Elliptic Integrals
entry:
@InCollection{Milne-Thomson:1964:EI,
  author =       "L. M. Milne-Thomson",
  title =        "Elliptic Integrals",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "587--626",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: incollection
filename: elefunt.bib
label: Milne-Thomson:1964:JEF
author: L. M. Milne-Thomson
title: Jacobian Elliptic Functions and Theta Functions
crossref: Abramowitz:1964:HMF
pages: 567--586
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: L. M. Milne-Thomson
rawtitle: {Jacobian} Elliptic Functions and Theta Functions
entry:
@InCollection{Milne-Thomson:1964:JEF,
  author =       "L. M. Milne-Thomson",
  title =        "{Jacobian} Elliptic Functions and Theta Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "567--586",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: article
filename: elefunt.bib
label: Morelock:1964:AAE
author: J. C. Morelock
title: ACM Algorithm 229: Elementary Functions by Continued Fractions
journal: j-CACM
volume: 7
number: 5
pages: 296
month: may
monthnumber: 5
year: 1964
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 08 09:32:21 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.08 09:32:21 ???
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: J. C. Morelock
rawtitle: {ACM} Algorithm 229: Elementary Functions by Continued Fractions
entry:
@Article{Morelock:1964:AAE,
  author =       "J. C. Morelock",
  title =        "{ACM} Algorithm 229: Elementary Functions by Continued
                 Fractions",
  journal =      j-CACM,
  volume =       "7",
  number =       "5",
  pages =        "296",
  month =        may,
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 08 09:32:21 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
}


bibtype: incollection
filename: elefunt.bib
label: Oberhettinger:1964:HF
author: Frtiz Oberhettinger
title: Hypergeometric Functions
crossref: Abramowitz:1964:HMF
pages: 555--566
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Frtiz Oberhettinger
rawtitle: Hypergeometric Functions
entry:
@InCollection{Oberhettinger:1964:HF,
  author =       "Frtiz Oberhettinger",
  title =        "Hypergeometric Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "555--566",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: incollection
filename: elefunt.bib
label: Olver:1964:BFI
author: F. W. J. Olver
title: Bessel Functions of Integer Order
crossref: Abramowitz:1964:HMF
pages: 355--434
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: F. W. J. Olver
rawtitle: {Bessel} Functions of Integer Order
entry:
@InCollection{Olver:1964:BFI,
  author =       "F. W. J. Olver",
  title =        "{Bessel} Functions of Integer Order",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "355--434",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: article
filename: elefunt.bib
label: Schmidt:1964:AEC
author: Paul W. Schmidt
title: Asymptotic Expansion of Certain Integrals Containing the Bessel Function $ J_0 (x) $
journal: j-J-MATH-PHYS
volume: 5
number: 8
pages: 1183--1184
month: aug
monthnumber: 8
year: 1964
CODEN: JMAPAQ
DOI: https://doi.org/10.1063/1.1704223
ISSNL: 0022-2488 OR 00222488
bibdate: Fri Oct 28 08:40:15 MDT 2011
bibtimestamp: 2011.10.28 08:40:15 MDT
URL: http://jmp.aip.org/resource/1/jmapaq/v5/i8/p1183_s1
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
onlinedate: 22 December 2004
rawauthor: Paul W. Schmidt
rawtitle: Asymptotic Expansion of Certain Integrals Containing the {Bessel} Function {$ J_0 (x) $}
ISSN:
0022-2488 (print), 1089-7658 (electronic), 1527-2427 OR 00222488 (print), 10897658 (electronic), 15272427

bibsource:
http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys1960.bib

entry:
@Article{Schmidt:1964:AEC,
  author =       "Paul W. Schmidt",
  title =        "Asymptotic Expansion of Certain Integrals Containing
                 the {Bessel} Function {$ J_0 (x) $}",
  journal =      j-J-MATH-PHYS,
  volume =       "5",
  number =       "8",
  pages =        "1183--1184",
  month =        aug,
  year =         "1964",
  CODEN =        "JMAPAQ",
  DOI =          "https://doi.org/10.1063/1.1704223",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Fri Oct 28 08:40:15 MDT 2011",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys1960.bib",
  URL =          "http://jmp.aip.org/resource/1/jmapaq/v5/i8/p1183_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
  onlinedate =   "22 December 2004",
  pagecount =    "2",
}


bibtype: article
filename: elefunt.bib
label: Simauti:1964:AFS
author: Takakazu Simauti
title: Approximation formulas for some elementary functions
journal: Comment. Math. Univ. St. Paul.
volume: 12
pages: 23--35
year: 1964
CODEN: COMAAC
ISSN: 0010-258X OR 0010258X
MRclass: 65.25
MRnumber: 28 \#5552
MRreviewer: John Todd
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: Takakazu Simauti
rawtitle: Approximation formulas for some elementary functions
entry:
@Article{Simauti:1964:AFS,
  author =       "Takakazu Simauti",
  title =        "Approximation formulas for some elementary functions",
  journal =      "Comment. Math. Univ. St. Paul.",
  volume =       "12",
  pages =        "23--35",
  year =         "1964",
  CODEN =        "COMAAC",
  ISSN =         "0010-258X",
  MRclass =      "65.25",
  MRnumber =     "28 \#5552",
  MRreviewer =   "John Todd",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: incollection
filename: elefunt.bib
label: Slater:1964:CHF
author: Lucy Joan Slater
title: Confluent Hvpergeometric Functions
crossref: Abramowitz:1964:HMF
pages: 503--536
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Lucy Joan Slater
rawtitle: Confluent Hvpergeometric Functions
entry:
@InCollection{Slater:1964:CHF,
  author =       "Lucy Joan Slater",
  title =        "Confluent Hvpergeometric Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "503--536",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: article
filename: elefunt.bib
label: Slepian:1964:PSW
author: David Slepian
journal: j-BELL-SYST-TECH-J
volume: 43
number: 6
pages: 3009--3057
month: nov
monthnumber: 11
year: 1964
CODEN: BSTJAN
ISSN: 0005-8580 OR 00058580
MRclass: 33.28
MRnumber: 0181766 (31 \#5993)
MRreviewer: J. Meixner
bibdate: Tue Nov 9 11:15:55 MST 2010
bibtimestamp: 2010.11.09 11:15:55 MST
URL: http://bstj.bell-labs.com/BSTJ/images/Vol43/bstj43-6-3009.pdf
fjournal: The Bell System Technical Journal
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: David Slepian
title:
Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty --- IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions

bibsource:
http://bstj.bell-labs.com/oldfiles/year.1964/BSTJ.1964.4306.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Prolate Spheroidal Wave Functions, {Fourier} Analysis and Uncertainty --- {IV}: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions

entry:
@Article{Slepian:1964:PSW,
  author =       "David Slepian",
  title =        "Prolate Spheroidal Wave Functions, {Fourier} Analysis
                 and Uncertainty --- {IV}: Extensions to Many
                 Dimensions; Generalized Prolate Spheroidal Functions",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "43",
  number =       "6",
  pages =        "3009--3057",
  month =        nov,
  year =         "1964",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  MRclass =      "33.28",
  MRnumber =     "0181766 (31 \#5993)",
  MRreviewer =   "J. Meixner",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1964/BSTJ.1964.4306.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol43/bstj43-6-3009.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}


bibtype: incollection
filename: elefunt.bib
label: Southard:1964:WER
author: Thomas H. Southard
title: Weierstrass Elliptic and Related Functions
crossref: Abramowitz:1964:HMF
pages: 627--684
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Thomas H. Southard
rawtitle: {Weierstrass} Elliptic and Related Functions
entry:
@InCollection{Southard:1964:WER,
  author =       "Thomas H. Southard",
  title =        "{Weierstrass} Elliptic and Related Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "627--684",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: incollection
filename: elefunt.bib
label: Stegun:1964:LF
author: Irene A. Stegun
title: Legendre Functions
crossref: Abramowitz:1964:HMF
pages: 331--354
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Irene A. Stegun
rawtitle: {Legendre} Functions
entry:
@InCollection{Stegun:1964:LF,
  author =       "Irene A. Stegun",
  title =        "{Legendre} Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "331--354",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: incollection
filename: elefunt.bib
label: Stegun:1964:MF
author: Irene A. Stegun
title: Miscellaneous Functions
crossref: Abramowitz:1964:HMF
pages: 997--1010
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Irene A. Stegun
rawtitle: Miscellaneous Functions
keywords:
Clausen's integral; Clebsch--Gordan coefficients; Debye function; Dilogarithm (Spence's integral); Einstein function; Planck function; Sievert and related integrals

remark:
Fullerton: Debye, Planck and Einstein functions. Sievert and related integrals. Dilogarithm (Spence's integral). Clausen's integral. Clebsch--Gordan coefficients.

entry:
@InCollection{Stegun:1964:MF,
  author =       "Irene A. Stegun",
  title =        "Miscellaneous Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "997--1010",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  keywords =     "Clausen's integral; Clebsch--Gordan coefficients;
                 Debye function; Dilogarithm (Spence's integral);
                 Einstein function; Planck function; Sievert and related
                 integrals",
  remark =       "Fullerton: Debye, Planck and Einstein functions.
                 Sievert and related integrals. Dilogarithm (Spence's
                 integral). Clausen's integral. Clebsch--Gordan
                 coefficients.",
}


bibtype: article
filename: elefunt.bib
label: Wengert:1964:SAD
author: R. E. Wengert
title: A simple automatic derivative evaluation program
journal: j-CACM
volume: 7
number: 8
pages: 463--464
year: 1964
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Mon May 19 13:30:58 1997
bibtimestamp: 1997.05.19 13:30:58 ???
fjournal: Communications of the ACM
keywords: computer program.; differentiation arithmetic; point algorithm
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: R. E. Wengert
rawtitle: A simple automatic derivative evaluation program
bibsource:
ftp://ftp.ira.uka.de/pub/bibliography/Math/auto.diff.bib.gz; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

abstract:
A procedure for automatic evaluation of total and partial derivatives of arbitrary algebraic functions is presented. The numerical values of derivatives are computed without developing analytic expressions for the derivatives. The function is decomposed into a sequence of elementary expressions A library is provided for differentiating of elementary functions.

rawabstract:
A procedure for automatic evaluation of total and partial derivatives of arbitrary algebraic functions is presented. The numerical values of derivatives are computed without developing analytic expressions for the derivatives. The function is decomposed into a sequence of elementary expressions A library is provided for differentiating of elementary functions.

entry:
@Article{Wengert:1964:SAD,
  author =       "R. E. Wengert",
  title =        "A simple automatic derivative evaluation program",
  journal =      j-CACM,
  volume =       "7",
  number =       "8",
  pages =        "463--464",
  year =         "1964",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Mon May 19 13:30:58 1997",
  bibsource =    "ftp://ftp.ira.uka.de/pub/bibliography/Math/auto.diff.bib.gz;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "A procedure for automatic evaluation of total and
                 partial derivatives of arbitrary algebraic functions is
                 presented. The numerical values of derivatives are
                 computed without developing analytic expressions for
                 the derivatives. The function is decomposed into a
                 sequence of elementary expressions A library is
                 provided for differentiating of elementary functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "computer program.; differentiation arithmetic; point
                 algorithm",
  referred =     "[Bell65a]; [Carl86a]; [Corl88a]; [Garc91a]; [Irim91a];
                 [Kala83b]; [Laws88a]; [Laws91a]; [Neid87a]; [Neid89a];
                 [Ostr71a]; [Pfei87a]; [Tesf91a]; [Voli85a]; [Wexl87a];
                 [Wilk64a].",
}


bibtype: incollection
filename: elefunt.bib
label: Zelen:1964:PF
author: Marvin Zelen and Norman C. Severo
title: Probability Functions
crossref: Abramowitz:1964:HMF
pages: 925--996
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Marvin Zelen and Norman C. Severo
rawtitle: Probability Functions
entry:
@InCollection{Zelen:1964:PF,
  author =       "Marvin Zelen and Norman C. Severo",
  title =        "Probability Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "925--996",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: incollection
filename: elefunt.bib
label: Zucker:1964:ETF
author: Ruth Zucker
title: Elementary Transcendental Functions. Logarithmic, Exponential, Circular and Hyperbolic Functions
crossref: Abramowitz:1964:HMF
pages: 65--226
year: 1964
bibdate: Sat Oct 30 19:37:56 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:37:56 ???
acknowledgement: ack-nhfb
rawauthor: Ruth Zucker
rawtitle: Elementary Transcendental Functions. {Logarithmic}, Exponential, Circular and Hyperbolic Functions
entry:
@InCollection{Zucker:1964:ETF,
  author =       "Ruth Zucker",
  title =        "Elementary Transcendental Functions. {Logarithmic},
                 Exponential, Circular and Hyperbolic Functions",
  crossref =     "Abramowitz:1964:HMF",
  pages =        "65--226",
  year =         "1964",
  bibdate =      "Sat Oct 30 19:37:56 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
}


bibtype: article
filename: elefunt.bib
label: Bingulac:1965:ACG
author: S. P. Bingulac and E. A. Humo
title: Analog Computer Generation of Bessel Functions of Arbitrary Order
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-14
number: 6
pages: 886--889
month: dec
monthnumber: 12
year: 1965
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1965.264084
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:26:41 MDT 2011
bibtimestamp: 2011.07.14 06:26:41 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038609
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: S. P. Bingulac and E. A. Humo
rawtitle: Analog Computer Generation of {Bessel} Functions of Arbitrary Order
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib

entry:
@Article{Bingulac:1965:ACG,
  author =       "S. P. Bingulac and E. A. Humo",
  title =        "Analog Computer Generation of {Bessel} Functions of
                 Arbitrary Order",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "6",
  pages =        "886--889",
  month =        dec,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264084",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:41 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038609",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: elefunt.bib
label: Braess:1965:MIG
author: Dietrich Braess
journal: j-NUM-MATH
volume: 7
number: 1
pages: 32--41
month: feb
monthnumber: 2
year: 1965
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon Oct 18 01:28:20 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.18 01:28:20 MDT
fjournal: Numerische Mathematik
keywords: convergence acceleration
language: German
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: Dietrich Braess
title:
Monotone Iterationsfolgen bei Gleichungssystemen mit fehlerhaften Koeffizienten und Iterationsbeschleunigung. (German) [Monotone Iteration Sequences for Equation Systems with Coefficients Having Errors, and Iteration Acceleration]

rawtitle:
{Monotone Iterationsfolgen bei Gleichungssystemen mit fehlerhaften Koeffizienten und Iterationsbeschleunigung}. ({German}) [{Monotone} Iteration Sequences for Equation Systems with Coefficients Having Errors, and Iteration Acceleration]

entry:
@Article{Braess:1965:MIG,
  author =       "Dietrich Braess",
  title =        "{Monotone Iterationsfolgen bei Gleichungssystemen mit
                 fehlerhaften Koeffizienten und
                 Iterationsbeschleunigung}. ({German}) [{Monotone}
                 Iteration Sequences for Equation Systems with
                 Coefficients Having Errors, and Iteration
                 Acceleration]",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "1",
  pages =        "32--41",
  month =        feb,
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 01:28:20 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "convergence acceleration",
  language =     "German",
}


bibtype: article
filename: elefunt.bib
label: Bulirsch:1965:NCEa
author: R. Bulirsch
title: Numerical calculation of elliptic integrals and elliptic functions
journal: j-NUM-MATH
volume: 7
number: 1
pages: 78--90
month: feb
monthnumber: 2
year: 1965
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon Oct 18 20:10:40 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.18 20:10:40 MDT
series: Handbook Series Special functions
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: R. Bulirsch
rawtitle: Numerical calculation of elliptic integrals and elliptic functions
entry:
@Article{Bulirsch:1965:NCEa,
  author =       "R. Bulirsch",
  title =        "Numerical calculation of elliptic integrals and
                 elliptic functions",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "1",
  pages =        "78--90",
  month =        feb,
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 20:10:40 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Handbook Series Special functions",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Bulirsch:1965:NCEb
author: R. Bulirsch
title: Numerical calculation of elliptic integrals and elliptic functions. II
journal: j-NUM-MATH
volume: 7
number: 4
pages: 353--354
month: aug
monthnumber: 8
year: 1965
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sun Oct 17 16:12:48 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.17 16:12:48 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: R. Bulirsch
rawtitle: Numerical calculation of elliptic integrals and elliptic functions. {II}
entry:
@Article{Bulirsch:1965:NCEb,
  author =       "R. Bulirsch",
  title =        "Numerical calculation of elliptic integrals and
                 elliptic functions. {II}",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "4",
  pages =        "353--354",
  month =        aug,
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 16:12:48 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Christiansen:1965:APE
author: S. Christiansen
title: Algol programming: Error Integral with Complex Argument
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 5
number: 4
pages: 287--293
month: dec
monthnumber: 12
year: 1965
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01937509
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:09 MST 2006
bibtimestamp: 2006.01.04 18:52:09 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=4&spage=287
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: S. Christiansen
rawtitle: {Algol} programming: Error Integral with Complex Argument
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=4; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

remark:
Fullerton: A 75-line Algol procedure with maximum absolute error about $ 2 times 10^-6 $ is given for $ w(z) = e^-z^2 erfc ( - i z) $.

entry:
@Article{Christiansen:1965:APE,
  author =       "S. Christiansen",
  title =        "{Algol} programming: Error Integral with Complex
                 Argument",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "5",
  number =       "4",
  pages =        "287--293",
  month =        dec,
  year =         "1965",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01937509",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:09 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=4;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=4&spage=287",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  journal-URL =  "http://link.springer.com/journal/10543",
  remark =       "Fullerton: A 75-line Algol procedure with maximum
                 absolute error about $ 2 \times 10^{-6} $ is given for
                 $ w(z) = e^{-z^2} \erfc ( - i z) $.",
}


bibtype: article
filename: elefunt.bib
label: Cochran:1965:ZHF
author: J. A. Cochran
title: The zeros of Hankel functions as functions of their order
journal: j-NUM-MATH
volume: 7
number: 3
pages: 238--250
month: jun
monthnumber: 6
year: 1965
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Mon Oct 18 10:06:00 MDT 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.18 10:06:00 MDT
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: J. A. Cochran
rawtitle: The zeros of {Hankel} functions as functions of their order
entry:
@Article{Cochran:1965:ZHF,
  author =       "J. A. Cochran",
  title =        "The zeros of {Hankel} functions as functions of their
                 order",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "3",
  pages =        "238--250",
  month =        jun,
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Mon Oct 18 10:06:00 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Cody:1965:CAC
author: W. J. Cody, Jr.
title: Chebyshev Approximations for the Complete Elliptic Integrals $K$ and $E$
journal: j-MATH-COMPUT
volume: 19
number: 89--92
pages: 105--112
month: apr
monthnumber: 4
year: 1965
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65.05
MRnumber: 30\#1601
bibdate: Fri Oct 23 11:10:16 1998
bibtimestamp: 1998.10.23 11:10:16 ???
note: See also cite Cody:1966:CCA.
URL: http://www.jstor.org/stable/2004103
fjournal: Mathematics of Computation
remark: Fullerton: Relative errors down to $ 4 times 10^-18 $.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: W. J. {Cody, Jr.}
rawnote: See also \cite{Cody:1966:CCA}.
rawtitle: {Chebyshev} Approximations for the Complete Elliptic Integrals {$K$} and {$E$}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Cody:1965:CAC,
  author =       "W. J. {Cody, Jr.}",
  title =        "{Chebyshev} Approximations for the Complete Elliptic
                 Integrals {$K$} and {$E$}",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89--92",
  pages =        "105--112",
  month =        apr,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.05",
  MRnumber =     "30\#1601",
  bibdate =      "Fri Oct 23 11:10:16 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Cody:1966:CCA}.",
  URL =          "http://www.jstor.org/stable/2004103",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Relative errors down to $ 4 \times 10^{-18}
                 $.",
}


bibtype: article
filename: elefunt.bib
label: Cody:1965:CPE
author: W. J. Cody, Jr.
title: Chebyshev Polynomial Expansions of Complete Elliptic Integrals
journal: j-MATH-COMPUT
volume: 19
number: 89--92
pages: 249--259
month: apr
monthnumber: 4
year: 1965
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
MRclass: 65.25
MRnumber: 31\#2820
bibdate: Fri Oct 23 11:10:33 1998
bibtimestamp: 1998.10.23 11:10:33 ???
URL: http://www.jstor.org/stable/2003350
fjournal: Mathematics of Computation
remark: Fullerton: 25-digit approximations.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: W. J. {Cody, Jr.}
rawtitle: {Chebyshev} Polynomial Expansions of Complete Elliptic Integrals
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Cody:1965:CPE,
  author =       "W. J. {Cody, Jr.}",
  title =        "{Chebyshev} Polynomial Expansions of Complete Elliptic
                 Integrals",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89--92",
  pages =        "249--259",
  month =        apr,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  MRclass =      "65.25",
  MRnumber =     "31\#2820",
  bibdate =      "Fri Oct 23 11:10:33 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2003350",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: 25-digit approximations.",
}


bibtype: article
filename: elefunt.bib
label: Combet:1965:CBT
author: M. Combet and H. Van Zonneveld and L. Verbeek
title: Computation of the Base Two Logarithm of Binary Numbers
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-14
number: 6
pages: 863--867
month: dec
monthnumber: 12
year: 1965
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1965.264080
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:26:41 MDT 2011
bibtimestamp: 2011.07.14 06:26:41 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038605
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: M. Combet and H. {Van Zonneveld} and L. Verbeek
rawtitle: Computation of the Base Two Logarithm of Binary Numbers
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/ieeetranscomput.bib

entry:
@Article{Combet:1965:CBT,
  author =       "M. Combet and H. {Van Zonneveld} and L. Verbeek",
  title =        "Computation of the Base Two Logarithm of Binary
                 Numbers",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "6",
  pages =        "863--867",
  month =        dec,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.264080",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:41 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/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038605",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: elefunt.bib
label: Dahlquist:1965:CAP
author: Germund Dahlquist and Sven-AA ke Gustafson and Karoly Siklosi
title: Convergence Acceleration from the Point of View of Linear Programming
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 5
number: 1
pages: 1--16
month: mar
monthnumber: 3
year: 1965
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01975719
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
bibdate: Wed Jan 4 18:52:08 MST 2006
bibtimestamp: 2006.01.04 18:52:08 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=1&spage=1
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Germund Dahlquist and Sven-{\AA}ke Gustafson and K{\'a}roly Sikl{\'o}si
rawtitle: Convergence Acceleration from the Point of View of Linear Programming
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=1; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Dahlquist:1965:CAP,
  author =       "Germund Dahlquist and Sven-{\AA}ke Gustafson and
                 K{\'a}roly Sikl{\'o}si",
  title =        "Convergence Acceleration from the Point of View of
                 Linear Programming",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "5",
  number =       "1",
  pages =        "1--16",
  month =        mar,
  year =         "1965",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01975719",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  bibdate =      "Wed Jan 4 18:52:08 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=5&issue=1;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=5&issue=1&spage=1",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Fettis:1965:CEI
author: Henry E. Fettis
title: Calculation of Elliptic Integrals of the Third Kind by Means of Gauss' Transformation
journal: j-MATH-COMPUT
volume: 19
number: 89
pages: 97--104
month: apr
monthnumber: 4
year: 1965
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
URL: http://www.jstor.org/stable/2004102
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Henry E. Fettis
rawtitle: Calculation of Elliptic Integrals of the Third Kind by Means of {Gauss}' Transformation
entry:
@Article{Fettis:1965:CEI,
  author =       "Henry E. Fettis",
  title =        "Calculation of Elliptic Integrals of the Third Kind by
                 Means of {Gauss}' Transformation",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89",
  pages =        "97--104",
  month =        apr,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  URL =          "http://www.jstor.org/stable/2004102",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Fields:1965:RAG
author: Jerry L. Fields
title: Rational Approximations to Generalized Hypergeometric Functions
journal: j-MATH-COMPUT
volume: 19
number: 92
pages: 606--624
month: oct
monthnumber: 10
year: 1965
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Jerry L. Fields
rawtitle: Rational Approximations to Generalized Hypergeometric Functions
entry:
@Article{Fields:1965:RAG,
  author =       "Jerry L. Fields",
  title =        "Rational Approximations to Generalized Hypergeometric
                 Functions",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "92",
  pages =        "606--624",
  month =        oct,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Franke:1965:NEE
author: Charles H. Franke
journal: j-MATH-COMPUT
volume: 19
number: 91
pages: 494--496
month: jul
monthnumber: 7
year: 1965
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Charles H. Franke
title:
Numerical Evaluation of the Elliptic Integral of the Third Kind (in Technical Notes and Short Papers)

rawtitle:
Numerical Evaluation of the Elliptic Integral of the Third Kind (in {Technical Notes and Short Papers})

entry:
@Article{Franke:1965:NEE,
  author =       "Charles H. Franke",
  title =        "Numerical Evaluation of the Elliptic Integral of the
                 Third Kind (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "91",
  pages =        "494--496",
  month =        jul,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Fraser:1965:SMC
author: W. Fraser
journal: j-J-ACM
volume: 12
number: 3
pages: 295--314
month: jul
monthnumber: 7
year: 1965
CODEN: JACOAH
DOI: https://doi.org/10.1145/321281.321282
ISSN: 0004-5411 (print), 1557-735X (electronic) OR 00045411 (print), 1557735X (electronic)
ISSNL: 0004-5411 OR 00045411
bibdate: Thu Nov 03 08:47:50 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.11.03 08:47:50 ???
fjournal: Journal of the ACM
acknowledgement: ack-nhfb
ajournal: J. Assoc. Comput. Mach.
journalURL: https://dl.acm.org/loi/jacm
rawauthor: W. Fraser
title:
A Survey of Methods for Computing Minimax and Near-Minimax Polynomial Approximations for Functions of a Single Independent Variable

abstract:
Methods are described for the derivation of minimax and near-minimax polynomial approximations. For minimax approximations techniques are considered for both analytically defined functions and functions defined by a table of values. For near-minimax approximations methods of determining the coefficients of the Fourier--Chebyshev expansion are first described. These consist of the rearrangement of the coefficients of a power polynomial, and also direct determination of the coefficients from the integral which defines them, or the differential equation which defines the function. Finally there is given a convenient modification of an interpolation scheme which finds coefficients of a near-minimax approximation without requiring numerical integration or the numerical solution of a system of equations.

rawabstract:
Methods are described for the derivation of minimax and near-minimax polynomial approximations. For minimax approximations techniques are considered for both analytically defined functions and functions defined by a table of values. For near-minimax approximations methods of determining the coefficients of the Fourier--Chebyshev expansion are first described. These consist of the rearrangement of the coefficients of a power polynomial, and also direct determination of the coefficients from the integral which defines them, or the differential equation which defines the function. Finally there is given a convenient modification of an interpolation scheme which finds coefficients of a near-minimax approximation without requiring numerical integration or the numerical solution of a system of equations.

rawtitle:
A Survey of Methods for Computing Minimax and Near-Minimax Polynomial Approximations for Functions of a Single Independent Variable

entry:
@Article{Fraser:1965:SMC,
  author =       "W. Fraser",
  title =        "A Survey of Methods for Computing Minimax and
                 Near-Minimax Polynomial Approximations for Functions of
                 a Single Independent Variable",
  journal =      j-J-ACM,
  volume =       "12",
  number =       "3",
  pages =        "295--314",
  month =        jul,
  year =         "1965",
  CODEN =        "JACOAH",
  DOI =          "https://doi.org/10.1145/321281.321282",
  ISSN =         "0004-5411 (print), 1557-735X (electronic)",
  ISSN-L =       "0004-5411",
  bibdate =      "Thu Nov 03 08:47:50 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Methods are described for the derivation of minimax
                 and near-minimax polynomial approximations. For minimax
                 approximations techniques are considered for both
                 analytically defined functions and functions defined by
                 a table of values. For near-minimax approximations
                 methods of determining the coefficients of the
                 Fourier--Chebyshev expansion are first described. These
                 consist of the rearrangement of the coefficients of a
                 power polynomial, and also direct determination of the
                 coefficients from the integral which defines them, or
                 the differential equation which defines the function.
                 Finally there is given a convenient modification of an
                 interpolation scheme which finds coefficients of a
                 near-minimax approximation without requiring numerical
                 integration or the numerical solution of a system of
                 equations.",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Assoc. Comput. Mach.",
  fjournal =     "Journal of the ACM",
  journal-URL =  "https://dl.acm.org/loi/jacm",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1965:ALF
author: W. Gautschi
title: Algorithm 259: Legendre Functions for Arguments Larger than One [S16]
journal: j-CACM
volume: 8
number: 8
pages: 488--492
month: aug
monthnumber: 8
year: 1965
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:01 MST 2005
bibtimestamp: 2005.11.25 18:20:01 MST
note: See also cite Jansen:1977:RLF.
fjournal: Communications of the ACM
keywords: Legendre functions; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: W. Gautschi
rawnote: See also \cite{Jansen:1977:RLF}.
rawtitle: {Algorithm 259}: {Legendre} Functions for Arguments Larger than One [{S16}]
remark:
Fullerton: Long Algol procedures for the associated Legendre functions of the first and second kinds: $ P_a^n(x) $ and $ Q_n^m $.

entry:
@Article{Gautschi:1965:ALF,
  author =       "W. Gautschi",
  title =        "{Algorithm 259}: {Legendre} Functions for Arguments
                 Larger than One [{S16}]",
  journal =      j-CACM,
  volume =       "8",
  number =       "8",
  pages =        "488--492",
  month =        aug,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:01 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Jansen:1977:RLF}.",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Legendre functions; special functions",
  remark =       "Fullerton: Long Algol procedures for the associated
                 Legendre functions of the first and second kinds: $
                 P_a^n(x) $ and $ Q_n^m $.",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1965:CAS
author: Walter Gautschi
title: Certification of Algorithm 236 [S17]: Bessel functions of the first kind
journal: j-CACM
volume: 8
number: 2
pages: 105--106
month: feb
monthnumber: 2
year: 1965
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:58 MST 2005
bibtimestamp: 2005.11.25 18:19:58 MST
fjournal: Communications of the ACM
keywords: $J_n(x)$; Bessel functions of the first kind; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Walter Gautschi
rawtitle: Certification of {Algorithm 236} [{S17}]: {Bessel} functions of the first kind
entry:
@Article{Gautschi:1965:CAS,
  author =       "Walter Gautschi",
  title =        "Certification of {Algorithm 236} [{S17}]: {Bessel}
                 functions of the first kind",
  journal =      j-CACM,
  volume =       "8",
  number =       "2",
  pages =        "105--106",
  month =        feb,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:58 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$J_n(x)$; Bessel functions of the first kind; special
                 functions",
}


bibtype: article
filename: elefunt.bib
label: Gunn:1965:ASa
author: J. H. Gunn
title: Algorithm 260: 6-$J$ symbols
journal: j-CACM
volume: 8
number: 8
pages: 492--492
month: aug
monthnumber: 8
year: 1965
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:01 MST 2005
bibtimestamp: 2005.11.25 18:20:01 MST
fjournal: Communications of the ACM
remark: Fullerton: Short Algol procedure.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: J. H. Gunn
rawtitle: {Algorithm 260}: {6-$J$} symbols
entry:
@Article{Gunn:1965:ASa,
  author =       "J. H. Gunn",
  title =        "{Algorithm 260}: {6-$J$} symbols",
  journal =      j-CACM,
  volume =       "8",
  number =       "8",
  pages =        "492--492",
  month =        aug,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:01 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: Short Algol procedure.",
}


bibtype: article
filename: elefunt.bib
label: Gunn:1965:ASb
author: J. H. Gunn
title: Algorithm 261: 9-$J$ symbols
journal: j-CACM
volume: 8
number: 8
pages: 492--493
month: aug
monthnumber: 8
year: 1965
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:01 MST 2005
bibtimestamp: 2005.11.25 18:20:01 MST
fjournal: Communications of the ACM
remark: Fullerton: Short Algol procedure.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: J. H. Gunn
rawtitle: {Algorithm 261}: {9-$J$} symbols
entry:
@Article{Gunn:1965:ASb,
  author =       "J. H. Gunn",
  title =        "{Algorithm 261}: {9-$J$} symbols",
  journal =      j-CACM,
  volume =       "8",
  number =       "8",
  pages =        "492--493",
  month =        aug,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:01 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: Short Algol procedure.",
}


bibtype: article
filename: elefunt.bib
label: Gunn:1965:AZV
author: J. H. Gunn
title: Algorithm 252 [Z]: Vector coupling or Clebsch--Gordan coefficients
journal: j-CACM
volume: 8
number: 4
pages: 217--217
month: apr
monthnumber: 4
year: 1965
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:19:59 MST 2005
bibtimestamp: 2005.11.25 18:19:59 MST
fjournal: Communications of the ACM
remark: Fullerton: Short Algol procedure.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: J. H. Gunn
rawtitle: {Algorithm 252} [{Z}]: {Vector} coupling or {Clebsch--Gordan} coefficients
entry:
@Article{Gunn:1965:AZV,
  author =       "J. H. Gunn",
  title =        "{Algorithm 252} [{Z}]: {Vector} coupling or
                 {Clebsch--Gordan} coefficients",
  journal =      j-CACM,
  volume =       "8",
  number =       "4",
  pages =        "217--217",
  month =        apr,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:19:59 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  remark =       "Fullerton: Short Algol procedure.",
}


bibtype: article
filename: elefunt.bib
label: Heatley:1965:ETT
author: A. H. Heatley
title: An Extension of the Table of the Toronto Function (in Technical Notes and Short Papers)
journal: j-MATH-COMPUT
volume: 19
number: 89
pages: 118--123
month: apr
monthnumber: 4
year: 1965
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: Some 5 and 7-digit values.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: A. H. Heatley
rawtitle: An Extension of the Table of the {Toronto} Function (in {Technical Notes and Short Papers})
entry:
@Article{Heatley:1965:ETT,
  author =       "A. H. Heatley",
  title =        "An Extension of the Table of the {Toronto} Function
                 (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89",
  pages =        "118--123",
  month =        apr,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Some 5 and 7-digit values.",
}


bibtype: article
filename: elefunt.bib
label: James:1965:GSR
author: Wendy James and P. Jarratt
journal: j-MATH-COMPUT
volume: 19
number: 91
pages: 497--500
month: jul
monthnumber: 7
year: 1965
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nj
journalURL: http://www.ams.org/mcom/
rawauthor: Wendy James and P. Jarratt
title:
The Generation of Square Roots on a Computer with Rapid Multiplication Compared with Division (in Technical Notes and Short Papers)

bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; 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/mathcomp1960.bib; JSTOR database

rawtitle:
The Generation of Square Roots on a Computer with Rapid Multiplication Compared with Division (in {Technical Notes and Short Papers})

entry:
@Article{James:1965:GSR,
  author =       "Wendy James and P. Jarratt",
  title =        "The Generation of Square Roots on a Computer with
                 Rapid Multiplication Compared with Division (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "91",
  pages =        "497--500",
  month =        jul,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 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/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Kazangapov:1965:REF
author: A. N. Kazangapov
title: Representation of elementary function in the system of residual classes. (Russian)
journal: Izv. Akad. Nauk Kazah. SSR Ser. Fiz.-Mat. Nauk
volume: 3
pages: 79--84
year: 1965
MRclass: 65.25
MRnumber: 33 \#5090
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: A. N. Kazangapov
rawtitle: Representation of elementary function in the system of residual classes. ({Russian})
entry:
@Article{Kazangapov:1965:REF,
  author =       "A. N. Kazangapov",
  title =        "Representation of elementary function in the system of
                 residual classes. ({Russian})",
  journal =      "Izv. Akad. Nauk Kazah. SSR Ser. Fiz.-Mat. Nauk",
  volume =       "3",
  pages =        "79--84",
  year =         "1965",
  MRclass =      "65.25",
  MRnumber =     "33 \#5090",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: King:1965:LED
author: R. King
title: Letter to the Editor: On the Double-Precision Square Root Routine
journal: j-CACM
volume: 8
number: 4
pages: 202
month: apr
monthnumber: 4
year: 1965
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 1 10:15:43 1994
bibtimestamp: 1994.09.01 10:15:43 ???
fjournal: Communications of the ACM
keywords: $sqrt (x)$; elementary functions; floating-point arithmetic
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: R. King
rawtitle: Letter to the {Editor}: On the Double-Precision Square Root Routine
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{King:1965:LED,
  author =       "R. King",
  title =        "Letter to the {Editor}: On the Double-Precision Square
                 Root Routine",
  journal =      j-CACM,
  volume =       "8",
  number =       "4",
  pages =        "202",
  month =        apr,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; floating-point
                 arithmetic",
}


bibtype: book
filename: elefunt.bib
label: Lebedev:1965:SFT
author: N. N. (Nikolaui i Nikolaevich) Lebedev
title: Special Functions and Their Applications
publisher: pub-PH
address: pub-PH:adr
pages: xii + 308
year: 1965
LCCN: QA351 .L3613
bibdate: Sat Apr 1 14:42:46 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:42:46 MDT
note: Revised English edition translated and edited by Richard A. Silverman.
series: Selected Russian publications in the mathematical sciences
subject: Functions, Special; Mathematical physics
acknowledgement: ack-nhfb
rawauthor: N. N. (Nikola{\u\i}i Nikolaevich) Lebedev
rawnote: Revised English edition translated and edited by Richard A. Silverman.
rawtitle: Special Functions and Their Applications
entry:
@Book{Lebedev:1965:SFT,
  author =       "N. N. (Nikola{\u\i}i Nikolaevich) Lebedev",
  title =        "Special Functions and Their Applications",
  publisher =    pub-PH,
  address =      pub-PH:adr,
  pages =        "xii + 308",
  year =         "1965",
  LCCN =         "QA351 .L3613",
  bibdate =      "Sat Apr 1 14:42:46 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  note =         "Revised English edition translated and edited by
                 Richard A. Silverman.",
  series =       "Selected Russian publications in the mathematical
                 sciences",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Mathematical physics",
}


bibtype: book
filename: elefunt.bib
label: Lyusternik:1965:HCE
author: L. A. Lyusternik and O. A. Chervonenkis and A. R. Yanpolskii
title: Handbook for Computing Elementary Functions
volume: 76
publisher: pub-PERGAMON
address: pub-PERGAMON:adr
pages: xiii + 251
year: 1965
LCCN: QA221.L513
MRclass: 65.25
MRnumber: 32 \#584
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
note: Translated from the Russian by G. J. Tee. Translation edited by K. L. Stewart.
series: International series of monographs on pure and applied mathematics
acknowledgement: ack-nhfb
rawauthor: L. A. Lyusternik and O. A. Chervonenkis and A. R. Yanpol{\'s}kii
rawnote: Translated from the Russian by G. J. Tee. Translation edited by K. L. Stewart.
rawtitle: Handbook for Computing Elementary Functions
entry:
@Book{Lyusternik:1965:HCE,
  author =       "L. A. Lyusternik and O. A. Chervonenkis and A. R.
                 Yanpol{\'s}kii",
  title =        "Handbook for Computing Elementary Functions",
  volume =       "76",
  publisher =    pub-PERGAMON,
  address =      pub-PERGAMON:adr,
  pages =        "xiii + 251",
  year =         "1965",
  LCCN =         "QA221.L513",
  MRclass =      "65.25",
  MRnumber =     "32 \#584",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Translated from the Russian by G. J. Tee. Translation
                 edited by K. L. Stewart.",
  series =       "International series of monographs on pure and applied
                 mathematics",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: MacLaren:1965:APN
author: M. D. MacLaren
title: Algorithm 272: Procedure for the Normal Distribution Functions [S15]
journal: j-CACM
volume: 8
number: 12
pages: 789--790
month: dec
monthnumber: 12
year: 1965
CODEN: CACMA2
DOI: https://doi.org/10.1145/365691.365957
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:03 MST 2005
bibtimestamp: 2005.11.25 18:20:03 MST
note: See remarks cite Hill:1967:RAS,MacLaren:1968:RAP.
fjournal: Communications of the ACM
keywords: probability functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: M. D. MacLaren
rawnote: See remarks \cite{Hill:1967:RAS,MacLaren:1968:RAP}.
rawtitle: {Algorithm 272}: {Procedure} for the Normal Distribution Functions [{S15}]
abstract:
The procedure gives $ Phi (a) = sqrt 1 / (2 pi ) int _- infty ^a exp ( - t^2 / 2) d t $ and $ Phi *(a) = 2 (Phi (|a|) - 0.5) = sqrt 2 / pi int _0^|a| exp ( - t^2 / 2) d t $.

rawabstract:
The procedure gives $ \Phi (a) = \sqrt {1 / (2 \pi)} \int_{- \infty }^a \exp ( - t^2 / 2) \, d t $ and $ \Phi *(a) = 2 (\Phi (|a|) - 0.5) = \sqrt {2 / \pi } \int_0^{|a|} \exp ( - t^2 / 2) \, d t $.

entry:
@Article{MacLaren:1965:APN,
  author =       "M. D. MacLaren",
  title =        "{Algorithm 272}: {Procedure} for the Normal
                 Distribution Functions [{S15}]",
  journal =      j-CACM,
  volume =       "8",
  number =       "12",
  pages =        "789--790",
  month =        dec,
  year =         "1965",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/365691.365957",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:03 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remarks \cite{Hill:1967:RAS,MacLaren:1968:RAP}.",
  abstract =     "The procedure gives $ \Phi (a) = \sqrt {1 / (2 \pi)}
                 \int_{- \infty }^a \exp ( - t^2 / 2) \, d t $ and $
                 \Phi *(a) = 2 (\Phi (|a|) - 0.5) = \sqrt {2 / \pi }
                 \int_0^{|a|} \exp ( - t^2 / 2) \, d t $.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "probability functions",
}


bibtype: article
filename: elefunt.bib
label: Maklovic:1965:IIC
author: S. T. Maklovic
title: Investigation of integrals containing Bessel and elementary functions. (Russian)
journal: Kisinev. Gos. Univ. Ucen. Zap.
volume: 82
pages: 75--81
year: 1965
MRclass: 33.25
MRnumber: 34 \#387
MRreviewer: H. A. Lauwerier
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
language: Russian
acknowledgement: ack-nhfb
rawauthor: S. T. Maklovi{\v{c}}
rawtitle: Investigation of integrals containing {Bessel} and elementary functions. ({Russian})
entry:
@Article{Maklovic:1965:IIC,
  author =       "S. T. Maklovi{\v{c}}",
  title =        "Investigation of integrals containing {Bessel} and
                 elementary functions. ({Russian})",
  journal =      "Ki{\v{s}}inev. Gos. Univ. U{\v{c}}en. Zap.",
  volume =       "82",
  pages =        "75--81",
  year =         "1965",
  MRclass =      "33.25",
  MRnumber =     "34 \#387",
  MRreviewer =   "H. A. Lauwerier",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "Russian",
}


bibtype: article
filename: elefunt.bib
label: Markman:1965:RZF
author: B. Markman
title: The Riemann Zeta Function
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 5
number: 2
pages: 138--141
year: 1965
bibdate: Sat Oct 30 08:53:17 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 08:53:17 ???
remark: Fullerton: A 25-line Algol procedure for evaluating $ zeta (s) $ for all $ s neq 1 $ is given.
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: B. Markman
rawtitle: The {Riemann} Zeta Function
entry:
@Article{Markman:1965:RZF,
  author =       "B. Markman",
  title =        "The {Riemann} Zeta Function",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "5",
  number =       "2",
  pages =        "138--141",
  year =         "1965",
  bibdate =      "Sat Oct 30 08:53:17 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  journal-URL =  "http://link.springer.com/journal/10543",
  remark =       "Fullerton: A 25-line Algol procedure for evaluating $
                 \zeta (s) $ for all $ s \neq 1 $ is given.",
}


bibtype: article
filename: elefunt.bib
label: Medhurst:1965:EI
author: R. G. Medhurst and J. H. Roberts
journal: j-MATH-COMPUT
volume: 19
number: 89
pages: 113--117
month: apr
monthnumber: 4
year: 1965
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: R. G. Medhurst and J. H. Roberts
title:
Evaluation of the Integral $ I_n(b) = frac 2pi int ^infty _0 bigg (frac sin xx bigg )^n cos (b x) d x $

rawtitle:
Evaluation of the Integral $ {I}_n(b) = \frac {2}{\pi } \int^\infty_0 \bigg (\frac {\sin x}{x} \bigg)^n \cos (b x) d x $

entry:
@Article{Medhurst:1965:EI,
  author =       "R. G. Medhurst and J. H. Roberts",
  title =        "Evaluation of the Integral $ {I}_n(b) = \frac {2}{\pi
                 } \int^\infty_0 \bigg (\frac {\sin x}{x} \bigg)^n \cos
                 (b x) d x $",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "89",
  pages =        "113--117",
  month =        apr,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Metze:1965:MSR
author: Gernot Metze
title: Minimal Square Rooting
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-14
number: 2
pages: 181--185
month: apr
monthnumber: 4
year: 1965
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1965.263963
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 06:26:22 MDT 2011
bibtimestamp: 2011.07.14 06:26:22 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038397
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: Gernot Metze
rawtitle: Minimal Square Rooting
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/ieeetranscomput.bib

entry:
@Article{Metze:1965:MSR,
  author =       "Gernot Metze",
  title =        "Minimal Square Rooting",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-14",
  number =       "2",
  pages =        "181--185",
  month =        apr,
  year =         "1965",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1965.263963",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 06:26:22 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/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038397",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: article
filename: elefunt.bib
label: Miller:1965:ASF
author: G. F. Miller
title: Algorithms for Special Functions II
journal: j-NUM-MATH
volume: 7
pages: 194--196
year: 1965
CODEN: NUMMA7
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Fri Sep 16 10:22:10 1994
bibsource: ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.16 10:22:10 ???
fjournal: Numerische Mathematik
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/211
rawauthor: G. F. Miller
rawtitle: Algorithms for Special Functions {II}
remark:
Fullerton: Corrections and simplifications of the $ sin $, $ cos $ and $ tan $ routines given in paper I. See Clenshaw (1963).

entry:
@Article{Miller:1965:ASF,
  author =       "G. F. Miller",
  title =        "Algorithms for Special Functions {II}",
  journal =      j-NUM-MATH,
  volume =       "7",
  pages =        "194--196",
  year =         "1965",
  CODEN =        "NUMMA7",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Fri Sep 16 10:22:10 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  remark =       "Fullerton: Corrections and simplifications of the $
                 \sin $, $ \cos $ and $ \tan $ routines given in paper
                 I. See Clenshaw (1963).",
  xxmonth =      "(none)",
  xxnumber =     "(none)",
}


bibtype: article
filename: elefunt.bib
label: Nemeth:1965:CEF
author: G. Nemeth
title: Chebyshev expansions for Fresnel integrals
journal: j-NUM-MATH
volume: 7
number: 4
pages: 310--312
month: aug
monthnumber: 8
year: 1965
CODEN: NUMMA7
DOI: https://doi.org/10.1007/BF01436524
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sun Oct 17 20:47:18 MDT 1999
bibtimestamp: 1999.10.17 20:47:18 MDT
fjournal: Numerische Mathematik
remark: Fullerton: Two series of 12-digit coefficients are given to cover the range $ 0 leq x < infty $.
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: G. N{\'e}meth
rawtitle: {Chebyshev} expansions for {Fresnel} integrals
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib

entry:
@Article{Nemeth:1965:CEF,
  author =       "G. N{\'e}meth",
  title =        "{Chebyshev} expansions for {Fresnel} integrals",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "4",
  pages =        "310--312",
  month =        aug,
  year =         "1965",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01436524",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Oct 17 20:47:18 MDT 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  remark =       "Fullerton: Two series of 12-digit coefficients are
                 given to cover the range $ 0 \leq x < \infty $.",
}


bibtype: article
filename: elefunt.bib
label: Rice:1965:CPR
author: John R. Rice
title: On the Conditioning of Polynomial and Rational Forms
journal: j-NUM-MATH
volume: 7
number: 5
pages: 426--435
month: oct
monthnumber: 10
year: 1965
CODEN: NUMMA7
DOI: https://doi.org/10.1007/BF01436257
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
MRclass: 65.99
MRnumber: MR0189283 (32 \#6710)
MRreviewer: James H. Wilkinson
bibdate: Sun Oct 16 17:22:04 GMT 1994
bibtimestamp: 1994.10.16 17:22:04 GMT
fjournal: Numerische Mathematik
keywords: number of multiplications to evaluate a polynomial
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: John R. Rice
rawtitle: On the Conditioning of Polynomial and Rational Forms
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/nummath.bib

entry:
@Article{Rice:1965:CPR,
  author =       "John R. Rice",
  title =        "On the Conditioning of Polynomial and Rational Forms",
  journal =      j-NUM-MATH,
  volume =       "7",
  number =       "5",
  pages =        "426--435",
  month =        oct,
  year =         "1965",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/BF01436257",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  MRclass =      "65.99",
  MRnumber =     "MR0189283 (32 \#6710)",
  MRreviewer =   "James H. Wilkinson",
  bibdate =      "Sun Oct 16 17:22:04 GMT 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/mirrors/ftp.ira.uka.de/bibliography/Math/nummath.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
  keywords =     "number of multiplications to evaluate a polynomial",
}


bibtype: article
filename: elefunt.bib
label: Slepian:1965:EAP
author: David Slepian and Estelle Sonnenblick
title: Eigenvalues associated with prolate spheroidal wave functions of zero order
journal: j-BELL-SYST-TECH-J
volume: 44
number: 8
pages: 1745--1759
month: oct
monthnumber: 10
year: 1965
CODEN: BSTJAN
ISSN: 0005-8580 OR 00058580
MRclass: 65.25
MRnumber: 0183103 (32 \#585)
MRreviewer: R. Nicolovius
bibdate: Tue Nov 9 11:15:55 MST 2010
bibtimestamp: 2010.11.09 11:15:55 MST
URL: http://bstj.bell-labs.com/BSTJ/images/Vol44/bstj44-8-1745.pdf
fjournal: The Bell System Technical Journal
acknowledgement: ack-nhfb
journalURL: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/
rawauthor: David Slepian and Estelle Sonnenblick
rawtitle: Eigenvalues associated with prolate spheroidal wave functions of zero order
bibsource:
http://bstj.bell-labs.com/oldfiles/year.1965/BSTJ.1965.4408.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Slepian:1965:EAP,
  author =       "David Slepian and Estelle Sonnenblick",
  title =        "Eigenvalues associated with prolate spheroidal wave
                 functions of zero order",
  journal =      j-BELL-SYST-TECH-J,
  volume =       "44",
  number =       "8",
  pages =        "1745--1759",
  month =        oct,
  year =         "1965",
  CODEN =        "BSTJAN",
  ISSN =         "0005-8580",
  MRclass =      "65.25",
  MRnumber =     "0183103 (32 \#585)",
  MRreviewer =   "R. Nicolovius",
  bibdate =      "Tue Nov 9 11:15:55 MST 2010",
  bibsource =    "http://bstj.bell-labs.com/oldfiles/year.1965/BSTJ.1965.4408.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://bstj.bell-labs.com/BSTJ/images/Vol44/bstj44-8-1745.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "The Bell System Technical Journal",
  journal-URL =  "http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1538-7305/issues/",
}


bibtype: article
filename: elefunt.bib
label: Slepian:1965:SAE
author: David Slepian
title: Some Asymptotic Expansions for Prolate Spheroidal Wave Functions
journal: J. Math. and Physics XLIV(2)
pages: 99--140
month: jun
monthnumber: 6
year: 1965
bibdate: Sat Oct 30 10:46:38 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 10:46:38 ???
URL: http://www.ams.org/mathscinet/search/publications.html?pg1=IID&s1=189661
remark: Fullerton: Several complicated expansions are derived and presented.
acknowledgement: ack-nhfb
authordates: 1923--2007
rawauthor: David Slepian
rawtitle: Some Asymptotic Expansions for Prolate Spheroidal Wave Functions
entry:
@Article{Slepian:1965:SAE,
  author =       "David Slepian",
  title =        "Some Asymptotic Expansions for Prolate Spheroidal Wave
                 Functions",
  journal =      "J. Math. and Physics {XLIV(2)}",
  volume =       "??",
  number =       "??",
  pages =        "99--140",
  month =        jun,
  year =         "1965",
  bibdate =      "Sat Oct 30 10:46:38 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/mathscinet/search/publications.html?pg1=IID&s1=189661",
  acknowledgement = ack-nhfb,
  author-dates = "1923--2007",
  citedby =      "Fullerton:1980:BEM",
  remark =       "Fullerton: Several complicated expansions are derived
                 and presented.",
}


bibtype: article
filename: elefunt.bib
label: Swarztrauber:1965:LED
author: P. N. Swarztrauber
title: Letter to the Editor: On the Double-Precision Square Root Routine
journal: j-CACM
volume: 8
number: 4
pages: 202
month: apr
monthnumber: 4
year: 1965
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Wed Aug 31 14:02:19 1994
bibtimestamp: 1994.08.31 14:02:19 ???
fjournal: Communications of the ACM
keywords: $sqrt (x)$; elementary functions; floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: P. N. Swarztrauber
rawtitle: Letter to the {Editor}: On the Double-Precision Square Root Routine
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

entry:
@Article{Swarztrauber:1965:LED,
  author =       "P. N. Swarztrauber",
  title =        "Letter to the {Editor}: On the Double-Precision Square
                 Root Routine",
  journal =      j-CACM,
  volume =       "8",
  number =       "4",
  pages =        "202",
  month =        apr,
  year =         "1965",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Wed Aug 31 14:02:19 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; floating-point
                 arithmetic",
}


bibtype: article
filename: elefunt.bib
label: Thompson:1965:AEI
author: G. T. Thompson
journal: j-MATH-COMPUT
volume: 19
number: 92
pages: 661--663
month: oct
monthnumber: 10
year: 1965
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
keywords: Doppler Broadening
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: G. T. Thompson
title:
The Asymptotic Expansion of the Integrals Psi and Chi in Terms of Tchebycheff Polynomials (in Technical Notes and Short Papers)

rawtitle:
The Asymptotic Expansion of the Integrals Psi and Chi in Terms of {Tchebycheff} Polynomials (in {Technical Notes and Short Papers})

entry:
@Article{Thompson:1965:AEI,
  author =       "G. T. Thompson",
  title =        "The Asymptotic Expansion of the Integrals Psi and Chi
                 in Terms of {Tchebycheff} Polynomials (in {Technical
                 Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "19",
  number =       "92",
  pages =        "661--663",
  month =        oct,
  year =         "1965",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  keywords =     "Doppler Broadening",
}


bibtype: book
filename: elefunt.bib
label: Clenshaw:1966:CSB
author: C. W. Clenshaw and Susan M. Picken
title: Chebyshev series for Bessel functions of fractional order
volume: 8
publisher: pub-HMSO
address: pub-HMSO:adr
pages: iii + 53
year: 1966
MRclass: 33.25
MRnumber: 203095
MRreviewer: L. J. Slater
bibdate: Sun Nov 12 06:18:24 2023
bibtimestamp: 2023.11.12 06:18:24 ???
series: National Physical Laboratory. Mathematical tables
acknowledgement: ack-nhfb
authordates: Charles William Clenshaw (15 March 1926--23 September 2004)
rawauthor: C. W. Clenshaw and Susan M. Picken
rawtitle: {Chebyshev} series for {Bessel} functions of fractional order
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Book{Clenshaw:1966:CSB,
  author =       "C. W. Clenshaw and Susan M. Picken",
  title =        "{Chebyshev} series for {Bessel} functions of
                 fractional order",
  volume =       "8",
  publisher =    pub-HMSO,
  address =      pub-HMSO:adr,
  pages =        "iii + 53",
  year =         "1966",
  MRclass =      "33.25",
  MRnumber =     "203095",
  MRreviewer =   "L. J. Slater",
  bibdate =      "Sun Nov 12 06:18:24 2023",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/clenshaw-charles-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "National Physical Laboratory. Mathematical tables",
  acknowledgement = ack-nhfb,
  author-dates = "Charles William Clenshaw (15 March 1926--23 September
                 2004)",
  xxpages =      "51",
  xxpages =      "iii + 54",
}


bibtype: article
filename: elefunt.bib
label: Cody:1966:CCA
author: W. J. Cody, Jr.
title: Corrigenda: ``Chebyshev Approximations for the Complete Elliptic Integrals $ K $ and $ E $''
journal: j-MATH-COMPUT
volume: 20
number: 93
pages: 207--207
month: jan
monthnumber: 1
year: 1966
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Fri Oct 23 11:13:58 1998
bibtimestamp: 1998.10.23 11:13:58 ???
note: See cite Cody:1965:CAC.
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: W. J. {Cody, Jr.}
rawnote: See \cite{Cody:1965:CAC}.
rawtitle: Corrigenda: ``{Chebyshev} Approximations for the Complete Elliptic Integrals $ {K} $ and $ {E} $''
entry:
@Article{Cody:1966:CCA,
  author =       "W. J. {Cody, Jr.}",
  title =        "Corrigenda: ``{Chebyshev} Approximations for the
                 Complete Elliptic Integrals $ {K} $ and $ {E} $''",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "93",
  pages =        "207--207",
  month =        jan,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Fri Oct 23 11:13:58 1998",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Cody:1965:CAC}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Doring:1966:CZC
author: Boro Doring
title: Complex Zeros of Cylinder Functions
journal: j-MATH-COMPUT
volume: 20
number: 94
pages: 215--222
month: apr
monthnumber: 4
year: 1966
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Boro Doring
rawtitle: Complex Zeros of Cylinder Functions
entry:
@Article{Doring:1966:CZC,
  author =       "Boro Doring",
  title =        "Complex Zeros of Cylinder Functions",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "94",
  pages =        "215--222",
  month =        apr,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Fike:1966:SAS
author: C. T. Fike
title: Starting Approximations for Square Root Calculation on IBM System / 360
journal: j-CACM
volume: 9
number: 4
pages: 297--299
month: apr
monthnumber: 4
year: 1966
CODEN: CACMA2
DOI: https://doi.org/10.1145/365278.365556
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Sep 1 10:15:43 1994
bibtimestamp: 1994.09.01 10:15:43 ???
note: See letter cite Fike:1967:LER.
fjournal: Communications of the ACM
keywords: $sqrt (x)$; elementary functions; IBM S/360
acknowledgement: ack-nj
journalURL: https://dl.acm.org/loi/cacm
rawauthor: C. T. Fike
rawnote: See letter \cite{Fike:1967:LER}.
rawtitle: Starting Approximations for Square Root Calculation on {IBM System\slash 360}
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Several starting approximations for square root calculation by Newton's method are presented in a form to facilitate their use in IBM System/360 square root routines. These approximations include several for the range [1/16, 1], which is the interval of primary interest on IBM System/360.

rawabstract:
Several starting approximations for square root calculation by Newton's method are presented in a form to facilitate their use in IBM System/360 square root routines. These approximations include several for the range [1/16, 1], which is the interval of primary interest on IBM System/360.

entry:
@Article{Fike:1966:SAS,
  author =       "C. T. Fike",
  title =        "Starting Approximations for Square Root Calculation on
                 {IBM System\slash 360}",
  journal =      j-CACM,
  volume =       "9",
  number =       "4",
  pages =        "297--299",
  month =        apr,
  year =         "1966",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/365278.365556",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Sep 1 10:15:43 1994",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See letter \cite{Fike:1967:LER}.",
  abstract =     "Several starting approximations for square root
                 calculation by Newton's method are presented in a form
                 to facilitate their use in IBM System/360 square root
                 routines. These approximations include several for the
                 range [1/16, 1], which is the interval of primary
                 interest on IBM System/360.",
  acknowledgement = ack-nj # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\sqrt(x)$; elementary functions; IBM S/360",
}


bibtype: article
filename: elefunt.bib
label: Filippi:1966:BEE
author: S. Filippi
journal: j-COMPUTING
volume: 1
number: 2
pages: 127--132
month: jun
monthnumber: 6
year: 1966
CODEN: CMPTA2
DOI: https://doi.org/10.1007/BF02342622
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Fri Sep 16 16:30:40 1994
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.16 16:30:40 ???
fjournal: Computing
acknowledgement: ack-nj
journalURL: http://link.springer.com/journal/607
rawauthor: S. Filippi
title:
Die Berechnung einiger elementarer transzendenter Funktionen mit Hilfe des Richardson-Algorithmus toenglish The Computation of Some Elementary Transcendental Functions by Means of the Richardson Algorithm endtoenglish 

rawtitle:
{Die Berechnung einiger elementarer transzendenter Funktionen mit Hilfe des Richardson-Algorithmus} \toenglish {The Computation of Some Elementary Transcendental Functions by Means of the Richardson Algorithm} \endtoenglish

entry:
@Article{Filippi:1966:BEE,
  author =       "S. Filippi",
  title =        "{Die Berechnung einiger elementarer transzendenter
                 Funktionen mit Hilfe des Richardson-Algorithmus}
                 \toenglish {The Computation of Some Elementary
                 Transcendental Functions by Means of the Richardson
                 Algorithm} \endtoenglish",
  journal =      j-COMPUTING,
  volume =       "1",
  number =       "2",
  pages =        "127--132",
  month =        jun,
  year =         "1966",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/BF02342622",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Fri Sep 16 16:30:40 1994",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1966:AD
author: Walter Gautschi
title: Algorithm 282: Derivatives of $ e^x / x $, $ cos (x) / x $, and $ sin (x) / x $
journal: j-CACM
volume: 9
number: 4
pages: 272--272
month: apr
monthnumber: 4
year: 1966
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:05 MST 2005
bibtimestamp: 2005.11.25 18:20:05 MST
note: See remark cite Gautschi:1970:RAD.
fjournal: Communications of the ACM
keywords: $cos (x)/x$; $sin (x)/x$; $e^x/x$; elementary functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Walter Gautschi
rawnote: See remark \cite{Gautschi:1970:RAD}.
rawtitle: {Algorithm 282}: {Derivatives} of $ e^x / x $, $ \cos (x) / x $, and $ \sin (x) / x $
entry:
@Article{Gautschi:1966:AD,
  author =       "Walter Gautschi",
  title =        "{Algorithm 282}: {Derivatives} of $ e^x / x $, $ \cos
                 (x) / x $, and $ \sin (x) / x $",
  journal =      j-CACM,
  volume =       "9",
  number =       "4",
  pages =        "272--272",
  month =        apr,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:05 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See remark \cite{Gautschi:1970:RAD}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\cos(x)/x$; $\sin(x)/x$; $e^x/x$; elementary
                 functions",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:1966:ARC
author: Walter Gautschi
title: Algorithm 292: Regular Coulomb Wave Functions
journal: j-CACM
volume: 9
number: 11
pages: 793--795
month: nov
monthnumber: 11
year: 1966
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:10 MST 2005
bibtimestamp: 2005.11.25 18:20:10 MST
fjournal: Communications of the ACM
keywords: Coulomb wave functions; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Walter Gautschi
rawtitle: {Algorithm 292}: {Regular} {Coulomb} Wave Functions
entry:
@Article{Gautschi:1966:ARC,
  author =       "Walter Gautschi",
  title =        "{Algorithm 292}: {Regular} {Coulomb} Wave Functions",
  journal =      j-CACM,
  volume =       "9",
  number =       "11",
  pages =        "793--795",
  month =        nov,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:10 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Coulomb wave functions; special functions",
}


bibtype: article
filename: elefunt.bib
label: Glasser:1966:ESI
author: M. L. Glasser
title: Evaluation of Some Integrals Involving the $ psi $-Function (in Technical Notes and Short Papers)
journal: j-MATH-COMPUT
volume: 20
number: 94
pages: 332--333
month: apr
monthnumber: 4
year: 1966
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: M. L. Glasser
rawtitle:
Evaluation of Some Integrals Involving the $ \psi $-Function (in {Technical Notes and Short Papers})

entry:
@Article{Glasser:1966:ESI,
  author =       "M. L. Glasser",
  title =        "Evaluation of Some Integrals Involving the $ \psi
                 $-Function (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "94",
  pages =        "332--333",
  month =        apr,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Gustafson:1966:CAM
author: Sven-AA ke Gustafson
title: Convergence Acceleration by Means of Numerical Quadrature
journal: j-NORDISK-TIDSKR-INFORM-BEHAND
volume: 6
number: 2
pages: 117--128
month: jun
monthnumber: 6
year: 1966
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01933103
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
bibdate: Wed Jan 4 18:52:09 MST 2006
bibtimestamp: 2006.01.04 18:52:09 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=2&spage=117
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Sven-{\AA}ke Gustafson
rawtitle: Convergence Acceleration by Means of Numerical Quadrature
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=6&issue=2; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Gustafson:1966:CAM,
  author =       "Sven-{\AA}ke Gustafson",
  title =        "Convergence Acceleration by Means of Numerical
                 Quadrature",
  journal =      j-NORDISK-TIDSKR-INFORM-BEHAND,
  volume =       "6",
  number =       "2",
  pages =        "117--128",
  month =        jun,
  year =         "1966",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01933103",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  bibdate =      "Wed Jan 4 18:52:09 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=6&issue=2;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=6&issue=2&spage=117",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Hart:1966:CAR
author: Roger G. Hart
title: A Close Approximation Related to the Error Function (in Technical Notes and Short Papers)
journal: j-MATH-COMPUT
volume: 20
number: 96
pages: 600--602
month: oct
monthnumber: 10
year: 1966
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Roger G. Hart
rawtitle: A Close Approximation Related to the Error Function (in {Technical Notes and Short Papers})
entry:
@Article{Hart:1966:CAR,
  author =       "Roger G. Hart",
  title =        "A Close Approximation Related to the Error Function
                 (in {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "96",
  pages =        "600--602",
  month =        oct,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Hastings:1966:RCB
author: C. W. Hastings
title: R66-78 Computation of the Base Two Logarithm of Binary Number
journal: j-IEEE-TRANS-ELEC-COMPUT
volume: EC-15
number: 6
pages: 956--957
month: dec
monthnumber: 12
year: 1966
CODEN: IEECA8
DOI: https://doi.org/10.1109/PGEC.1966.264517
ISSN: 0367-7508 OR 03677508
bibdate: Thu Jul 14 05:46:46 MDT 2011
bibtimestamp: 2011.07.14 05:46:46 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038956
fjournal: IEEE Transactions on Electronic Computers
acknowledgement: ack-nhfb
rawauthor: C. W. Hastings
rawtitle: {R66-78} Computation of the Base Two Logarithm of Binary Number
entry:
@Article{Hastings:1966:RCB,
  author =       "C. W. Hastings",
  title =        "{R66-78} Computation of the Base Two Logarithm of
                 Binary Number",
  journal =      j-IEEE-TRANS-ELEC-COMPUT,
  volume =       "EC-15",
  number =       "6",
  pages =        "956--957",
  month =        dec,
  year =         "1966",
  CODEN =        "IEECA8",
  DOI =          "https://doi.org/10.1109/PGEC.1966.264517",
  ISSN =         "0367-7508",
  bibdate =      "Thu Jul 14 05:46:46 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4038956",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Electronic Computers",
}


bibtype: book
filename: elefunt.bib
label: Jurimae:1966:KFT
author: E. Jurimae
publisher: Tartu Riiklik Ulikool
address: Tartu, Estonia
pages: 131
year: 1966
MRclass: 30.00
MRnumber: 40 \#5827a
bibdate: Sat Jan 11 17:44:01 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 17:44:01 MST
acknowledgement: ack-nhfb
rawauthor: E. J{\"u}rim{\"a}e
title:
Kompleksmuutuja funktsioonide teooria. I: Elementaarsed funktsioonid. (Estonian) [Theory of functions of a complex variable. I: Elementary functions]

rawtitle:
Kompleksmuutuja funktsioonide teooria. {I}: Elementaarsed funktsioonid. ({Estonian}) [Theory of functions of a complex variable. {I}: Elementary functions]

entry:
@Book{Jurimae:1966:KFT,
  author =       "E. J{\"u}rim{\"a}e",
  title =        "Kompleksmuutuja funktsioonide teooria. {I}:
                 Elementaarsed funktsioonid. ({Estonian}) [Theory of
                 functions of a complex variable. {I}: Elementary
                 functions]",
  publisher =    "Tartu Riiklik {\"U}likool",
  address =      "Tartu, Estonia",
  pages =        "131",
  year =         "1966",
  MRclass =      "30.00",
  MRnumber =     "40 \#5827a",
  bibdate =      "Sat Jan 11 17:44:01 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: incollection
filename: elefunt.bib
label: Kogbetliantz:1966:GEF
author: E. G. Kogbetliantz
title: Generation of Elementary Functions
crossref: Ralston:1960:MMD
pages: 7--35
year: 1966
bibdate: Sat Dec 09 14:09:27 1995
bibsource: garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1995.12.09 14:09:27 ???
acknowledgement: ack-nj
rawauthor: E. G. Kogbetliantz
rawtitle: Generation of Elementary Functions
entry:
@InCollection{Kogbetliantz:1966:GEF,
  author =       "E. G. Kogbetliantz",
  title =        "Generation of Elementary Functions",
  crossref =     "Ralston:1960:MMD",
  pages =        "7--35",
  year =         "1966",
  bibdate =      "Sat Dec 09 14:09:27 1995",
  bibsource =    "garbo.uwasa.fi:/pc/doc-soft/fpbiblio.txt;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nj,
}


bibtype: techreport
filename: elefunt.bib
label: Kuki:1966:CAE
author: H. Kuki
title: Comments on the ANL Evaluation of the OS / 360 FORTRAN Math Function Library
number: SSD 169, C4773
institution: SHARE Secretary Distribution
pages: 47--53
year: 1966
bibdate: Wed Feb 14 19:13:50 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2007.02.14 19:13:50 ???
acknowledgement: ack-nhfb
rawauthor: H. Kuki
rawtitle: Comments on the {ANL} Evaluation of the {OS\slash 360 FORTRAN} Math Function Library
entry:
@TechReport{Kuki:1966:CAE,
  author =       "H. Kuki",
  title =        "Comments on the {ANL} Evaluation of the {OS\slash 360
                 FORTRAN} Math Function Library",
  type =         "????",
  number =       "SSD 169, C4773",
  institution =  "SHARE Secretary Distribution",
  address =      "????",
  pages =        "47--53",
  year =         "1966",
  bibdate =      "Wed Feb 14 19:13:50 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Larssen:1966:CAC
author: Gerhard Meidell Larssen
title: Certification of Algorithm 56: Complete elliptic integral of the second kind
journal: j-CACM
volume: 9
number: 1
pages: 12--12
month: jan
monthnumber: 1
year: 1966
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:04 MST 2005
bibtimestamp: 2005.11.25 18:20:04 MST
fjournal: Communications of the ACM
keywords: special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Gerhard Meidell Larssen
rawtitle: Certification of {Algorithm 56}: {Complete} elliptic integral of the second kind
entry:
@Article{Larssen:1966:CAC,
  author =       "Gerhard Meidell Larssen",
  title =        "Certification of {Algorithm 56}: {Complete} elliptic
                 integral of the second kind",
  journal =      j-CACM,
  volume =       "9",
  number =       "1",
  pages =        "12--12",
  month =        jan,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:04 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "special functions",
}


bibtype: article
filename: elefunt.bib
label: Mechel:1966:CMB
author: Fr. Mechel
title: Calculation of the Modified Bessel Functions of the Second Kind with Complex Argument
journal: j-MATH-COMPUT
volume: 20
number: 95
pages: 407--412
month: jul
monthnumber: 7
year: 1966
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Fr. Mechel
rawtitle: Calculation of the Modified {Bessel} Functions of the Second Kind with Complex Argument
entry:
@Article{Mechel:1966:CMB,
  author =       "Fr. Mechel",
  title =        "Calculation of the Modified {Bessel} Functions of the
                 Second Kind with Complex Argument",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "95",
  pages =        "407--412",
  month =        jul,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Nellis:1966:REE
author: W. J. Nellis and B. C. Carlson
title: Reduction and Evaluation of Elliptic Integrals
journal: j-MATH-COMPUT
volume: 20
number: 94
pages: 223--231
month: apr
monthnumber: 4
year: 1966
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: W. J. Nellis and B. C. Carlson
rawtitle: Reduction and Evaluation of Elliptic Integrals
entry:
@Article{Nellis:1966:REE,
  author =       "W. J. Nellis and B. C. Carlson",
  title =        "Reduction and Evaluation of Elliptic Integrals",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "94",
  pages =        "223--231",
  month =        apr,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Pike:1966:ALG
author: M. C. Pike and I. D. Hill
title: Algorithm 291: Logarithm of Gamma Function
journal: j-CACM
volume: 9
number: 9
pages: 684--684
month: sep
monthnumber: 9
year: 1966
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:09 MST 2005
bibtimestamp: 2005.11.25 18:20:09 MST
fjournal: Communications of the ACM
keywords: $log (Gamma (x))$; special functions
remark: Fullerton: Short Algol procedure valid only for $ x > 0 $. Accurate to 10 digits.
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: M. C. Pike and I. D. Hill
rawtitle: {Algorithm 291}: {Logarithm} of Gamma Function
entry:
@Article{Pike:1966:ALG,
  author =       "M. C. Pike and I. D. Hill",
  title =        "{Algorithm 291}: {Logarithm} of Gamma Function",
  journal =      j-CACM,
  volume =       "9",
  number =       "9",
  pages =        "684--684",
  month =        sep,
  year =         "1966",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:09 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "$\log(\Gamma(x))$; special functions",
  remark =       "Fullerton: Short Algol procedure valid only for $ x >
                 0 $. Accurate to 10 digits.",
}


bibtype: techreport
filename: elefunt.bib
label: Price:1966:NAR
author: James F. Price
title: Numerical Analysis and Related Literature for Scientific Computer Users
type: Mathematical Note
number: 456 (D1-82-0517)
institution: Mathematics Research Laboratory, Boeing Scientific Research Laboratories
address: Seattle, WA, USA
edition: Second
pages: ix + 191
month: mar
monthnumber: 3
year: 1966
bibdate: Mon Jun 18 06:55:22 2018
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2018.06.18 06:55:22 ???
URL: http://www.dtic.mil/dtic/tr/fulltext/u2/632244.pdf
acknowledgement: ack-nhfb
rawauthor: James F. Price
rawtitle: Numerical Analysis and Related Literature for Scientific Computer Users
abstract:
The Second Edition of this annotated bibliography lists the contents of over 150 books in English on numerical analysis and related literature. It is meant for the general scientific computer user and not for the research numerical analyst; the descriptions and suggestions are given with this in mind. It is expected that the most useful section will be the 27-page index which tells in which books various topics may be found. There is also a section describing how to look up further information on such topics which may be found in the literature.

TOC:
Introduction / iv I. Numerical Procedures in Books / 1 II. How to Find What You Want / 157 A. Bibliographies, lists of books, abstracting journals / 157 B. Looking for Tables of Various Functions / 161 C. Keeping Up with Some of the New Literature / 163 III. Subject Index / 165

rawabstract:
The Second Edition of this annotated bibliography lists the contents of over 150 books in English on numerical analysis and related literature. It is meant for the general scientific computer user and not for the research numerical analyst; the descriptions and suggestions are given with this in mind. It is expected that the most useful section will be the 27-page index which tells in which books various topics may be found. There is also a section describing how to look up further information on such topics which may be found in the literature.

rawTOC:
Introduction / iv \\ I. Numerical Procedures in Books / 1 \\ II. How to Find What You Want / 157 \\ A. Bibliographies, lists of books, abstracting journals / 157 \\ B. Looking for Tables of Various Functions / 161 \\ C. Keeping Up with Some of the New Literature / 163 \\ III. Subject Index / 165

entry:
@TechReport{Price:1966:NAR,
  author =       "James F. Price",
  title =        "Numerical Analysis and Related Literature for
                 Scientific Computer Users",
  type =         "Mathematical Note",
  number =       "456 (D1-82-0517)",
  institution =  "Mathematics Research Laboratory, Boeing Scientific
                 Research Laboratories",
  address =      "Seattle, WA, USA",
  edition =      "Second",
  pages =        "ix + 191",
  month =        mar,
  year =         "1966",
  bibdate =      "Mon Jun 18 06:55:22 2018",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.dtic.mil/dtic/tr/fulltext/u2/632244.pdf",
  abstract =     "The Second Edition of this annotated bibliography
                 lists the contents of over 150 books in English on
                 numerical analysis and related literature. It is meant
                 for the general scientific computer user and not for
                 the research numerical analyst; the descriptions and
                 suggestions are given with this in mind. It is expected
                 that the most useful section will be the 27-page index
                 which tells in which books various topics may be found.
                 There is also a section describing how to look up
                 further information on such topics which may be found
                 in the literature.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Introduction / iv \\
                 I. Numerical Procedures in Books / 1 \\
                 II. How to Find What You Want / 157 \\
                 A. Bibliographies, lists of books, abstracting journals
                 / 157 \\
                 B. Looking for Tables of Various Functions / 161 \\
                 C. Keeping Up with Some of the New Literature / 163 \\
                 III. Subject Index / 165",
}


bibtype: book
filename: elefunt.bib
label: Slater:1966:GHF
author: Lucy Joan Slater
title: Generalized Hypergeometric Functions
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: xiii + 273
year: 1966
LCCN: QA351 .S565
bibdate: Sat Oct 30 21:01:55 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 21:01:55 MDT
subject: Hypergeometric functions
acknowledgement: ack-nhfb
rawauthor: Lucy Joan Slater
rawtitle: Generalized Hypergeometric Functions
entry:
@Book{Slater:1966:GHF,
  author =       "Lucy Joan Slater",
  title =        "Generalized Hypergeometric Functions",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xiii + 273",
  year =         "1966",
  LCCN =         "QA351 .S565",
  bibdate =      "Sat Oct 30 21:01:55 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions",
}


bibtype: article
filename: elefunt.bib
label: Takenaga:1966:EIG
author: Roy Takenaga
title: On the Evaluation of the Incomplete Gamma Function (in Technical Notes and Short Papers)
journal: j-MATH-COMPUT
volume: 20
number: 96
pages: 606--610
month: oct
monthnumber: 10
year: 1966
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Roy Takenaga
rawtitle: On the Evaluation of the Incomplete Gamma Function (in {Technical Notes and Short Papers})
entry:
@Article{Takenaga:1966:EIG,
  author =       "Roy Takenaga",
  title =        "On the Evaluation of the Incomplete Gamma Function (in
                 {Technical Notes and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "96",
  pages =        "606--610",
  month =        oct,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Thompson:1966:ESI
author: Rory Thompson
journal: j-MATH-COMPUT
volume: 20
number: 94
pages: 330--332
month: apr
monthnumber: 4
year: 1966
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Rory Thompson
title:
Evaluation of $ I_n(b) = 2 pi ^-1 int ^infty _0 big (frac sin xx big )^n cos (b x) d x $ and of Similar Integrals (in Technical Notes and Short Papers)

rawtitle:
Evaluation of $ {I}_n(b) = 2 \pi^{-1} \int^\infty_0 \big (\frac {sin x}{x} \big)^n \cos (b x) d x $ and of Similar Integrals (in {Technical Notes and Short Papers})

entry:
@Article{Thompson:1966:ESI,
  author =       "Rory Thompson",
  title =        "Evaluation of $ {I}_n(b) = 2 \pi^{-1} \int^\infty_0
                 \big (\frac {sin x}{x} \big)^n \cos (b x) d x $ and of
                 Similar Integrals (in {Technical Notes and Short
                 Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "94",
  pages =        "330--332",
  month =        apr,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: book
filename: elefunt.bib
label: Tolke:1966:PFT
author: Friedrich Tolke
publisher: pub-SV
address: pub-SV:adr
pages: vii + 248
year: 1966
bibdate: Mon Feb 13 19:01:10 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.13 19:01:10 ???
language: German
acknowledgement: ack-nhfb
rawauthor: Friedrich T{\"o}lke
title:
Praktische Funktionenlehre. 2. Theta-Funktionen und spezielle Weierstrasssche Funktionen. (German) [Practical functional theory. 2. Theta functions and special Weierstrass functions]

rawtitle:
{Praktische Funktionenlehre. 2. Theta-Funktionen und spezielle Weierstrasssche Funktionen}. ({German}) [{Practical} functional theory. 2. {Theta} functions and special {Weierstrass} functions]

entry:
@Book{Tolke:1966:PFT,
  author =       "Friedrich T{\"o}lke",
  title =        "{Praktische Funktionenlehre. 2. Theta-Funktionen und
                 spezielle Weierstrasssche Funktionen}. ({German})
                 [{Practical} functional theory. 2. {Theta} functions
                 and special {Weierstrass} functions]",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "vii + 248",
  year =         "1966",
  ISBN =         "",
  ISBN-13 =      "",
  LCCN =         "????",
  bibdate =      "Mon Feb 13 19:01:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  language =     "German",
}


bibtype: techreport
filename: elefunt.bib
label: Tricomi:1966:RUS
author: F. G. Tricomi
title: Lectures on the use of special functions by calculations with electronic computers
type: Lecture Series
number: 47
institution: The Institute for Fluid Dynamics and Applied Mathematics, University of Maryland, College Park
address: College Park, MD, USA
pages: vii + 248
year: 1966
bibdate: Tue Mar 14 18:48:58 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.14 18:48:58 ???
acknowledgement: ack-nhfb
rawauthor: F. G. Tricomi
rawtitle: Lectures on the use of special functions by calculations with electronic computers
entry:
@TechReport{Tricomi:1966:RUS,
  author =       "F. G. Tricomi",
  title =        "Lectures on the use of special functions by
                 calculations with electronic computers",
  type =         "Lecture Series",
  number =       "47",
  institution =  "The Institute for Fluid Dynamics and Applied
                 Mathematics, University of Maryland, College Park",
  address =      "College Park, MD, USA",
  year =         "1966",
  bibdate =      "Tue Mar 14 18:48:58 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Watson:1966:TTB
author: G. N. Watson
title: A Treatise on the Theory of Bessel Functions
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
edition: Second
pages: vi + 804
year: 1966
ISBN: 0-521-09382-1 OR 0521093821
ISBN13: 978-0-521-09382-8 OR 9780521093828
LCCN: QA 408 W33t 1966
bibdate: Fri Nov 24 13:53:35 MST 1995
bibtimestamp: 1995.11.24 13:53:35 MST
rawauthor: G. N. Watson
rawtitle: A Treatise on the Theory of {Bessel} Functions
bibsource:
https://www.math.utah.edu/pub/bibnet/subjects/matched-field-proc.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Book{Watson:1966:TTB,
  author =       "G. N. Watson",
  title =        "A Treatise on the Theory of {Bessel} Functions",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  edition =      "Second",
  pages =        "vi + 804",
  year =         "1966",
  ISBN =         "0-521-09382-1",
  ISBN-13 =      "978-0-521-09382-8",
  LCCN =         "QA 408 W33t 1966",
  bibdate =      "Fri Nov 24 13:53:35 MST 1995",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/matched-field-proc.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  alias =        "Watson 66a",
  sthbib =       "M2 Wat 82 55",
}


bibtype: article
filename: elefunt.bib
label: Wood:1966:DBI
author: Van E. Wood and R. P. Kenan and M. L. Glasser
title: Doppler Broadening Integrals (in Technical Notes and Short Papers)
journal: j-MATH-COMPUT
volume: 20
number: 96
pages: 610--611
month: oct
monthnumber: 10
year: 1966
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Van E. Wood and R. P. Kenan and M. L. Glasser
rawtitle: {Doppler} Broadening Integrals (in {Technical Notes and Short Papers})
entry:
@Article{Wood:1966:DBI,
  author =       "Van E. Wood and R. P. Kenan and M. L. Glasser",
  title =        "{Doppler} Broadening Integrals (in {Technical Notes
                 and Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "20",
  number =       "96",
  pages =        "610--611",
  month =        oct,
  year =         "1966",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Anonymous:1967:CAP
author: Anonymous
title: Convergence acceleration from the point of view of linear programming
journal: j-BIT
volume: 7
number: 3
pages: 256--256
month: sep
monthnumber: 9
year: 1967
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1007/BF01939269
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 18:52:10 MST 2006
bibtimestamp: 2006.01.04 18:52:10 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=7&issue=3&spage=256
fjournal: BIT (Nordisk tidskrift for informationsbehandling)
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Anonymous
rawtitle: Convergence acceleration from the point of view of linear programming
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=7&issue=3; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Anonymous:1967:CAP,
  author =       "Anonymous",
  title =        "Convergence acceleration from the point of view of
                 linear programming",
  journal =      j-BIT,
  volume =       "7",
  number =       "3",
  pages =        "256--256",
  month =        sep,
  year =         "1967",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1007/BF01939269",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 18:52:10 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=7&issue=3;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=7&issue=3&spage=256",
  acknowledgement = ack-nhfb,
  fjournal =     "BIT (Nordisk tidskrift for informationsbehandling)",
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Bond:1967:AAF
author: Gillian Bond and M. L. V. Pitteway
title: Algorithm 301: Airy Function
journal: j-CACM
volume: 10
number: 5
pages: 291--292
month: may
monthnumber: 5
year: 1967
CODEN: CACMA2
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:13 MST 2005
bibtimestamp: 2005.11.25 18:20:13 MST
fjournal: Communications of the ACM
keywords: Airy functions; special functions
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: Gillian Bond and M. L. V. Pitteway
rawtitle: {Algorithm 301}: {Airy} Function
remark:
Fullerton: 100-line Algol program for $ operatorname Ai $, $ operatorname Bi $. and their derivatives.

entry:
@Article{Bond:1967:AAF,
  author =       "Gillian Bond and M. L. V. Pitteway",
  title =        "{Algorithm 301}: {Airy} Function",
  journal =      j-CACM,
  volume =       "10",
  number =       "5",
  pages =        "291--292",
  month =        may,
  year =         "1967",
  CODEN =        "CACMA2",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:13 MST 2005",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "Airy functions; special functions",
  remark =       "Fullerton: 100-line Algol program for $ \operatorname
                 {Ai} $, $ \operatorname {Bi} $. and their
                 derivatives.",
}


bibtype: article
filename: elefunt.bib
label: Cody:1967:CAN
author: W. J. Cody and K. E. Hillstrom
title: Chebyshev Approximations for the Natural Logarithm of the Gamma Function
journal: j-MATH-COMPUT
volume: 21
number: 98
pages: 198--203
month: apr
monthnumber: 4
year: 1967
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
remark: Fullerton: Relative errors down to $ 10^-17 $.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: W. J. Cody and K. E. Hillstrom
rawtitle: {Chebyshev} Approximations for the Natural Logarithm of the Gamma Function
entry:
@Article{Cody:1967:CAN,
  author =       "W. J. Cody and K. E. Hillstrom",
  title =        "{Chebyshev} Approximations for the Natural Logarithm
                 of the Gamma Function",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "98",
  pages =        "198--203",
  month =        apr,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Relative errors down to $ 10^{-17} $.",
}


bibtype: article
filename: elefunt.bib
label: Cody:1967:CRC
author: W. J. Cody and Henry C. Thacher, Jr.
journal: j-MATH-COMPUT
volume: 21
number: 99
pages: 525--525
month: jul
monthnumber: 7
year: 1967
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Mon Sep 26 19:36:03 1994
bibtimestamp: 1994.09.26 19:36:03 ???
note: See cite Cody:1967:RCA.
URL: http://www.jstor.org/stable/2003289
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: W. J. Cody and Henry C. {Thacher, Jr.}
rawnote: See \cite{Cody:1967:RCA}.
title:
Corrigendum: ``Rational Chebyshev approximations for Fermi--Dirac integrals of orders $ - 1 / 2 $, $ 1 / 2 $, and $ 3 / 2 $''

rawtitle:
Corrigendum: ``{Rational Chebyshev approximations for Fermi--Dirac integrals of orders $ - 1 / 2 $, $ 1 / 2 $, and $ 3 / 2 $''}

entry:
@Article{Cody:1967:CRC,
  author =       "W. J. Cody and Henry C. {Thacher, Jr.}",
  title =        "Corrigendum: ``{Rational Chebyshev approximations for
                 Fermi--Dirac integrals of orders $ - 1 / 2 $, $ 1 / 2
                 $, and $ 3 / 2 $''}",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "99",
  pages =        "525--525",
  month =        jul,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Sep 26 19:36:03 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See \cite{Cody:1967:RCA}.",
  URL =          "http://www.jstor.org/stable/2003289",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  xxmonth =      "(none)",
}


bibtype: article
filename: elefunt.bib
label: Cody:1967:LEA
author: William J. Cody, Jr.
title: Letter to the Editor: Another Aspect of Economical Polynomials
journal: j-CACM
volume: 10
number: 9
pages: 531--531
month: sep
monthnumber: 9
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363566.363577
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Thu Nov 17 10:20:03 1994
bibtimestamp: 1994.11.17 10:20:03 ???
note: See cite Fike:1967:MEP.
fjournal: Communications of the ACM
keywords: floating-point arithmetic
acknowledgement: ack-wjc
journalURL: https://dl.acm.org/loi/cacm
rawauthor: William J. {Cody, Jr.}
rawnote: See \cite{Fike:1967:MEP}.
rawtitle: Letter to the {Editor}: Another Aspect of Economical Polynomials
bibsource:
http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
In his paper ``Methods of Evaluating Polynomial Approximations in Function Evaluation Routines'' [Comm. ACM 10, (March 1967)], C. T. Fike fails to discuss one very important aspect of the ``economical'' methods for polynomials. Since these evaluation methods involve a decreased number of arithmetic operations over the usual Horner's method (or at least replace a multiplication by an addition) the implication is that they are faster to execute. Dr. Fike points out that these methods can be poorly conditioned for particular polynomials, thus requiring extended precision or fixed-point arithmetic to maintain accuracy and costing more in time than Horner's method. But even if we assume the methods are well conditioned, the need to store away and retrieve intermediate results in some machines with only one floating-point arithmetic register can wipe out the time savings effected by a reduction in the number of arithmetic operations. On many of today's high-performance computers the time required to store away and retrieve a result is about the same as the time required for a floating-point addition. It is no longer sufficient to estimate the efficiency of a method by a count of arithmetic operations alone.

rawabstract:
In his paper ``Methods of Evaluating Polynomial Approximations in Function Evaluation Routines'' [Comm. ACM 10, (March 1967)], C. T. Fike fails to discuss one very important aspect of the ``economical'' methods for polynomials. Since these evaluation methods involve a decreased number of arithmetic operations over the usual Horner's method (or at least replace a multiplication by an addition) the implication is that they are faster to execute. Dr. Fike points out that these methods can be poorly conditioned for particular polynomials, thus requiring extended precision or fixed-point arithmetic to maintain accuracy and costing more in time than Horner's method. But even if we assume the methods are well conditioned, the need to store away and retrieve intermediate results in some machines with only one floating-point arithmetic register can wipe out the time savings effected by a reduction in the number of arithmetic operations. On many of today's high-performance computers the time required to store away and retrieve a result is about the same as the time required for a floating-point addition. It is no longer sufficient to estimate the efficiency of a method by a count of arithmetic operations alone.

entry:
@Article{Cody:1967:LEA,
  author =       "William J. {Cody, Jr.}",
  title =        "Letter to the {Editor}: Another Aspect of Economical
                 Polynomials",
  journal =      j-CACM,
  volume =       "10",
  number =       "9",
  pages =        "531--531",
  month =        sep,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363566.363577",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Thu Nov 17 10:20:03 1994",
  bibsource =    "http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Fike:1967:MEP}.",
  abstract =     "In his paper ``Methods of Evaluating Polynomial
                 Approximations in Function Evaluation Routines'' [Comm.
                 ACM 10, (March 1967)], C. T. Fike fails to discuss one
                 very important aspect of the ``economical'' methods for
                 polynomials. Since these evaluation methods involve a
                 decreased number of arithmetic operations over the
                 usual Horner's method (or at least replace a
                 multiplication by an addition) the implication is that
                 they are faster to execute. Dr. Fike points out that
                 these methods can be poorly conditioned for particular
                 polynomials, thus requiring extended precision or
                 fixed-point arithmetic to maintain accuracy and costing
                 more in time than Horner's method. But even if we
                 assume the methods are well conditioned, the need to
                 store away and retrieve intermediate results in some
                 machines with only one floating-point arithmetic
                 register can wipe out the time savings effected by a
                 reduction in the number of arithmetic operations. On
                 many of today's high-performance computers the time
                 required to store away and retrieve a result is about
                 the same as the time required for a floating-point
                 addition. It is no longer sufficient to estimate the
                 efficiency of a method by a count of arithmetic
                 operations alone.",
  acknowledgement = ack-wjc # " and " # ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "floating-point arithmetic",
}


bibtype: article
filename: elefunt.bib
label: Cody:1967:RCA
author: W. J. Cody and Henry C. Thacher, Jr.
journal: j-MATH-COMPUT
volume: 21
number: 97
pages: 30--40
month: jan
monthnumber: 1
year: 1967
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Mon Sep 26 19:23:19 1994
bibtimestamp: 1994.09.26 19:23:19 ???
note: See also cite Cody:1967:CRC.
URL: http://www.jstor.org/stable/2003468
fjournal: Mathematics of Computation
remark: Fullerton: Relative errors down to $ 10^-9 $.
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: W. J. Cody and Henry C. {Thacher, Jr.}
rawnote: See also \cite{Cody:1967:CRC}.
title:
Rational Chebyshev approximations for Fermi--Dirac integrals of orders $ - 1 / 2 $, $ 1 / 2 $, and $ 3 / 2 $

rawtitle:
Rational {Chebyshev} approximations for {Fermi--Dirac} integrals of orders $ - 1 / 2 $, $ 1 / 2 $, and $ 3 / 2 $

entry:
@Article{Cody:1967:RCA,
  author =       "W. J. Cody and Henry C. {Thacher, Jr.}",
  title =        "Rational {Chebyshev} approximations for {Fermi--Dirac}
                 integrals of orders $ - 1 / 2 $, $ 1 / 2 $, and $ 3 / 2
                 $",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "97",
  pages =        "30--40",
  month =        jan,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Mon Sep 26 19:23:19 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See also \cite{Cody:1967:CRC}.",
  URL =          "http://www.jstor.org/stable/2003468",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
  remark =       "Fullerton: Relative errors down to $ 10^{-9} $.",
}


bibtype: article
filename: elefunt.bib
label: DiDonato:1967:ECI
author: A. R. DiDonato and M. P. Jarnagin
journal: j-MATH-COMPUT
volume: 21
number: 100
pages: 652--662
month: oct
monthnumber: 10
year: 1967
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: A. R. DiDonato and M. P. Jarnagin
title:
The Efficient Calculation of the Incomplete Beta-Function Ratio for Half-Integer Values of the Parameters $ a, b $

rawtitle:
The Efficient Calculation of the Incomplete Beta-Function Ratio for Half-Integer Values of the Parameters $ a, b $

entry:
@Article{DiDonato:1967:ECI,
  author =       "A. R. DiDonato and M. P. Jarnagin",
  title =        "The Efficient Calculation of the Incomplete
                 Beta-Function Ratio for Half-Integer Values of the
                 Parameters $ a, b $",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "100",
  pages =        "652--662",
  month =        oct,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Fair:1967:RAI
author: Wyman G. Fair and Yudell L. Luke
title: Rational Approximations to the Incomplete Elliptic Integrals of the First and Second Kinds
journal: j-MATH-COMPUT
volume: 21
number: 99
pages: 418--422
month: jul
monthnumber: 7
year: 1967
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Wyman G. Fair and Yudell L. Luke
rawtitle: Rational Approximations to the Incomplete Elliptic Integrals of the First and Second Kinds
entry:
@Article{Fair:1967:RAI,
  author =       "Wyman G. Fair and Yudell L. Luke",
  title =        "Rational Approximations to the Incomplete Elliptic
                 Integrals of the First and Second Kinds",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "99",
  pages =        "418--422",
  month =        jul,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Fettis:1967:MCI
author: Henry E. Fettis
journal: j-MATH-COMPUT
volume: 21
number: 100
pages: 727--730
month: oct
monthnumber: 10
year: 1967
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Tue Oct 13 08:06:19 MDT 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; JSTOR database
bibtimestamp: 1998.10.13 08:06:19 MDT
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Henry E. Fettis
title:
More on the Calculation of the Integral $ I_n(b) = frac 2pi int ^infty _0 big (frac sin xx big )^n cos b x d x $ (in Technical Notes and Short Papers)

rawtitle:
More on the Calculation of the Integral $ {I}_n(b) = \frac {2}{\pi } \int^\infty_0 \big (\frac {\sin x}{x} \big)^n \cos b x \, d x $ (in {Technical Notes and Short Papers})

entry:
@Article{Fettis:1967:MCI,
  author =       "Henry E. Fettis",
  title =        "More on the Calculation of the Integral $ {I}_n(b) =
                 \frac {2}{\pi } \int^\infty_0 \big (\frac {\sin x}{x}
                 \big)^n \cos b x \, d x $ (in {Technical Notes and
                 Short Papers})",
  journal =      j-MATH-COMPUT,
  volume =       "21",
  number =       "100",
  pages =        "727--730",
  month =        oct,
  year =         "1967",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Tue Oct 13 08:06:19 MDT 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 JSTOR database",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Fike:1967:LER
author: C. T. Fike
title: Letter to the Editor: A rational approximation optimal by Moursund's criterion
journal: j-CACM
volume: 10
number: 11
pages: 683--684
month: nov
monthnumber: 11
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363790.363795
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:16 MST 2005
bibtimestamp: 2005.11.25 18:20:16 MST
note: See cite Moursund:1967:OSV,Fike:1966:SAS
fjournal: Communications of the ACM
keywords: elementary function; square root
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: C. T. Fike
rawnote: See \cite{Moursund:1967:OSV,Fike:1966:SAS}
rawtitle: Letter to the {Editor}: {A} rational approximation optimal by {Moursund}'s criterion
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

remark:
Gives a starting value for $ sqrt x $ ($x$ on $ [1 / 16, 1]$) of $ R*(x) = 1.68212586 - 1.28977371 / (x + 0.84106293)$, with an error of $ 2^-12.496$.

entry:
@Article{Fike:1967:LER,
  author =       "C. T. Fike",
  title =        "Letter to the {Editor}: {A} rational approximation
                 optimal by {Moursund}'s criterion",
  journal =      j-CACM,
  volume =       "10",
  number =       "11",
  pages =        "683--684",
  month =        nov,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363790.363795",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:16 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See \cite{Moursund:1967:OSV,Fike:1966:SAS}",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  keywords =     "elementary function; square root",
  remark =       "Gives a starting value for $ \sqrt {x} $ ($x$ on $ [1
                 / 16, 1]$) of $ R*(x) = 1.68212586 - 1.28977371 / (x +
                 0.84106293)$, with an error of $ 2^{-12.496}$.",
}


bibtype: article
filename: elefunt.bib
label: Fike:1967:MEP
author: C. T. Fike
title: Methods of Evaluating Polynomial Approximations in Function Evaluation Routines
journal: j-CACM
volume: 10
number: 3
pages: 175--178
month: mar
monthnumber: 3
year: 1967
CODEN: CACMA2
DOI: https://doi.org/10.1145/363162.363200
ISSN: 0001-0782 (print), 1557-7317 (electronic) OR 00010782 (print), 15577317 (electronic)
ISSNL: 0001-0782 OR 00010782
bibdate: Fri Nov 25 18:20:12 MST 2005
bibtimestamp: 2005.11.25 18:20:12 MST
note: See remark on efficiency cite Cody:1967:LEA.
fjournal: Communications of the ACM
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/cacm
rawauthor: C. T. Fike
rawnote: See remark on efficiency \cite{Cody:1967:LEA}.
rawtitle: Methods of Evaluating Polynomial Approximations in Function Evaluation Routines
bibsource:
ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip; http://www.acm.org/pubs/contents/journals/cacm/; https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib; https://www.math.utah.edu/pub/tex/bib/cacm1960.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
The method of nested multiplication is commonly used in function evaluation routines to evaluate approximation polynomials. New polynomial evaluation methods have been developed in recent years which require fewer multiplications than nested multiplication and may therefore be preferable for use in function evaluation routines. Although some of these methods do not appear to be practically useful because of rounding-error difficulties, several methods of evaluating low-degree polynomials have been found to be satisfactory. Three such methods are described and illustrated.

rawabstract:
The method of nested multiplication is commonly used in function evaluation routines to evaluate approximation polynomials. New polynomial evaluation methods have been developed in recent years which require fewer multiplications than nested multiplication and may therefore be preferable for use in function evaluation routines. Although some of these methods do not appear to be practically useful because of rounding-error difficulties, several methods of evaluating low-degree polynomials have been found to be satisfactory. Three such methods are described and illustrated.

entry:
@Article{Fike:1967:MEP,
  author =       "C. T. Fike",
  title =        "Methods of Evaluating Polynomial Approximations in
                 Function Evaluation Routines",
  journal =      j-CACM,
  volume =       "10",
  number =       "3",
  pages =        "175--178",
  month =        mar,
  year =         "1967",
  CODEN =        "CACMA2",
  DOI =          "https://doi.org/10.1145/363162.363200",
  ISSN =         "0001-0782 (print), 1557-7317 (electronic)",
  ISSN-L =       "0001-0782",
  bibdate =      "Fri Nov 25 18:20:12 MST 2005",
  bibsource =    "ftp://garbo.uwasa.fi/pc/doc-soft/fpbibl18.zip;
                 http://www.acm.org/pubs/contents/journals/cacm/;
                 https://www.math.utah.edu/pub/bibnet/authors/c/cody-william-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/cacm1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "See remark on efficiency \cite{Cody:1967:LEA}.",
  abstract =     "The method of nested multiplication is commonly used
                 in function evaluation routines to evaluate
                 approximation polynomials. New polynomial evaluation
                 methods have been developed in recent years which
                 require fewer multiplications than nested
                 multiplication and may therefore be preferable for use
                 in function evaluation routines. Although some of these
                 methods do not appear to be practically useful because
                 of rounding-error difficulties, several methods of
                 evaluating low-degree polynomials have been found to be
                 satisfactory. Three such methods are described and
                 illustrated.",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications of the ACM",
  journal-URL =  "https://dl.acm.org/loi/cacm",
  received =     "August 1966 (revised December 1966)",
}


