# bibtab

bibtype: book
filename: elefunt.bib
label: Birkhoff:1954:SMM
editor: Garrett Birkhoff
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: ix + 353
year: 1954
ISBN: 1-4832-6356-8 OR 1483263568
ISBN13: 978-1-4832-6356-4 OR 9781483263564
LCCN: QA3 .S853
bibdate: Fri Oct 20 10:13:10 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.10.20 10:13:10 ???
acknowledgement: ack-nhfb
subjectdates: Richard von Mises (1883--1953)
raweditor: Garrett Birkhoff
booktitle:
Studies in Mathematics and Mechanics Presented to Richard von Mises by friends, colleagues, and pupils

title:
Studies in Mathematics and Mechanics Presented to Richard von Mises by friends, colleagues, and pupils

abstract:
Studies in Mathematics and Mechanics is a collection of studies presented to Professor Richard von Mises as a token of reverence and appreciation on the occasion of his seventieth birthday which occurred on April 19, 1953. von Mises' thought has been a stimulus in many seemingly unconnected fields of mathematics, science, and philosophy, to which he has contributed decisive results and new formulations of fundamental concepts. The book contains 42 chapters organized into five parts. Part I contains papers on algebra, number theory and geometry. These include a study of Poincare's representation of a hyperbolic space on an Euclidean half-space and elementary estimates for the least primitive root. Part II on analysis includes papers on a generalization of Green's Formula and its application to the Cauchy problem for a hyperbolic equation, and the fundamental solutions of a singular Beltrami operator. Part III deals with theoretical mechanics and covers topics such as turbulent flow, axially symmetric flow, and oscillating wakes. The papers in Part IV focus on applied mechanics. These include studies on plastic flow under high stresses and the problem of inelastic thermal stresses. Part V presents studies on probability and statistics, including a finite frequency theory of probability and the problem of expansion of clusters of galaxies.

rawabstract:
Studies in Mathematics and Mechanics is a collection of studies presented to Professor Richard von Mises as a token of reverence and appreciation on the occasion of his seventieth birthday which occurred on April 19, 1953. von Mises' thought has been a stimulus in many seemingly unconnected fields of mathematics, science, and philosophy, to which he has contributed decisive results and new formulations of fundamental concepts. The book contains 42 chapters organized into five parts. Part I contains papers on algebra, number theory and geometry. These include a study of Poincar{\'e}'s representation of a hyperbolic space on an Euclidean half-space and elementary estimates for the least primitive root. Part II on analysis includes papers on a generalization of Green's Formula and its application to the Cauchy problem for a hyperbolic equation, and the fundamental solutions of a singular Beltrami operator. Part III deals with theoretical mechanics and covers topics such as turbulent flow, axially symmetric flow, and oscillating wakes. The papers in Part IV focus on applied mechanics. These include studies on plastic flow under high stresses and the problem of inelastic thermal stresses. Part V presents studies on probability and statistics, including a finite frequency theory of probability and the problem of expansion of clusters of galaxies.

rawbooktitle:
Studies in Mathematics and Mechanics Presented to {Richard von Mises} by friends, colleagues, and pupils

rawtitle:
Studies in Mathematics and Mechanics Presented to {Richard von Mises} by friends, colleagues, and pupils

entry:
@Book{Birkhoff:1954:SMM,
  editor =       "Garrett Birkhoff",
  booktitle =    "Studies in Mathematics and Mechanics Presented to
                 {Richard von Mises} by friends, colleagues, and
                 pupils",
  title =        "Studies in Mathematics and Mechanics Presented to
                 {Richard von Mises} by friends, colleagues, and
                 pupils",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "ix + 353",
  year =         "1954",
  ISBN =         "1-4832-6356-8",
  ISBN-13 =      "978-1-4832-6356-4",
  LCCN =         "QA3 .S853",
  bibdate =      "Fri Oct 20 10:13:10 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "Studies in Mathematics and Mechanics is a collection
                 of studies presented to Professor Richard von Mises as
                 a token of reverence and appreciation on the occasion
                 of his seventieth birthday which occurred on April 19,
                 1953. von Mises' thought has been a stimulus in many
                 seemingly unconnected fields of mathematics, science,
                 and philosophy, to which he has contributed decisive
                 results and new formulations of fundamental concepts.
                 The book contains 42 chapters organized into five
                 parts. Part I contains papers on algebra, number theory
                 and geometry. These include a study of Poincar{\'e}'s
                 representation of a hyperbolic space on an Euclidean
                 half-space and elementary estimates for the least
                 primitive root. Part II on analysis includes papers on
                 a generalization of Green's Formula and its application
                 to the Cauchy problem for a hyperbolic equation, and
                 the fundamental solutions of a singular Beltrami
                 operator. Part III deals with theoretical mechanics and
                 covers topics such as turbulent flow, axially symmetric
                 flow, and oscillating wakes. The papers in Part IV
                 focus on applied mechanics. These include studies on
                 plastic flow under high stresses and the problem of
                 inelastic thermal stresses. Part V presents studies on
                 probability and statistics, including a finite
                 frequency theory of probability and the problem of
                 expansion of clusters of galaxies.",
  acknowledgement = ack-nhfb,
  subject-dates = "Richard von Mises (1883--1953)",
}


bibtype: book
filename: elefunt.bib
label: Langer:1959:NAP
editor: R. E. Langer
booktitle: On numerical approximation. Proceedings of a Symposium, Madison, April 21--23, 1958
title: On numerical approximation. Proceedings of a Symposium, Madison, April 21--23, 1958
publisher: The University of Wisconsin Press
address: Madison, WI, USA
pages: x + 462
year: 1959
LCCN: QA3 .U45 no. 1
bibdate: Tue Jun 19 06:45:47 2018
bibtimestamp: 2018.06.19 06:45:47 ???
note: Publication no. 1 of the Mathematics Research Center, U.S. Army, the University of Wisconsin.
acknowledgement: ack-nhfb
rawbooktitle: On numerical approximation. {Proceedings of a Symposium, Madison, April 21--23, 1958}
raweditor: R. E. Langer
rawnote: Publication no. 1 of the Mathematics Research Center, U.S. Army, the University of Wisconsin.
rawtitle: On numerical approximation. {Proceedings of a Symposium, Madison, April 21--23, 1958}
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib; https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

TOC:
1. On trends and problems in numerical approximation / Ostrowski 2. Linear spaces and approximation theory / Buck 3. Operational methods in numerical analysis based on rational approximations / Kopal 4. On the numerical integration of periodic analytic functions / Davis S. Some new divided difference algorithms in two variables / Salzer 6. Numerical evaluation of multiple integrals / Hammer 7. Optimal approximation and error bounds / Golomb and Weinberger 8. The rationale of approximation / Sard 9. On extremal approximations / Walsh 10. Numerical methods of Tchebycheff approximation / Stiefel 11. Minimax methods in table construction / Fox 12. Existence of essentially nonlinear families suitable for oscillatory approximation / Motzkin 13. On variation diminishing approximation methods / Schoenberg 14. Approximation by functions of fewer variables / Golomb 15. Extremal approximations --- a summary / Miller 16. Survey of recent Russian literature on approximation / Buck 17. The quotient--difference and epsilon algorithms / Bauer 18. Some sufficient conditions for the existence of an asymptotic formula or an asymptotic expansion / Rosser 19. The estimation of (power) spectra and related quantities / Tukey 20. Approximation in partial differential equations / Collatz 21. Special polynomials in numerical analysis / Todd

rawTOC:
1. On trends and problems in numerical approximation / Ostrowski \\ 2. Linear spaces and approximation theory / Buck \\ 3. Operational methods in numerical analysis based on rational approximations / Kopal \\ 4. On the numerical integration of periodic analytic functions / Davis \\ S. Some new divided difference algorithms in two variables / Salzer \\ 6. Numerical evaluation of multiple integrals / Hammer \\ 7. Optimal approximation and error bounds / Golomb and Weinberger \\ 8. The rationale of approximation / Sard \\ 9. On extremal approximations / Walsh \\ 10. Numerical methods of Tchebycheff approximation / Stiefel \\ 11. Minimax methods in table construction / Fox \\ 12. Existence of essentially nonlinear families suitable for oscillatory approximation / Motzkin \\ 13. On variation diminishing approximation methods / Schoenberg \\ 14. Approximation by functions of fewer variables / Golomb \\ 15. Extremal approximations --- a summary / Miller \\ 16. Survey of recent Russian literature on approximation / Buck \\ 17. The quotient--difference and epsilon algorithms / Bauer \\ 18. Some sufficient conditions for the existence of an asymptotic formula or an asymptotic expansion / Rosser \\ 19. The estimation of (power) spectra and related quantities / Tukey \\ 20. Approximation in partial differential equations / Collatz \\ 21. Special polynomials in numerical analysis / Todd

entry:
@Book{Langer:1959:NAP,
  editor =       "R. E. Langer",
  booktitle =    "On numerical approximation. {Proceedings of a
                 Symposium, Madison, April 21--23, 1958}",
  title =        "On numerical approximation. {Proceedings of a
                 Symposium, Madison, April 21--23, 1958}",
  publisher =    "The University of Wisconsin Press",
  address =      "Madison, WI, USA",
  pages =        "x + 462",
  year =         "1959",
  LCCN =         "QA3 .U45 no. 1",
  bibdate =      "Tue Jun 19 06:45:47 2018",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/bauer-friedrich-ludwig.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stiefel-eduard.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Publication no. 1 of the Mathematics Research Center,
                 U.S. Army, the University of Wisconsin.",
  acknowledgement = ack-nhfb,
  subjects =     "statistics",
  tableofcontents = "1. On trends and problems in numerical
                 approximation / Ostrowski \\
                 2. Linear spaces and approximation theory / Buck \\
                 3. Operational methods in numerical analysis based on
                 rational approximations / Kopal \\
                 4. On the numerical integration of periodic analytic
                 functions / Davis \\
                 S. Some new divided difference algorithms in two
                 variables / Salzer \\
                 6. Numerical evaluation of multiple integrals / Hammer
                 \\
                 7. Optimal approximation and error bounds / Golomb and
                 Weinberger \\
                 8. The rationale of approximation / Sard \\
                 9. On extremal approximations / Walsh \\
                 10. Numerical methods of Tchebycheff approximation /
                 Stiefel \\
                 11. Minimax methods in table construction / Fox \\
                 12. Existence of essentially nonlinear families
                 suitable for oscillatory approximation / Motzkin \\
                 13. On variation diminishing approximation methods /
                 Schoenberg \\
                 14. Approximation by functions of fewer variables /
                 Golomb \\
                 15. Extremal approximations --- a summary / Miller \\
                 16. Survey of recent Russian literature on
                 approximation / Buck \\
                 17. The quotient--difference and epsilon algorithms /
                 Bauer \\
                 18. Some sufficient conditions for the existence of an
                 asymptotic formula or an asymptotic expansion / Rosser
                 \\
                 19. The estimation of (power) spectra and related
                 quantities / Tukey \\
                 20. Approximation in partial differential equations /
                 Collatz \\
                 21. Special polynomials in numerical analysis / Todd",
}


bibtype: book
filename: elefunt.bib
label: Ralston:1960:MMD
editor: Anthony Ralston and Herbert S. Wilf
booktitle: Mathematical methods for digital computers
title: Mathematical methods for digital computers
publisher: pub-WILEY
address: pub-WILEY:adr
pages: various
year: 1960 -- 1977
ISBN: 0-471-70690-6 OR 0471706906
ISBN13: 978-0-471-70690-8 OR 9780471706908
LCCN: QA39 .R26
bibdate: Mon Jan 13 10:36:06 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.13 10:36:06 ???
note: Three volumes.
acknowledgement: ack-nhfb
rawbooktitle: Mathematical methods for digital computers
raweditor: Anthony Ralston and Herbert S. Wilf
rawnote: Three volumes.
rawtitle: Mathematical methods for digital computers
entry:
@Book{Ralston:1960:MMD,
  editor =       "Anthony Ralston and Herbert S. Wilf",
  booktitle =    "Mathematical methods for digital computers",
  title =        "Mathematical methods for digital computers",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "various",
  year =         "1960--1977",
  ISBN =         "0-471-70690-6",
  ISBN-13 =      "978-0-471-70690-8",
  LCCN =         "QA39 .R26",
  bibdate =      "Mon Jan 13 10:36:06 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Three volumes.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Abramowitz:1964:HMF
editor: Milton Abramowitz and Irene A. Stegun
booktitle: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
title: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
volume: 55
publisher: U. S. Department of Commerce
address: Washington, DC, USA
pages: xiv + 1046
year: 1964
LCCN: QA47.A161 1972; QA 55 A16h 1972
bibdate: Thu Jan 27 07:58:12 2000
bibtimestamp: 2000.01.27 07:58:12 ???
series: Applied mathematics series
acknowledgement: ack-nhfb
key: NBS
rawbooktitle: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
raweditor: Milton Abramowitz and Irene A. Stegun
rawtitle: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables
bibsource:
https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/master.bib

note:
Tenth printing, with corrections (December 1972). This book is also available online at path =http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP= in bitmap image format.

abstract:
This book is a compendium of mathematical formulas, tables, and graphs. It contains a table of analytical integrals, differential equations, and numerical series; and includes tables of trigonometric and hyperbolic functions, tables for numerical integration, rules for differentiation and integration, and techniques for point interpolation and function approximation. Additionally, it devotes a entire section to mathematical and physical constants as fractions and powers of Pi, e, and prime numbers; and discusses statistics by presenting combinatorial analysis and probability functions.

TOC:
Mathematical constants / David S. Liepman Physical constants and conversion factors / A. G. McNish Elementary analytical methods / Milton Abramowitz Elementary transcendental functions: logarithmic, exponential, circular and hyperbolic functions / Ruth Zucker Exponential integral and related functions / Walter Gautschi and William F. Cahill Gamma function and related functions / Philip J. Davis Error function and Fresnel integrals / Walter Gautschi Legendre functions / Irene A. Stegun Bessel functions of integer order / F. W. J. Olver Bessell functions of fractional order / H. A. Antosiewicz Integrals of Bessel functions / Yudell L. Luke Struve functions and related functions / Milton Abramowitz Confluent hypergeometric functions / Lucy Joan Slater Coulomb wave functions / Milton Abramowitz Hypergeometric functions / Fritz Oberhettinger Jacobian elliptic functions and theta functions; Elliptic integrals / L. M. Milne-Thomson Weierstrass elliptic and related functions / Thomas H. Southard Parabolic cylinder functions / J. C. P. Millerldots Mathieu functions / Gertrude Blanch Spheroidal wave functions / Arnold N. Lowan Orthogonal polynomials / Urs W. Hochstrasser Bernoulli and Euler polynomials, Riemann zeta function / Emilie V. Haynesworth and Karl Goldberg Combinatorial analysis / K. Goldberg, M. Newman and E. Haynesworth Numerical interpolation, differentiation and integration / Philip J. Davis and Ivan Polonsky Probability functions / Marvin Zelen and Norman C. Severo Miscellaneous functions / Irene A. Stegun Scales of notation / S. Peavy and A. Schopf Laplace transforms

rawabstract:
This book is a compendium of mathematical formulas, tables, and graphs. It contains a table of analytical integrals, differential equations, and numerical series; and includes tables of trigonometric and hyperbolic functions, tables for numerical integration, rules for differentiation and integration, and techniques for point interpolation and function approximation. Additionally, it devotes a entire section to mathematical and physical constants as fractions and powers of Pi, e, and prime numbers; and discusses statistics by presenting combinatorial analysis and probability functions.

rawnote:
Tenth printing, with corrections (December 1972). This book is also available online at \path=http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP= in bitmap image format.

rawTOC:
Mathematical constants / David S. Liepman \\ Physical constants and conversion factors / A. G. McNish \\ Elementary analytical methods / Milton Abramowitz \\ Elementary transcendental functions: logarithmic, exponential, circular and hyperbolic functions / Ruth Zucker \\ Exponential integral and related functions / Walter Gautschi and William F. Cahill \\ Gamma function and related functions / Philip J. Davis \\ Error function and Fresnel integrals / Walter Gautschi \\ Legendre functions / Irene A. Stegun \\ Bessel functions of integer order / F. W. J. Olver \\ Bessell functions of fractional order / H. A. Antosiewicz \\ Integrals of Bessel functions / Yudell L. Luke \\ Struve functions and related functions / Milton Abramowitz \\ Confluent hypergeometric functions / Lucy Joan Slater \\ Coulomb wave functions / Milton Abramowitz \\ Hypergeometric functions / Fritz Oberhettinger \\ Jacobian elliptic functions and theta functions; Elliptic integrals / L. M. Milne-Thomson \\ Weierstrass elliptic and related functions / Thomas H. Southard \\ Parabolic cylinder functions / J. C. P. Miller\ldots{} Mathieu functions / Gertrude Blanch \\ Spheroidal wave functions / Arnold N. Lowan \\ Orthogonal polynomials / Urs W. Hochstrasser \\ Bernoulli and Euler polynomials, Riemann zeta function / Emilie V. Haynesworth and Karl Goldberg \\ Combinatorial analysis / K. Goldberg, M. Newman and E. Haynesworth \\ Numerical interpolation, differentiation and integration / Philip J. Davis and Ivan Polonsky \\ Probability functions / Marvin Zelen and Norman C. Severo \\ Miscellaneous functions / Irene A. Stegun \\ Scales of notation / S. Peavy and A. Schopf \\ Laplace transforms

entry:
@Book{Abramowitz:1964:HMF,
  editor =       "Milton Abramowitz and Irene A. Stegun",
  key =          "NBS",
  booktitle =    "Handbook of Mathematical Functions with Formulas,
                 Graphs, and Mathematical Tables",
  title =        "Handbook of Mathematical Functions with Formulas,
                 Graphs, and Mathematical Tables",
  volume =       "55",
  publisher =    "U. S. Department of Commerce",
  address =      "Washington, DC, USA",
  pages =        "xiv + 1046",
  year =         "1964",
  LCCN =         "QA47.A161 1972; QA 55 A16h 1972",
  bibdate =      "Thu Jan 27 07:58:12 2000",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/han-wri-mat-sci-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib",
  note =         "Tenth printing, with corrections (December 1972). This
                 book is also available online at
                 \path=http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP=
                 in bitmap image format.",
  series =       "Applied mathematics series",
  abstract =     "This book is a compendium of mathematical formulas,
                 tables, and graphs. It contains a table of analytical
                 integrals, differential equations, and numerical
                 series; and includes tables of trigonometric and
                 hyperbolic functions, tables for numerical integration,
                 rules for differentiation and integration, and
                 techniques for point interpolation and function
                 approximation. Additionally, it devotes a entire
                 section to mathematical and physical constants as
                 fractions and powers of Pi, e, and prime numbers; and
                 discusses statistics by presenting combinatorial
                 analysis and probability functions.",
  acknowledgement = ack-nhfb,
  tableofcontents = "Mathematical constants / David S. Liepman \\
                 Physical constants and conversion factors / A. G.
                 McNish \\
                 Elementary analytical methods / Milton Abramowitz \\
                 Elementary transcendental functions: logarithmic,
                 exponential, circular and hyperbolic functions / Ruth
                 Zucker \\
                 Exponential integral and related functions / Walter
                 Gautschi and William F. Cahill \\
                 Gamma function and related functions / Philip J. Davis
                 \\
                 Error function and Fresnel integrals / Walter Gautschi
                 \\
                 Legendre functions / Irene A. Stegun \\
                 Bessel functions of integer order / F. W. J. Olver \\
                 Bessell functions of fractional order / H. A.
                 Antosiewicz \\
                 Integrals of Bessel functions / Yudell L. Luke \\
                 Struve functions and related functions / Milton
                 Abramowitz \\
                 Confluent hypergeometric functions / Lucy Joan Slater
                 \\
                 Coulomb wave functions / Milton Abramowitz \\
                 Hypergeometric functions / Fritz Oberhettinger \\
                 Jacobian elliptic functions and theta functions;
                 Elliptic integrals / L. M. Milne-Thomson \\
                 Weierstrass elliptic and related functions / Thomas H.
                 Southard \\
                 Parabolic cylinder functions / J. C. P. Miller\ldots{}
                 Mathieu functions / Gertrude Blanch \\
                 Spheroidal wave functions / Arnold N. Lowan \\
                 Orthogonal polynomials / Urs W. Hochstrasser \\
                 Bernoulli and Euler polynomials, Riemann zeta function
                 / Emilie V. Haynesworth and Karl Goldberg \\
                 Combinatorial analysis / K. Goldberg, M. Newman and E.
                 Haynesworth \\
                 Numerical interpolation, differentiation and
                 integration / Philip J. Davis and Ivan Polonsky \\
                 Probability functions / Marvin Zelen and Norman C.
                 Severo \\
                 Miscellaneous functions / Irene A. Stegun \\
                 Scales of notation / S. Peavy and A. Schopf \\
                 Laplace transforms",
}


bibtype: book
filename: elefunt.bib
label: Magnus:1966:FTS
author: Wilhelm Magnus and Fritz Oberhettinger and Raj Pal Soni
booktitle: Formulas and theorems for the special functions of mathematical physics
title: Formulas and theorems for the special functions of mathematical physics
publisher: pub-SV
address: pub-SV:adr
edition: Third
pages: viii + 508
year: 1966
LCCN: QA1 G88 v. 52, 1966
bibdate: Sat Oct 30 18:23:25 2010
bibtimestamp: 2010.10.30 18:23:25 ???
note: See errata cite Cohl:2012:TEF,Szmytkowski:2013:EBT.
acknowledgement: ack-nhfb
rawauthor: Wilhelm Magnus and Fritz Oberhettinger and Raj Pal Soni
rawbooktitle: Formulas and theorems for the special functions of mathematical physics
rawnote: See errata \cite{Cohl:2012:TEF,Szmytkowski:2013:EBT}.
rawtitle: Formulas and theorems for the special functions of mathematical physics
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib

entry:
@Book{Magnus:1966:FTS,
  author =       "Wilhelm Magnus and Fritz Oberhettinger and Raj Pal
                 Soni",
  booktitle =    "Formulas and theorems for the special functions of
                 mathematical physics",
  title =        "Formulas and theorems for the special functions of
                 mathematical physics",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Third",
  pages =        "viii + 508",
  year =         "1966",
  LCCN =         "QA1 G88 v. 52, 1966",
  bibdate =      "Sat Oct 30 18:23:25 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp2010.bib",
  note =         "See errata
                 \cite{Cohl:2012:TEF,Szmytkowski:2013:EBT}.",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: AFIPS:1969:ACPb
booktitle: 1969 Fall Joint Computer Conference, November 18--20, 1969, Las Vegas, Nevada
title: 1969 Fall Joint Computer Conference, November 18--20, 1969, Las Vegas, Nevada
volume: 35
publisher: pub-AFIPS
address: pub-AFIPS:adr
pages: 807
year: 1969
LCCN: TK7885.A1 J6 1969
bibdate: Sat Sep 24 01:06:00 1994
bibtimestamp: 1994.09.24 01:06:00 ???
series: AFIPS conference proceedings
acknowledgement: ack-nhfb
key: AFIPS FJCC '69
rawbooktitle: 1969 Fall Joint Computer Conference, November 18--20, 1969, Las Vegas, Nevada
rawtitle: 1969 Fall Joint Computer Conference, November 18--20, 1969, Las Vegas, Nevada
entry:
@Proceedings{AFIPS:1969:ACPb,
  key =          "AFIPS FJCC '69",
  booktitle =    "1969 Fall Joint Computer Conference, November 18--20,
                 1969, Las Vegas, Nevada",
  title =        "1969 Fall Joint Computer Conference, November 18--20,
                 1969, Las Vegas, Nevada",
  volume =       "35",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "807",
  year =         "1969",
  LCCN =         "TK7885.A1 J6 1969",
  bibdate =      "Sat Sep 24 01:06:00 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",
  series =       "AFIPS conference proceedings",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: AFIPS:1971:ACP
booktitle: 1971 Spring Joint Computer Conference, May 18--20, 1971, Atlantic City, New Jersey
title: 1971 Spring Joint Computer Conference, May 18--20, 1971, Atlantic City, New Jersey
volume: 38
publisher: pub-AFIPS
address: pub-AFIPS:adr
pages: 631
year: 1971
bibdate: Fri Sep 16 10:47:01 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.16 10:47:01 ???
series: AFIPS conference proceedings
acknowledgement: ack-nj
key: AFIPS SJCC '71
rawbooktitle: 1971 Spring Joint Computer Conference, May 18--20, 1971, Atlantic City, New Jersey
rawtitle: 1971 Spring Joint Computer Conference, May 18--20, 1971, Atlantic City, New Jersey
entry:
@Proceedings{AFIPS:1971:ACP,
  key =          "AFIPS SJCC '71",
  booktitle =    "1971 Spring Joint Computer Conference, May 18--20,
                 1971, Atlantic City, New Jersey",
  title =        "1971 Spring Joint Computer Conference, May 18--20,
                 1971, Atlantic City, New Jersey",
  volume =       "38",
  publisher =    pub-AFIPS,
  address =      pub-AFIPS:adr,
  pages =        "631",
  year =         "1971",
  LCCN =         "????",
  bibdate =      "Fri Sep 16 10:47:01 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "AFIPS conference proceedings",
  acknowledgement = ack-nj # " and " # ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Rice:1971:MS
author: John R. Rice
booktitle: Mathematical Software
title: Mathematical Software
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xvii + 515
year: 1971
ISBN: 0-12-587250-X OR 012587250X
ISBN13: 978-0-12-587250-8 OR 9780125872508
LCCN: QA1 .M26
bibdate: Thu Sep 15 18:56:52 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.15 18:56:52 ???
acknowledgement: ack-nhfb
rawauthor: John R. Rice
rawbooktitle: Mathematical Software
rawtitle: Mathematical Software
note:
Based on the proceedings of the Mathematical Software Symposium held at Purdue University, Lafayette, Indiana, USA, April 1--3, 1970.

rawnote:
Based on the proceedings of the Mathematical Software Symposium held at Purdue University, Lafayette, Indiana, USA, April 1--3, 1970.

entry:
@Book{Rice:1971:MS,
  author =       "John R. Rice",
  booktitle =    "Mathematical Software",
  title =        "Mathematical Software",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xvii + 515",
  year =         "1971",
  ISBN =         "0-12-587250-X",
  ISBN-13 =      "978-0-12-587250-8",
  LCCN =         "QA1 .M26",
  bibdate =      "Thu Sep 15 18:56:52 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Based on the proceedings of the Mathematical Software
                 Symposium held at Purdue University, Lafayette,
                 Indiana, USA, April 1--3, 1970.",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Askey:1975:TAS
editor: Richard Askey
number: 35
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: xi + 560
year: 1975
ISBN: 0-12-064850-4 OR 0120648504
ISBN13: 978-0-12-064850-4 OR 9780120648504
LCCN: QA3 .U45 no. 35 QA351
bibdate: Sat Oct 30 07:41:32 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 07:41:32 MDT
series: Publication of the Mathematics Research Center, the University of Wisconsin
subject: Functions, Special; Congresses
acknowledgement: ack-nhfb
raweditor: Richard Askey
booktitle:
Theory and application of special functions: proceedings of an advanced seminar sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31--April 2, 1975

title:
Theory and application of special functions: proceedings of an advanced seminar sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31--April 2, 1975

rawbooktitle:
{Theory and application of special functions: proceedings of an advanced seminar sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31--April 2, 1975}

rawtitle:
{Theory and application of special functions: proceedings of an advanced seminar sponsored by the Mathematics Research Center, the University of Wisconsin-Madison, March 31--April 2, 1975}

entry:
@Proceedings{Askey:1975:TAS,
  editor =       "Richard Askey",
  booktitle =    "{Theory and application of special functions:
                 proceedings of an advanced seminar sponsored by the
                 Mathematics Research Center, the University of
                 Wisconsin-Madison, March 31--April 2, 1975}",
  title =        "{Theory and application of special functions:
                 proceedings of an advanced seminar sponsored by the
                 Mathematics Research Center, the University of
                 Wisconsin-Madison, March 31--April 2, 1975}",
  number =       "35",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "xi + 560",
  year =         "1975",
  ISBN =         "0-12-064850-4",
  ISBN-13 =      "978-0-12-064850-4",
  LCCN =         "QA3 .U45 no. 35 QA351",
  bibdate =      "Sat Oct 30 07:41:32 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Publication of the Mathematics Research Center, the
                 University of Wisconsin",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  meetingname =  "Advanced Seminar on Special Functions, Madison, Wis.,
                 1975.",
  subject =      "Functions, Special; Congresses",
}


bibtype: proceedings
filename: elefunt.bib
label: Miller:1975:TNA
editor: John J. H. Miller
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: various
year: 1975
ISBN: 0-12-496950-X OR 012496950X
ISBN13: 978-0-12-496950-6 OR 9780124969506
LCCN: QA297 .R69 1973
bibdate: Mon Jan 13 10:41:13 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.13 10:41:13 ???
acknowledgement: ack-nhfb
raweditor: John J. H. Miller
booktitle:
Topics in numerical analysis: proceedings of the Royal Irish Academy Conference on Numerical Analysis, 1972, 1974, 1976

title:
Topics in numerical analysis: proceedings of the Royal Irish Academy Conference on Numerical Analysis, 1972, 1974, 1976

rawbooktitle:
Topics in numerical analysis: proceedings of the Royal Irish Academy Conference on Numerical Analysis, 1972, 1974, 1976

entry:
@Proceedings{Miller:1975:TNA,
  editor =       "John J. H. Miller",
  booktitle =    "Topics in numerical analysis: proceedings of the Royal
                 Irish Academy Conference on Numerical Analysis, 1972,
                 1974, 1976",
  title =        "Topics in numerical analysis: proceedings of the Royal
                 Irish Academy Conference on Numerical Analysis, 1972,
                 1974, 1976",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "various",
  year =         "1975",
  ISBN =         "0-12-496950-X",
  ISBN-13 =      "978-0-12-496950-6",
  LCCN =         "QA297 .R69 1973",
  bibdate =      "Mon Jan 13 10:41:13 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Traub:1976:ACC
editor: J. F. (Joseph Frederick) Traub
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: ix + 239
year: 1976
ISBN: 0-12-697560-4 OR 0126975604
ISBN13: 978-0-12-697560-4 OR 9780126975604
LCCN: QA297.S9151 1975
bibdate: Mon Jan 13 10:18:33 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.13 10:18:33 ???
acknowledgement: ack-nhfb
raweditor: J. F. (Joseph Frederick) Traub
booktitle:
Analytic computational complexity: Proceedings of the Symposium on Analytic Computational Complexity, held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7--8, 1975

title:
Analytic computational complexity: Proceedings of the Symposium on Analytic Computational Complexity, held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7--8, 1975

rawbooktitle:
{Analytic computational complexity: Proceedings of the Symposium on Analytic Computational Complexity, held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7--8, 1975}

rawtitle:
{Analytic computational complexity: Proceedings of the Symposium on Analytic Computational Complexity, held by the Computer Science Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania, on April 7--8, 1975}

entry:
@Proceedings{Traub:1976:ACC,
  editor =       "J. F. (Joseph Frederick) Traub",
  booktitle =    "{Analytic computational complexity: Proceedings of the
                 Symposium on Analytic Computational Complexity, held by
                 the Computer Science Department, Carnegie-Mellon
                 University, Pittsburgh, Pennsylvania, on April 7--8,
                 1975}",
  title =        "{Analytic computational complexity: Proceedings of the
                 Symposium on Analytic Computational Complexity, held by
                 the Computer Science Department, Carnegie-Mellon
                 University, Pittsburgh, Pennsylvania, on April 7--8,
                 1975}",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "ix + 239",
  year =         "1976",
  ISBN =         "0-12-697560-4",
  ISBN-13 =      "978-0-12-697560-4",
  LCCN =         "QA297.S9151 1975",
  bibdate =      "Mon Jan 13 10:18:33 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Cowell:1977:PMS
editor: Wayne Cowell
booktitle: Portability of Numerical Software Workshop, Oak Brook, Illinois, June 21--23, 1976
title: Portability of Numerical Software Workshop, Oak Brook, Illinois, June 21--23, 1976
volume: 57
publisher: pub-SV
address: pub-SV:adr
pages: viii + 539
year: 1977
ISBN: 0-387-08446-0 OR 0387084460
ISBN13: 978-0-387-08446-6 OR 9780387084466
LCCN: QA297 .W65 1976
bibdate: Sat Sep 24 00:24:09 1994
bibtimestamp: 1994.09.24 00:24:09 ???
series: Lecture Notes in Computer Science
remark: Workshop organized by Argonne National Laboratory.
acknowledgement: ack-nhfb
rawbooktitle: {Portability of Numerical Software Workshop, Oak Brook, Illinois, June 21--23, 1976}
raweditor: Wayne Cowell
rawtitle: {Portability of Numerical Software Workshop, Oak Brook, Illinois, June 21--23, 1976}
entry:
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  editor =       "Wayne Cowell",
  booktitle =    "{Portability of Numerical Software Workshop, Oak
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  title =        "{Portability of Numerical Software Workshop, Oak
                 Brook, Illinois, June 21--23, 1976}",
  volume =       "57",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "viii + 539",
  year =         "1977",
  ISBN =         "0-387-08446-0",
  ISBN-13 =      "978-0-387-08446-6",
  LCCN =         "QA297 .W65 1976",
  bibdate =      "Sat Sep 24 00:24:09 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",
  series =       "Lecture Notes in Computer Science",
  acknowledgement = ack-nhfb,
  citedby =      "Fullerton:1980:BEM",
  remark =       "Workshop organized by Argonne National Laboratory.",
}


bibtype: proceedings
filename: elefunt.bib
label: IEEE:1978:PSC
editor: IEEE
booktitle: Proceedings of the Symposium on Computer Arithmetic (4th: 1978: Santa Monica, CA)
title: Proceedings of the Symposium on Computer Arithmetic (4th: 1978: Santa Monica, CA)
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xi + 274
year: 1978
ISSN: 1063-6889 OR 10636889
LCCN: QA76.6 .S919a
bibdate: Mon May 19 15:22:15 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.19 15:22:15 ???
note: IEEE catalog no. 78 CH1412-6C.
acknowledgement: ack-nhfb
rawbooktitle: Proceedings of the Symposium on Computer Arithmetic {(4th: 1978: Santa Monica, CA)}
raweditor: {IEEE}
rawnote: IEEE catalog no. 78 CH1412-6C.
rawtitle: Proceedings of the Symposium on Computer Arithmetic {(4th: 1978: Santa Monica, CA)}
keywords:
Computer arithmetic --- Congresses.; Electronic digital computers --- Programming --- Congresses.; Floating-point arithmetic --- Congresses.

entry:
@Proceedings{IEEE:1978:PSC,
  editor =       "{IEEE}",
  booktitle =    "Proceedings of the Symposium on Computer Arithmetic
                 {(4th: 1978: Santa Monica, CA)}",
  title =        "Proceedings of the Symposium on Computer Arithmetic
                 {(4th: 1978: Santa Monica, CA)}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 274",
  year =         "1978",
  ISSN =         "1063-6889",
  LCCN =         "QA76.6 .S919a",
  bibdate =      "Mon May 19 15:22:15 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE catalog no. 78 CH1412-6C.",
  acknowledgement = ack-nhfb,
  keywords =     "Computer arithmetic --- Congresses.; Electronic
                 digital computers --- Programming --- Congresses.;
                 Floating-point arithmetic --- Congresses.",
}


bibtype: proceedings
filename: elefunt.bib
label: Alefeld:1980:PSE
editor: G. Alefeld and R. D. Grigorieff and R. Albrecht and U. Kulisch and F. Stummel
volume: 2
publisher: pub-SV
address: pub-SV:adr
pages: 229
year: 1980
ISBN: 0-387-81566-X OR 038781566X
ISBN13: 978-0-387-81566-4 OR 9780387815664
ISSN: 0344-8029 OR 03448029
LCCN: QA297 .F84
bibdate: Mon Jan 13 10:20:47 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.13 10:20:47 ???
series: Computing. Supplementum
acknowledgement: ack-nhfb
raweditor: G. Alefeld and R. D. Grigorieff and R. Albrecht and U. Kulisch and F. Stummel
booktitle:
Fundamentals of numerical computation (computer-oriented numerical analysis). Proceedings of a conference held June 5--8, 1979, on the occasion of the centennial of the Technical University of Berlin

title:
Fundamentals of numerical computation (computer-oriented numerical analysis). Proceedings of a conference held June 5--8, 1979, on the occasion of the centennial of the Technical University of Berlin

rawbooktitle:
{Fundamentals of numerical computation (computer-oriented numerical analysis). Proceedings of a conference held June 5--8, 1979, on the occasion of the centennial of the Technical University of Berlin}

rawtitle:
{Fundamentals of numerical computation (computer-oriented numerical analysis). Proceedings of a conference held June 5--8, 1979, on the occasion of the centennial of the Technical University of Berlin}

entry:
@Proceedings{Alefeld:1980:PSE,
  editor =       "G. Alefeld and R. D. Grigorieff and R. Albrecht and U.
                 Kulisch and F. Stummel",
  booktitle =    "{Fundamentals of numerical computation
                 (computer-oriented numerical analysis). Proceedings of
                 a conference held June 5--8, 1979, on the occasion of
                 the centennial of the Technical University of Berlin}",
  title =        "{Fundamentals of numerical computation
                 (computer-oriented numerical analysis). Proceedings of
                 a conference held June 5--8, 1979, on the occasion of
                 the centennial of the Technical University of Berlin}",
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  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "229",
  year =         "1980",
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  ISBN-13 =      "978-0-387-81566-4",
  ISSN =         "0344-8029",
  LCCN =         "QA297 .F84",
  bibdate =      "Mon Jan 13 10:20:47 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Computing. Supplementum",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Dieudonne:1980:SFL
editor: Jean Dieudonne
booktitle: Special functions and linear representations of Lie groups
title: Special functions and linear representations of Lie groups
volume: 42
address: Providence, RI, USA
pages: iii + 59
year: 1980
ISBN: 0-8218-1692-6 OR 0821816926
ISBN13: 978-0-8218-1692-9 OR 9780821816929
bibdate: Sat Oct 30 17:14:47 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.bibsys.no:2100/BIBSYS
bibtimestamp: 2010.10.30 17:14:47 MDT
series: Regional conference series in mathematics
acknowledgement: ack-nhfb
rawbooktitle: {Special functions and linear representations of Lie groups}
raweditor: Jean Dieudonn{\'e}
rawtitle: {Special functions and linear representations of Lie groups}
publisher:
Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society

remark:
Expository lectures from the CBMS regional conference held at East Carolina University, March 5--9, 1979.

entry:
@Proceedings{Dieudonne:1980:SFL,
  editor =       "Jean Dieudonn{\'e}",
  booktitle =    "{Special functions and linear representations of Lie
                 groups}",
  title =        "{Special functions and linear representations of Lie
                 groups}",
  volume =       "42",
  publisher =    "Published for the Conference Board of the Mathematical
                 Sciences by the American Mathematical Society",
  address =      "Providence, RI, USA",
  pages =        "iii + 59",
  year =         "1980",
  ISBN =         "0-8218-1692-6",
  ISBN-13 =      "978-0-8218-1692-9",
  LCCN =         "????",
  bibdate =      "Sat Oct 30 17:14:47 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
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  series =       "Regional conference series in mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Expository lectures from the CBMS regional conference
                 held at East Carolina University, March 5--9, 1979.",
}


bibtype: proceedings
filename: elefunt.bib
label: Lavington:1980:IPP
editor: Simon Hugh Lavington
publisher: pub-ENH
address: pub-ENH:adr
pages: xiii + 1070
year: 1980
ISBN: 0-444-86034-7 OR 0444860347
ISBN13: 978-0-444-86034-7 OR 9780444860347
LCCN: QA 75.5 I57 1980
bibdate: Thu Sep 01 23:09:20 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 23:09:20 ???
acknowledgement: ack-nhfb
raweditor: Simon Hugh Lavington
booktitle:
Information Processing 80: Proceedings of IFIP Congress 80, Tokyo, Japan, October 6--9, 1980, Melbourne, Australia, October 14--17, 1980

title:
Information Processing 80: Proceedings of IFIP Congress 80, Tokyo, Japan, October 6--9, 1980, Melbourne, Australia, October 14--17, 1980

rawbooktitle:
Information Processing 80: Proceedings of {IFIP} Congress 80, Tokyo, Japan, October 6--9, 1980, Melbourne, Australia, October 14--17, 1980

rawtitle:
Information Processing 80: Proceedings of {IFIP} Congress 80, Tokyo, Japan, October 6--9, 1980, Melbourne, Australia, October 14--17, 1980

entry:
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  editor =       "Simon Hugh Lavington",
  booktitle =    "Information Processing 80: Proceedings of {IFIP}
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                 Melbourne, Australia, October 14--17, 1980",
  title =        "Information Processing 80: Proceedings of {IFIP}
                 Congress 80, Tokyo, Japan, October 6--9, 1980,
                 Melbourne, Australia, October 14--17, 1980",
  publisher =    pub-ENH,
  address =      pub-ENH:adr,
  pages =        "xiii + 1070",
  year =         "1980",
  ISBN =         "0-444-86034-7",
  ISBN-13 =      "978-0-444-86034-7",
  LCCN =         "QA 75.5 I57 1980",
  bibdate =      "Thu Sep 01 23:09:20 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: IEEE:1981:PIS
editor: IEEE
publisher: pub-IEEE
address: pub-IEEE:adr
pages: vii + 278
year: 1981
LCCN: QA76.9.C62 S95 1981
bibdate: Mon May 19 13:17:13 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.05.19 13:17:13 ???
note: IEEE Catalog No. 81CH1630-3. Computer Society Order No. 347.
acknowledgement: ack-nhfb
raweditor: {IEEE}
rawnote: IEEE Catalog No. 81CH1630-3. Computer Society Order No. 347.
booktitle:
Proceedings: 5th Symposium on Computer Arithmetic, May 18-19, 1981, University of Michigan, Ann Arbor, Michigan

title:
Proceedings: 5th Symposium on Computer Arithmetic, May 18-19, 1981, University of Michigan, Ann Arbor, Michigan

rawbooktitle:
Proceedings: 5th Symposium on Computer Arithmetic, May 18-19, 1981, University of Michigan, Ann Arbor, Michigan

entry:
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  booktitle =    "Proceedings: 5th Symposium on Computer Arithmetic, May
                 18-19, 1981, University of Michigan, Ann Arbor,
                 Michigan",
  title =        "Proceedings: 5th Symposium on Computer Arithmetic, May
                 18-19, 1981, University of Michigan, Ann Arbor,
                 Michigan",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "vii + 278",
  year =         "1981",
  LCCN =         "QA76.9.C62 S95 1981",
  bibdate =      "Mon May 19 13:17:13 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE Catalog No. 81CH1630-3. Computer Society Order
                 No. 347.",
  acknowledgement = ack-nhfb,
  xxISBN =       "none",
}


bibtype: proceedings
filename: elefunt.bib
label: IEEE:1981:PSC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: vii + 278
year: 1981
LCCN: QA 76.6 S985t 1981
bibdate: Sat Feb 24 15:01:45 MST 1996
bibtimestamp: 1996.02.24 15:01:45 MST
note: IEEE catalog number 81CH1630-C.
acknowledgement: ack-nhfb
key: IEEE CA5 '81
rawnote: IEEE catalog number 81CH1630-C.
booktitle:
Proceedings: 5th Symposium on Computer Arithmetic, May 18--19, 1981, University of Michigan, Ann Arbor, Michigan

title:
Proceedings: 5th Symposium on Computer Arithmetic: May 18--19, 1981, University of Michigan, Ann Arbor, Michigan

keywords:
ARITH-5; Computer arithmetic and logic units --- Congresses.; Electronic digital computers --- Programming --- Congresses.; Floating-point arithmetic Congresses.

rawbooktitle:
Proceedings: 5th Symposium on Computer Arithmetic, May 18--19, 1981, University of Michigan, Ann Arbor, Michigan

rawtitle:
Proceedings: 5th Symposium on Computer Arithmetic: May 18--19, 1981, University of Michigan, Ann Arbor, Michigan

entry:
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  booktitle =    "Proceedings: 5th Symposium on Computer Arithmetic, May
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  title =        "Proceedings: 5th Symposium on Computer Arithmetic: May
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  publisher =    pub-IEEE,
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  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
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  xxISBN =       "(none)",
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bibtype: proceedings
filename: elefunt.bib
label: Mulvey:1982:EMP
editor: J. M. Mulvey
volume: 199
publisher: pub-SV
address: pub-SV:adr
pages: xi + 379
year: 1982
ISBN: 0-387-11495-5 OR 0387114955
ISBN13: 978-0-387-11495-8 OR 9780387114958
LCCN: QA402.5 .E94 1982
bibdate: Thu Nov 17 06:36:49 1994
bibtimestamp: 1994.11.17 06:36:49 ???
series: Lecture Notes in Economics and Mathematical Systems
acknowledgement: ack-nhfb
raweditor: J. M. Mulvey
booktitle:
Evaluating Mathematical Programming Techniques: Proceedings of a Conference Held at the National Bureau of Standards, Boulder, Colorado, January 5--6, 1981

title:
Evaluating Mathematical Programming Techniques: Proceedings of a Conference Held at the National Bureau of Standards, Boulder, Colorado, January 5--6, 1981

rawbooktitle:
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rawtitle:
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  editor =       "J. M. Mulvey",
  booktitle =    "{Evaluating Mathematical Programming Techniques:
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  title =        "{Evaluating Mathematical Programming Techniques:
                 Proceedings of a Conference Held at the National Bureau
                 of Standards, Boulder, Colorado, January 5--6, 1981}",
  volume =       "199",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xi + 379",
  year =         "1982",
  ISBN =         "0-387-11495-5",
  ISBN-13 =      "978-0-387-11495-8",
  LCCN =         "QA402.5 .E94 1982",
  bibdate =      "Thu Nov 17 06:36:49 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",
  series =       "Lecture Notes in Economics and Mathematical Systems",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Hwang:1985:PSC
editor: Kai Hwang
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xi + 343
year: 1985
LCCN: QA76.9.C62 S95 1985
bibdate: Thu Sep 08 00:11:41 1994
bibtimestamp: 1994.09.08 00:11:41 ???
note: IEEE catalog number 85CH2146-9. IEEE Computer Society order number 632.
keywords: ARITH-7
acknowledgement: ack-nj
raweditor: Kai Hwang
rawnote: IEEE catalog number 85CH2146-9. IEEE Computer Society order number 632.
booktitle:
Proceedings: 7th Symposium on Computer Arithmetic, June 4--6, 1985, University of Illinois, Urbana, Illinois

title:
Proceedings: 7th Symposium on Computer Arithmetic, June 4--6, 1985, University of Illinois, Urbana, Illinois

ISBN:
0-8186-0632-0 (paperback), 0-8186-8632-4 (hard), 0-8186-4632-2 (microfiche) OR 0818606320 (paperback), 0818686324 (hard), 0818646322 (microfiche)

ISBN13:
978-0-8186-0632-8 (paperback), 978-0-8186-8632-0 (hard), 978-0-8186-4632-4 (microfiche) OR 9780818606328 (paperback), 9780818686320 (hard), 9780818646324 (microfiche)

rawbooktitle:
Proceedings: 7th Symposium on Computer Arithmetic, June 4--6, 1985, University of Illinois, Urbana, Illinois

entry:
@Proceedings{Hwang:1985:PSC,
  editor =       "Kai Hwang",
  booktitle =    "Proceedings: 7th Symposium on Computer Arithmetic,
                 June 4--6, 1985, University of Illinois, Urbana,
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  title =        "Proceedings: 7th Symposium on Computer Arithmetic,
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bibtype: proceedings
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label: IEEE:1985:ERC
booktitle: 1985 IEEE Region 5 Conference, March 13--15, 1985, Holiday Inn Civic Center, Lubbock, Texas
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LCCN: TK 7801 N56 1985
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bibtype: proceedings
filename: elefunt.bib
label: Marron:1985:FEP
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title: Function estimates: proceedings of a conference held July 28--August 3, 1985
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publisher: pub-AMS
address: pub-AMS:adr
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LCCN: QA276.8 .C651 1985
bibdate: Fri Nov 8 18:01:57 MST 2002
bibsource: ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.08 18:01:57 MST
note: Held at Humboldt State University, Arcata, California.
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bibtype: proceedings
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label: Miranker:1985:ASC
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LCCN: QA76.95 .A231 1986
bibdate: Fri Apr 12 07:14:49 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.04.12 07:14:49 ???
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bibtype: proceedings
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label: ACM:1987:UAA
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ISBN: 0-89791-243-8 OR 0897912438
ISBN13: 978-0-89791-243-3 OR 9780897912433
LCCN: QA 76.73 A35 U85 1987
bibdate: Mon May 19 13:18:54 1997
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bibtype: proceedings
filename: elefunt.bib
label: Iserles:1987:SAN
editor: A. Iserles and M. J. D. Powell
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The State of the Art in Numerical Analysis: Proceedings of the Joint IMA / SIAM Conference on the State of the Art in Numerical Analysis held at the University of Birmingham, 14--18 April 1986

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The State of the Art in Numerical Analysis: Proceedings of the Joint IMA / SIAM Conference on the State of the Art in Numerical Analysis held at the University of Birmingham, 14--18 April 1986

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bibtype: proceedings
filename: elefunt.bib
label: Mason:1987:AAB
editor: J. C. Mason and M. G. Cox
volume: 10
publisher: pub-CLARENDON
address: pub-CLARENDON:adr
pages: xvi + 694 + 8
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ISBN: 0-19-853612-7 OR 0198536127
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bibdate: Fri Nov 8 18:01:57 MST 2002
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acknowledgement: ack-nhfb
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booktitle:
Algorithms for approximation: based on the proceedings of the IMA Conference on Algorithms for the Approximation of Functions and Data, held at the Royal Military College of Science, Shrivenham, July 1985

title:
Algorithms for approximation: based on the proceedings of the IMA Conference on Algorithms for the Approximation of Functions and Data, held at the Royal Military College of Science, Shrivenham, July 1985

bibsource:
ACM Computing Archive CD-ROM database (1991); https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib; https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; https://www.math.utah.edu/pub/bibnet/authors/r/ruhe-axel.bib; https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager

subject:
Approximation theory; Data processing; Congresses; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G. Mathematics of Computing; G.1 NUMERICAL ANALYSIS

TOC:
Preface / v Contributors / xiii I Development of Algorithms 1. Spline Approximation and Smoothing G. T. Anthony and M. G. Cox / The fitting of extremely large data sets by bivariate splines / 5 W. Dahmen / Subdivision algorithms --- recent results, some extensions and further developments / 21 P. Dierckx / Fast algorithms for smoothing data over a disc or a sphere using tensor product splines / 51 T. Lyche and K. Morken / A discrete approach to knot removal and degree reduction algorithms for splines / 67 R. H. J. Gmelig Meyling / On algorithms and applications for bivariate B-splines / 83 2. Spline Interpolation and Shape Preservation R. E. Carlson / Shape preserving interpolation / 97 M. G. Cox and H. M. Jones / Shape preserving spline approximation in the $ell _1$-norm / 115 J. A. Gregory / A review of curve interpolation with shape control / 131 3. Multivariate Interpolation M. J. D. Powell / Radial basis functions for multivariable interpolation: a review / 143 R. A. Lorentz / On the determinant of a bivariate Birkhoff interpolation problem / 169 A. Le Mehaute / Interpolation with piecewise polynomials in more than one variable / 181 4. Least Square Methods R. Farwig / Multivariate interpolation of scattered data by moving least squares methods / 193 F. Yoshimoto / Least squares approximation by one-pass methods with piecewise polynomials / 213 5. Rational Approximation L. N. Trefethen and M. H. Gutknecht / Pade, stable Pade, and Chebyshev--Pade approximation / 227 P. T. Breuer / A new method for real rational uniform approximation / 265 C. B. Dunham / Rationals with repeated poles / 285 A. Iserles and S. P. Norsett / Error control of rational approximation with a matrix argument / 293 6. Complex and Nonlinear Approximation K. Madsen / General algorithms for discrete non-linear parameter estimation / 309 G. Opfer / Complex rational approximation with numerical experiments / 327 G. A. Watson / Data fitting by positive sums of exponentials / 337 J. C. Mason and P. Owen / Some simple algorithms for constrained complex and rational approximation / 357 7. Computer-Aided Design and Blending L. L. Schumaker / Numerical aspects of spaces of piecewise polynomials on triangulations / 373 M. V. Golitschek / The $H$-sets of the blending functions / 407 D. Levin / Multidimensional reconstruction by set-valued approximations/ 421 II Applications 8. Applications in Numerical Analysis H. P. Blatt, A, Iserles and E. B. Saff / Remarks on the behaviour of zeros of best approximating polynomials and rational functions / 437 J. Gilbert and W. A. Light / Multigrid methods and the alternating algorithm / 447 K. Jetter and J. Stockler / On the computation of Gauss--Birkhoff quadrature formulas / 459 E. Schock / Error bounds for the solution of integral equations by Galerkin-like methods / 471 N. M. Temme / On the computation of the incomplete gamma functions for large values of the parameters / 479 9. Applications in Partial Differential Equations J. R. Rice / Adaptive tensor product grids for singular problems / 493 W. Freeden / Harmonic splines for solving boundary value problems of potential theory / 507 D. C. Hanscomb / Recovery of fluid flow fields / 531 L. Reichel / The selection of subspace and collocation points in the boundary collocation method for some plane elliptic boundary problems / 541 10. Applications in Other Disciplines L. Andersson, K. Holmstrom and A. Ruhe / Complex formation constants --- a problem from solution chemistry / 557 D. E. Roberts and P. R. Graves-Morris / The application of generalised inverse rational interpolants in the model analysis of vibrating structures I / 573 A. Daman and J. C. Mason / A generalised cross-validation method for meteorological data with gaps / 595 K. P. Jackson and J. C. Mason / The approximation by complex functions of stresses in cracked domains / 611 J. H. McDonnell / Equally spaced cubic splines for representing time histories / 623 B. L. Rahimi and S. W. Ellacott / Dynamic phase analysis of heart anomalies / 641 III Software J. G. Hayes / NAG algorithms for the approximation of functions and data / 653 G. T. Anthony and M. G. Cox / The National Physical Laboratory's Data Approximation Subroutine Library / 669 M. G. Cox (editor) / Panel Discussion / 689

rawbooktitle:
{Algorithms for approximation: based on the proceedings of the IMA Conference on Algorithms for the Approximation of Functions and Data, held at the Royal Military College of Science, Shrivenham, July 1985}

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{Algorithms for approximation: based on the proceedings of the IMA Conference on Algorithms for the Approximation of Functions and Data, held at the Royal Military College of Science, Shrivenham, July 1985}

rawTOC:
Preface / v \\ Contributors / xiii \\ \\ I Development of Algorithms \\ \\ 1. Spline Approximation and Smoothing \\ \\ G. T. Anthony and M. G. Cox / The fitting of extremely large data sets by bivariate splines / 5 \\ W. Dahmen / Subdivision algorithms --- recent results, some extensions and further developments / 21 \\ P. Dierckx / Fast algorithms for smoothing data over a disc or a sphere using tensor product splines / 51 \\ T. Lyche and K. M{\o}rken / A discrete approach to knot removal and degree reduction algorithms for splines / 67 \\ R. H. J. Gmelig Meyling / On algorithms and applications for bivariate B-splines / 83 \\ \\ 2. Spline Interpolation and Shape Preservation \\ \\ R. E. Carlson / Shape preserving interpolation / 97 \\ M. G. Cox and H. M. Jones / Shape preserving spline approximation in the $\ell_1$-norm / 115 \\ J. A. Gregory / A review of curve interpolation with shape control / 131 \\ \\ 3. Multivariate Interpolation \\ \\ M. J. D. Powell / Radial basis functions for multivariable interpolation: a review / 143 \\ R. A. Lorentz / On the determinant of a bivariate Birkhoff interpolation problem / 169 \\ A. Le Mehaute / Interpolation with piecewise polynomials in more than one variable / 181 \\ \\ 4. Least Square Methods \\ \\ R. Farwig / Multivariate interpolation of scattered data by moving least squares methods / 193 \\ F. Yoshimoto / Least squares approximation by one-pass methods with piecewise polynomials / 213 \\ \\ 5. Rational Approximation \\ \\ L. N. Trefethen and M. H. Gutknecht / Pad{\'e}, stable Pad{\'e}, and Chebyshev--Pad{\'e} approximation / 227 \\ P. T. Breuer / A new method for real rational uniform approximation / 265 \\ C. B. Dunham / Rationals with repeated poles / 285 \\ A. Iserles and S. P. N{\o}rsett / Error control of rational approximation with a matrix argument / 293 \\ \\ 6. Complex and Nonlinear Approximation \\ \\ K. Madsen / General algorithms for discrete non-linear parameter estimation / 309 \\ G. Opfer / Complex rational approximation with numerical experiments / 327 \\ G. A. Watson / Data fitting by positive sums of exponentials / 337 \\ J. C. Mason and P. Owen / Some simple algorithms for constrained complex and rational approximation / 357 \\ \\ 7. Computer-Aided Design and Blending \\ \\ L. L. Schumaker / Numerical aspects of spaces of piecewise polynomials on triangulations / 373 \\ M. V. Golitschek / The $H$-sets of the blending functions / 407 \\ D. Levin / Multidimensional reconstruction by set-valued approximations/ 421 \\ \\ II Applications \\ \\ 8. Applications in Numerical Analysis \\ \\ H. P. Blatt, A, Iserles and E. B. Saff / Remarks on the behaviour of zeros of best approximating polynomials and rational functions / 437 \\ J. Gilbert and W. A. Light / Multigrid methods and the alternating algorithm / 447 \\ K. Jetter and J. St{\"o}ckler / On the computation of Gauss--Birkhoff quadrature formulas / 459 \\ E. Schock / Error bounds for the solution of integral equations by Galerkin-like methods / 471 \\ N. M. Temme / On the computation of the incomplete gamma functions for large values of the parameters / 479 \\ \\ 9. Applications in Partial Differential Equations \\ \\ J. R. Rice / Adaptive tensor product grids for singular problems / 493 \\ W. Freeden / Harmonic splines for solving boundary value problems of potential theory / 507 \\ D. C. Hanscomb / Recovery of fluid flow fields / 531 \\ L. Reichel / The selection of subspace and collocation points in the boundary collocation method for some plane elliptic boundary problems / 541 \\ \\ 10. Applications in Other Disciplines \\ \\ L. Andersson, K. Holmstr{\"o}m and A. Ruhe / Complex formation constants --- a problem from solution chemistry / 557 \\ D. E. Roberts and P. R. Graves-Morris / The application of generalised inverse rational interpolants in the model analysis of vibrating structures I / 573 \\ A. Daman and J. C. Mason / A generalised cross-validation method for meteorological data with gaps / 595 \\ K. P. Jackson and J. C. Mason / The approximation by complex functions of stresses in cracked domains / 611 \\ J. H. McDonnell / Equally spaced cubic splines for representing time histories / 623 \\ B. L. Rahimi and S. W. Ellacott / Dynamic phase analysis of heart anomalies / 641 \\ \\ III Software \\ \\ J. G. Hayes / NAG algorithms for the approximation of functions and data / 653 \\ G. T. Anthony and M. G. Cox / The National Physical Laboratory's Data Approximation Subroutine Library / 669 \\ \\ M. G. Cox (editor) / Panel Discussion / 689

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                 Elementary function approximation",
  descriptor =   "Mathematics of Computing, NUMERICAL ANALYSIS,
                 Approximation; Mathematics of Computing, NUMERICAL
                 ANALYSIS, Approximation, Elementary function
                 approximation",
  genterm =      "theory; algorithms",
  guideno =      "1987-16080",
  meetingname =  "IMA Conference on Algorithms for the Approximation of
                 Functions and Data (1985: Royal Military College of
                 Science, Shrivenham)",
  procdate =     "The Institute of mathematics and its applications
                 conference series; 10 July 1985",
  procloc =      "Shrivenham, UK",
  sub =          "Proceedings of the IMA Conference on Algorithms for
                 the approximation of functions",
  subject =      "Approximation theory; Data processing; Congresses; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS; G.
                 Mathematics of Computing; G.1 NUMERICAL ANALYSIS",
  tableofcontents = "Preface / v \\
                 Contributors / xiii \\
                 \\
                 I Development of Algorithms \\
                 \\
                 1. Spline Approximation and Smoothing \\
                 \\
                 G. T. Anthony and M. G. Cox / The fitting of extremely
                 large data sets by bivariate splines / 5 \\
                 W. Dahmen / Subdivision algorithms --- recent results,
                 some extensions and further developments / 21 \\
                 P. Dierckx / Fast algorithms for smoothing data over a
                 disc or a sphere using tensor product splines / 51 \\
                 T. Lyche and K. M{\o}rken / A discrete approach to knot
                 removal and degree reduction algorithms for splines /
                 67 \\
                 R. H. J. Gmelig Meyling / On algorithms and
                 applications for bivariate B-splines / 83 \\
                 \\
                 2. Spline Interpolation and Shape Preservation \\
                 \\
                 R. E. Carlson / Shape preserving interpolation / 97 \\
                 M. G. Cox and H. M. Jones / Shape preserving spline
                 approximation in the $\ell_1$-norm / 115 \\
                 J. A. Gregory / A review of curve interpolation with
                 shape control / 131 \\
                 \\
                 3. Multivariate Interpolation \\
                 \\
                 M. J. D. Powell / Radial basis functions for
                 multivariable interpolation: a review / 143 \\
                 R. A. Lorentz / On the determinant of a bivariate
                 Birkhoff interpolation problem / 169 \\
                 A. Le Mehaute / Interpolation with piecewise
                 polynomials in more than one variable / 181 \\
                 \\
                 4. Least Square Methods \\
                 \\
                 R. Farwig / Multivariate interpolation of scattered
                 data by moving least squares methods / 193 \\
                 F. Yoshimoto / Least squares approximation by one-pass
                 methods with piecewise polynomials / 213 \\
                 \\
                 5. Rational Approximation \\
                 \\
                 L. N. Trefethen and M. H. Gutknecht / Pad{\'e}, stable
                 Pad{\'e}, and Chebyshev--Pad{\'e} approximation / 227
                 \\
                 P. T. Breuer / A new method for real rational uniform
                 approximation / 265 \\
                 C. B. Dunham / Rationals with repeated poles / 285 \\
                 A. Iserles and S. P. N{\o}rsett / Error control of
                 rational approximation with a matrix argument / 293 \\
                 \\
                 6. Complex and Nonlinear Approximation \\
                 \\
                 K. Madsen / General algorithms for discrete non-linear
                 parameter estimation / 309 \\
                 G. Opfer / Complex rational approximation with
                 numerical experiments / 327 \\
                 G. A. Watson / Data fitting by positive sums of
                 exponentials / 337 \\
                 J. C. Mason and P. Owen / Some simple algorithms for
                 constrained complex and rational approximation / 357
                 \\
                 \\
                 7. Computer-Aided Design and Blending \\
                 \\
                 L. L. Schumaker / Numerical aspects of spaces of
                 piecewise polynomials on triangulations / 373 \\
                 M. V. Golitschek / The $H$-sets of the blending
                 functions / 407 \\
                 D. Levin / Multidimensional reconstruction by
                 set-valued approximations/ 421 \\
                 \\
                 II Applications \\
                 \\
                 8. Applications in Numerical Analysis \\
                 \\
                 H. P. Blatt, A, Iserles and E. B. Saff / Remarks on the
                 behaviour of zeros of best approximating polynomials
                 and rational functions / 437 \\
                 J. Gilbert and W. A. Light / Multigrid methods and the
                 alternating algorithm / 447 \\
                 K. Jetter and J. St{\"o}ckler / On the computation of
                 Gauss--Birkhoff quadrature formulas / 459 \\
                 E. Schock / Error bounds for the solution of integral
                 equations by Galerkin-like methods / 471 \\
                 N. M. Temme / On the computation of the incomplete
                 gamma functions for large values of the parameters /
                 479 \\
                 \\
                 9. Applications in Partial Differential Equations \\
                 \\
                 J. R. Rice / Adaptive tensor product grids for singular
                 problems / 493 \\
                 W. Freeden / Harmonic splines for solving boundary
                 value problems of potential theory / 507 \\
                 D. C. Hanscomb / Recovery of fluid flow fields / 531
                 \\
                 L. Reichel / The selection of subspace and collocation
                 points in the boundary collocation method for some
                 plane elliptic boundary problems / 541 \\
                 \\
                 10. Applications in Other Disciplines \\
                 \\
                 L. Andersson, K. Holmstr{\"o}m and A. Ruhe / Complex
                 formation constants --- a problem from solution
                 chemistry / 557 \\
                 D. E. Roberts and P. R. Graves-Morris / The application
                 of generalised inverse rational interpolants in the
                 model analysis of vibrating structures I / 573 \\
                 A. Daman and J. C. Mason / A generalised
                 cross-validation method for meteorological data with
                 gaps / 595 \\
                 K. P. Jackson and J. C. Mason / The approximation by
                 complex functions of stresses in cracked domains / 611
                 \\
                 J. H. McDonnell / Equally spaced cubic splines for
                 representing time histories / 623 \\
                 B. L. Rahimi and S. W. Ellacott / Dynamic phase
                 analysis of heart anomalies / 641 \\
                 \\
                 III Software \\
                 \\
                 J. G. Hayes / NAG algorithms for the approximation of
                 functions and data / 653 \\
                 G. T. Anthony and M. G. Cox / The National Physical
                 Laboratory's Data Approximation Subroutine Library /
                 669 \\
                 \\
                 M. G. Cox (editor) / Panel Discussion / 689",
}


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filename: elefunt.bib
label: USENIX:1988:UPC
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booktitle: USENIX proceedings: C++ Conference, Denver, CO, October 17--21, 1988
title: USENIX proceedings: C++ Conference, Denver, CO, October 17--21, 1988
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year: 1988
bibdate: Sun Feb 18 07:46:09 MST 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.02.18 07:46:09 MST
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bibtype: book
filename: elefunt.bib
label: Campbell-Kelly:1989:WCB-3
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title: The works of Charles Babbage, Vol. 3, The analytical engine and mechanical notation
publisher: William Pickering
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MRnumber: 998151 (90g:01064)
MRreviewer: A. D. Booth
bibdate: Sat Jan 12 22:42:35 MST 2013
bibtimestamp: 2013.01.12 22:42:35 MST
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bibtype: proceedings
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label: Ercegovac:1989:PSC
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bibdate: Thu Sep 01 22:36:52 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 22:36:52 ???
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Proceedings: 9th Symposium on Computer Arithmetic: September 6--8, 1989, Santa Monica, California, USA

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Proceedings: 9th Symposium on Computer Arithmetic: September 6--8, 1989, Santa Monica, California, USA

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bibdate: Sat Nov 29 08:19:35 2003
bibtimestamp: 2003.11.29 08:19:35 ???
note: Conference publication no. 308.
acknowledgement: ack-nhfb
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ECCTD 89: European Conference on Circuit Theory and Design, 5--8 September 1989: venue, University of Sussex, Brighton, United Kingdom

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label: IEEE:1989:ASF
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  acknowledgement = ack-nhfb,
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bibtype: proceedings
filename: elefunt.bib
label: Megiddo:1989:PMP
editor: N. Megiddo
booktitle: Progress in Mathematical Programming: Interior-Point and Related Methods
title: Progress in Mathematical Programming: Interior-Point and Related Methods
publisher: pub-SV
address: pub-SV:adr
pages: x + 158
year: 1989
ISBN: 0-387-96847-4 OR 0387968474
ISBN13: 978-0-387-96847-6 OR 9780387968476
LCCN: QA402.5 .P7851 1989
bibdate: Sat Nov 09 07:07:37 2002
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.11.09 07:07:37 ???
acknowledgement: ack-nhfb
rawbooktitle: Progress in Mathematical Programming: Interior-Point and Related Methods
raweditor: N. Megiddo
rawtitle: Progress in Mathematical Programming: Interior-Point and Related Methods
note:
Proceedings of the conference held at the Asilomar conference center in Pacific Grove, California, March 1--4, 1987.

rawnote:
Proceedings of the conference held at the Asilomar conference center in Pacific Grove, California, March 1--4, 1987.

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  editor =       "N. Megiddo",
  booktitle =    "Progress in Mathematical Programming: Interior-Point
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  title =        "Progress in Mathematical Programming: Interior-Point
                 and Related Methods",
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filename: elefunt.bib
label: Srivastava:1989:UFF
editor: H. M. Srivastava and Shigeyoshi Owa
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title: Univalent functions, fractional calculus, and their applications (Koriyama, 1988)
publisher: pub-ELLIS-HORWOOD
address: pub-ELLIS-HORWOOD:adr
pages: 404
year: 1989
ISBN: 0-470-21630-1, 0-7458-0701-1 OR 0470216301, 0745807011
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LCCN: QA331 .U55 1989
bibdate: Mon Jan 13 09:52:29 1997
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bibtimestamp: 1997.01.13 09:52:29 ???
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  title =        "Univalent functions, fractional calculus, and their
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  address =      pub-ELLIS-HORWOOD:adr,
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  LCCN =         "QA331 .U55 1989",
  bibdate =      "Mon Jan 13 09:52:29 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  price =        "UK\pounds 39.95",
  acknowledgement = ack-nhfb,
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bibtype: proceedings
filename: elefunt.bib
label: Cray:1990:PCU
booktitle: Proceedings Cray User Group
title: Proceedings Cray User Group
month: Spring
year: 1990
bibdate: Thu Sep 08 08:56:01 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.08 08:56:01 ???
acknowledgement: ack-nj
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entry:
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bibtype: proceedings
filename: elefunt.bib
label: Mason:1990:AAI
editor: J. C. Mason and M. G. Cox
publisher: pub-CHAPMAN-HALL
address: pub-CHAPMAN-HALL:adr
pages: 514
year: 1990
ISBN: 0-412-34580-3 OR 0412345803
ISBN13: 978-0-412-34580-7 OR 9780412345807
LCCN: QA221 .I54 1988
bibdate: Thu Sep 01 23:55:44 1994
bibtimestamp: 1994.09.01 23:55:44 ???
subject: Approximation theory; Data processing; Congresses
acknowledgement: ack-nhfb
raweditor: J. C. Mason and M. G. Cox
booktitle:
Algorithms for approximation II: based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988

title:
Algorithms for approximation II: based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib; https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib; https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; z3950.loc.gov:7090/Voyager

TOC:
Part One: Development of Algorithms / 1 1. Spline Approximation / 3 E. Arge, M. Dcehlen, T. Lyche and K. Morken / Constrained spline approximation of functions and data based on constrained knot removal / 4 G. T. Anthony and M. G. Cox / Near real-time spline fitting of long sequences of uniformly-spaced data / 21 M. Bozzini and F. de Tisi / An algorithm for knot location in bivariate least squares spline approximation / 30 M. G. Cox, P. M. Harris and H. M. Jones / A knot placement strategy for least squares spline fitting based on the use of local polynomial approximations / 37 G. Opfer / An algorithm for nonlinear splines with non-negativity constraints / 46 C. Potier and C. Vercken / Spline curve fitting of digitized contours / 54 C. Rabut / A B-spline approximation algorithm for quasi-interpolation or filtering / 62 P. W. Smith / On knots and nodes for spline interpolation / 72 2. Polynomial and Piecewise Polynomial Approximation / 79 W. Dahmen / A basis for certain spaces of multivariate polynomials and exponentials / 80 F. N. Fritschi / Monotone piecewise cubic data fitting / 99 M. Heilmann and M. W. Muller / Direct and converse results on simultaneous approximation by the method of Bernstein--Durrmeyer operators / 107 A. Iserles, P. E. Koch, S. P. Norsett and J. M. Sanz-Serna / Orthogonality and approximation in a Sobolev space / 117 M. A. Lachance / Piecewise polynomial approximation of polynomial curves / 125 E. Quak and L. L. Schumaker / Calculation of the energy of a piecewise polynomial surface / 134 3. Interpolation / 145 M. D. Buhmann and M. J. D. Powell / Radial basis function interpolation on an infinite regular grid / 146 L. Brutman / The Fourier operator of even order and its application to an extremum problem in interpolation / 170 N. Dyn and A. Ron / On multivariate polynomial interpolation / 177 N. Dyn, D. Levin and S. Rippen / Algorithms for the construction of data dependent triangulations / 185 C. Rademacher and K. Scherer / Algorithms for computing best parametric cubic interpolation / 193 4. Smoothing and Constraint Methods / 209 M. Von Golitschek and L. L. Schumaker / Data fitting by penalized least squares / 210 K. W. Bosworth / A semiinfinite programming algorithm for constrained best approximation / 228 M. Bozzini and L. Lenarduzzi / Inference region for a method of local approximation by using the residuals / 236 5. Complex Approximation / 245 G. A. Watson / Numerical methods for Chebyshev approximation of complex-valued functions / 246 P. T. P. Tang / A fast algorithm for linear complex Chebyshev approximation / 265 Part Two: Applications / 275 6. Computer Aided Design and Geometric Modelling / 277 N. Dyn, J. A. Gregory and D. Levin / Uniform subdivision algorithms for curves and surfaces / 278 T. B. Boffey, M. G. Cox, L. M. Delves and C. J. Pursglove / Approximation by spheres / 296 T. A. Foley / Interpolation of scattered data on a spherical domain / 303 A. B. Forbes / Least squares best fit geometric elements / 311 W. Freeden and J. C. Mason / Uniform piecewise approximation on the sphere / 320 7. Applications in Numerical Analysis / 335 L. N. Trefethen / Approximation theory and numerical linear algebra / 336 M. Frontini, G. Rodriguez and S. Seatzu / An algorithm for computing minimum norm solutions of the finite moment problem / 361 R. H. J. Gmelig Meyling / Numerical solution of the biharmonic equation using different types of bivariate spline functions / 369 G. O. Olaofe / Quadrature solution of integral equations: a uniform treatment of Fredholm and Volterra equations / 377 G. Walz / Increasing the convergence modulus of an asymptotic expansion: an algorithm for numerical differentiation / 387 J. Williams / Approximation and parameter estimation in ordinary differential equations / 395 8. Applications in Other Disciplines / 405 C. Zala and I. Barrodale / Applications of discrete $L_1$ methods in science and engineering / 406 J. C. Mason, A. E. Trefethen and S. J. Wilde / Constrained complex approximation algorithms in communication engineering / 424 R. W. Allen and J. G. Metcalfe / Integration of absolute amplitude from a decibel B-spline fit / 449 M. G. Cox and H. M. Jones / A nonlinear least squares data fitting problem arising in microwave measurement / 458 J. C. Mason and S. J. Wilde / A complex minimax algorithm for phase-only adaptation in antenna arrays / 466 Part Three: Catalogue of Algorithms / 477 E. Grosse / A catalogue of algorithms for approximation / 479

rawbooktitle:
{Algorithms for approximation II: based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988}

rawtitle:
{Algorithms for approximation II: based on the proceedings of the Second International Conference on Algorithms for Approximation, held at Royal Military College of Science, Shrivenham, July 1988}

rawTOC:
Part One: Development of Algorithms / 1 \\ 1. Spline Approximation / 3 \\ E. Arge, M. Dcehlen, T. Lyche and K. Morken / Constrained spline approximation of functions and data based on constrained knot removal / 4 \\ G. T. Anthony and M. G. Cox / Near real-time spline fitting of long sequences of uniformly-spaced data / 21 \\ M. Bozzini and F. de Tisi / An algorithm for knot location in bivariate least squares spline approximation / 30 \\ M. G. Cox, P. M. Harris and H. M. Jones / A knot placement strategy for least squares spline fitting based on the use of local polynomial approximations / 37 \\ G. Opfer / An algorithm for nonlinear splines with non-negativity constraints / 46 \\ C. Potier and C. Vercken / Spline curve fitting of digitized contours / 54 \\ C. Rabut / A B-spline approximation algorithm for quasi-interpolation or filtering / 62 \\ P. W. Smith / On knots and nodes for spline interpolation / 72 \\ 2. Polynomial and Piecewise Polynomial Approximation / 79 \\ W. Dahmen / A basis for certain spaces of multivariate polynomials and exponentials / 80 \\ F. N. Fritschi / Monotone piecewise cubic data fitting / 99 \\ M. Heilmann and M. W. M{\"u}ller / Direct and converse results on simultaneous approximation by the method of Bernstein--Durrmeyer operators / 107 \\ A. Iserles, P. E. Koch, S. P. N{\o}rsett and J. M. Sanz-Serna / Orthogonality and approximation in a Sobolev space / 117 \\ M. A. Lachance / Piecewise polynomial approximation of polynomial curves / 125 \\ E. Quak and L. L. Schumaker / Calculation of the energy of a piecewise polynomial surface / 134 \\ 3. Interpolation / 145 \\ M. D. Buhmann and M. J. D. Powell / Radial basis function interpolation on an infinite regular grid / 146 \\ L. Brutman / The Fourier operator of even order and its application to an extremum problem in interpolation / 170 \\ N. Dyn and A. Ron / On multivariate polynomial interpolation / 177 \\ N. Dyn, D. Levin and S. Rippen / Algorithms for the construction of data dependent triangulations / 185 \\ C. Rademacher and K. Scherer / Algorithms for computing best parametric cubic interpolation / 193 \\ 4. Smoothing and Constraint Methods / 209 \\ M. Von Golitschek and L. L. Schumaker / Data fitting by penalized least squares / 210 \\ K. W. Bosworth / A semiinfinite programming algorithm for constrained best approximation / 228 \\ M. Bozzini and L. Lenarduzzi / Inference region for a method of local approximation by using the residuals / 236 \\ 5. Complex Approximation / 245 \\ G. A. Watson / Numerical methods for Chebyshev approximation of complex-valued functions / 246 \\ P. T. P. Tang / A fast algorithm for linear complex Chebyshev approximation / 265 \\ Part Two: Applications / 275 \\ 6. Computer Aided Design and Geometric Modelling / 277 \\ N. Dyn, J. A. Gregory and D. Levin / Uniform subdivision algorithms for curves and surfaces / 278 \\ T. B. Boffey, M. G. Cox, L. M. Delves and C. J. Pursglove / Approximation by spheres / 296 \\ T. A. Foley / Interpolation of scattered data on a spherical domain / 303 \\ A. B. Forbes / Least squares best fit geometric elements / 311 \\ W. Freeden and J. C. Mason / Uniform piecewise approximation on the sphere / 320 \\ 7. Applications in Numerical Analysis / 335 \\ L. N. Trefethen / Approximation theory and numerical linear algebra / 336 \\ M. Frontini, G. Rodriguez and S. Seatzu / An algorithm for computing minimum norm solutions of the finite moment problem / 361 \\ R. H. J. Gmelig Meyling / Numerical solution of the biharmonic equation using different types of bivariate spline functions / 369 \\ G. O. Olaofe / Quadrature solution of integral equations: a uniform treatment of Fredholm and Volterra equations / 377 \\ G. Walz / Increasing the convergence modulus of an asymptotic expansion: an algorithm for numerical differentiation / 387 \\ J. Williams / Approximation and parameter estimation in ordinary differential equations / 395 \\ 8. Applications in Other Disciplines / 405 \\ C. Zala and I. Barrodale / Applications of discrete $L_1$ methods in science and engineering / 406 \\ J. C. Mason, A. E. Trefethen and S. J. Wilde / Constrained complex approximation algorithms in communication engineering / 424 \\ R. W. Allen and J. G. Metcalfe / Integration of absolute amplitude from a decibel B-spline fit / 449 \\ M. G. Cox and H. M. Jones / A nonlinear least squares data fitting problem arising in microwave measurement / 458 \\ J. C. Mason and S. J. Wilde / A complex minimax algorithm for phase-only adaptation in antenna arrays / 466 \\ Part Three: Catalogue of Algorithms / 477 \\ E. Grosse / A catalogue of algorithms for approximation / 479

entry:
@Proceedings{Mason:1990:AAI,
  editor =       "J. C. Mason and M. G. Cox",
  booktitle =    "{Algorithms for approximation II: based on the
                 proceedings of the Second International Conference on
                 Algorithms for Approximation, held at Royal Military
                 College of Science, Shrivenham, July 1988}",
  title =        "{Algorithms for approximation II: based on the
                 proceedings of the Second International Conference on
                 Algorithms for Approximation, held at Royal Military
                 College of Science, Shrivenham, July 1988}",
  publisher =    pub-CHAPMAN-HALL,
  address =      pub-CHAPMAN-HALL:adr,
  pages =        "514",
  year =         "1990",
  ISBN =         "0-412-34580-3",
  ISBN-13 =      "978-0-412-34580-7",
  LCCN =         "QA221 .I54 1988",
  bibdate =      "Thu Sep 01 23:55:44 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/g/grosse-eric.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/powell-m-j-d.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/trefethen-lloyd-n.bib;
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  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Algorithms for
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                 Science, Shrivenham, England)",
  subject =      "Approximation theory; Data processing; Congresses",
  tableofcontents = "Part One: Development of Algorithms / 1 \\
                 1. Spline Approximation / 3 \\
                 E. Arge, M. Dcehlen, T. Lyche and K. Morken /
                 Constrained spline approximation of functions and data
                 based on constrained knot removal / 4 \\
                 G. T. Anthony and M. G. Cox / Near real-time spline
                 fitting of long sequences of uniformly-spaced data / 21
                 \\
                 M. Bozzini and F. de Tisi / An algorithm for knot
                 location in bivariate least squares spline
                 approximation / 30 \\
                 M. G. Cox, P. M. Harris and H. M. Jones / A knot
                 placement strategy for least squares spline fitting
                 based on the use of local polynomial approximations /
                 37 \\
                 G. Opfer / An algorithm for nonlinear splines with
                 non-negativity constraints / 46 \\
                 C. Potier and C. Vercken / Spline curve fitting of
                 digitized contours / 54 \\
                 C. Rabut / A B-spline approximation algorithm for
                 quasi-interpolation or filtering / 62 \\
                 P. W. Smith / On knots and nodes for spline
                 interpolation / 72 \\
                 2. Polynomial and Piecewise Polynomial Approximation /
                 79 \\
                 W. Dahmen / A basis for certain spaces of multivariate
                 polynomials and exponentials / 80 \\
                 F. N. Fritschi / Monotone piecewise cubic data fitting
                 / 99 \\
                 M. Heilmann and M. W. M{\"u}ller / Direct and converse
                 results on simultaneous approximation by the method of
                 Bernstein--Durrmeyer operators / 107 \\
                 A. Iserles, P. E. Koch, S. P. N{\o}rsett and J. M.
                 Sanz-Serna / Orthogonality and approximation in a
                 Sobolev space / 117 \\
                 M. A. Lachance / Piecewise polynomial approximation of
                 polynomial curves / 125 \\
                 E. Quak and L. L. Schumaker / Calculation of the energy
                 of a piecewise polynomial surface / 134 \\
                 3. Interpolation / 145 \\
                 M. D. Buhmann and M. J. D. Powell / Radial basis
                 function interpolation on an infinite regular grid /
                 146 \\
                 L. Brutman / The Fourier operator of even order and its
                 application to an extremum problem in interpolation /
                 170 \\
                 N. Dyn and A. Ron / On multivariate polynomial
                 interpolation / 177 \\
                 N. Dyn, D. Levin and S. Rippen / Algorithms for the
                 construction of data dependent triangulations / 185 \\
                 C. Rademacher and K. Scherer / Algorithms for computing
                 best parametric cubic interpolation / 193 \\
                 4. Smoothing and Constraint Methods / 209 \\
                 M. Von Golitschek and L. L. Schumaker / Data fitting by
                 penalized least squares / 210 \\
                 K. W. Bosworth / A semiinfinite programming algorithm
                 for constrained best approximation / 228 \\
                 M. Bozzini and L. Lenarduzzi / Inference region for a
                 method of local approximation by using the residuals /
                 236 \\
                 5. Complex Approximation / 245 \\
                 G. A. Watson / Numerical methods for Chebyshev
                 approximation of complex-valued functions / 246 \\
                 P. T. P. Tang / A fast algorithm for linear complex
                 Chebyshev approximation / 265 \\
                 Part Two: Applications / 275 \\
                 6. Computer Aided Design and Geometric Modelling / 277
                 \\
                 N. Dyn, J. A. Gregory and D. Levin / Uniform
                 subdivision algorithms for curves and surfaces / 278
                 \\
                 T. B. Boffey, M. G. Cox, L. M. Delves and C. J.
                 Pursglove / Approximation by spheres / 296 \\
                 T. A. Foley / Interpolation of scattered data on a
                 spherical domain / 303 \\
                 A. B. Forbes / Least squares best fit geometric
                 elements / 311 \\
                 W. Freeden and J. C. Mason / Uniform piecewise
                 approximation on the sphere / 320 \\
                 7. Applications in Numerical Analysis / 335 \\
                 L. N. Trefethen / Approximation theory and numerical
                 linear algebra / 336 \\
                 M. Frontini, G. Rodriguez and S. Seatzu / An algorithm
                 for computing minimum norm solutions of the finite
                 moment problem / 361 \\
                 R. H. J. Gmelig Meyling / Numerical solution of the
                 biharmonic equation using different types of bivariate
                 spline functions / 369 \\
                 G. O. Olaofe / Quadrature solution of integral
                 equations: a uniform treatment of Fredholm and Volterra
                 equations / 377 \\
                 G. Walz / Increasing the convergence modulus of an
                 asymptotic expansion: an algorithm for numerical
                 differentiation / 387 \\
                 J. Williams / Approximation and parameter estimation in
                 ordinary differential equations / 395 \\
                 8. Applications in Other Disciplines / 405 \\
                 C. Zala and I. Barrodale / Applications of discrete
                 $L_1$ methods in science and engineering / 406 \\
                 J. C. Mason, A. E. Trefethen and S. J. Wilde /
                 Constrained complex approximation algorithms in
                 communication engineering / 424 \\
                 R. W. Allen and J. G. Metcalfe / Integration of
                 absolute amplitude from a decibel B-spline fit / 449
                 \\
                 M. G. Cox and H. M. Jones / A nonlinear least squares
                 data fitting problem arising in microwave measurement /
                 458 \\
                 J. C. Mason and S. J. Wilde / A complex minimax
                 algorithm for phase-only adaptation in antenna arrays /
                 466 \\
                 Part Three: Catalogue of Algorithms / 477 \\
                 E. Grosse / A catalogue of algorithms for approximation
                 / 479",
}


bibtype: proceedings
filename: elefunt.bib
label: Ullrich:1990:CCA
editor: Christian Ullrich
volume: 7
publisher: pub-BALTZER
address: pub-BALTZER:adr
pages: 526
year: 1990
LCCN: QA76.9.C62 C664 1990
bibdate: Sat Nov 29 08:36:57 2003
bibtimestamp: 2003.11.29 08:36:57 ???
series: IMACS annals on computing and applied mathematics
keywords: computer arithmetic --- congresses; numerical analysis --- congresses
acknowledgement: ack-nhfb
raweditor: Christian Ullrich
booktitle:
Contributions to Computer Arithmetic and Self-Validating Numerical Methods. (Proceedings of SCAN 89, held in Basel, Oct. 2--6, 1989)

title:
Contributions to Computer Arithmetic and Self-Validating Numerical Methods. (Proceedings of SCAN 89, held in Basel, Oct. 2--6, 1989)

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/numana1990.bib

rawbooktitle:
Contributions to Computer Arithmetic and Self-Validating Numerical Methods. (Proceedings of {SCAN 89}, held in Basel, Oct. 2--6, 1989)

rawtitle:
Contributions to Computer Arithmetic and Self-Validating Numerical Methods. (Proceedings of {SCAN} 89, held in Basel, Oct. 2--6, 1989)

entry:
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  editor =       "Christian Ullrich",
  booktitle =    "Contributions to Computer Arithmetic and
                 Self-Validating Numerical Methods. (Proceedings of
                 {SCAN 89}, held in Basel, Oct. 2--6, 1989)",
  title =        "Contributions to Computer Arithmetic and
                 Self-Validating Numerical Methods. (Proceedings of
                 {SCAN} 89, held in Basel, Oct. 2--6, 1989)",
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  series =       "IMACS annals on computing and applied mathematics",
  acknowledgement = ack-nhfb,
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  xxbooktitle =  "SCAN-89, International Symposium on Scientific
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bibtype: proceedings
filename: elefunt.bib
label: Anonymous:1991:PIS
editor: Anonymous
booktitle: Proceedings of the International Symposium on Supercomputing: Fukuoka, Japan, November 6--8, 1991
title: Proceedings of the International Symposium on Supercomputing: Fukuoka, Japan, November 6--8, 1991
publisher: Kyushu University Press
address: Fukuoka, Japan
pages: iv + 261
year: 1991
ISBN: 4-87378-284-8 OR 4873782848
ISBN13: 978-4-87378-284-3 OR 9784873782843
LCCN: QA76.88.I 1991
bibdate: Sat Jan 11 10:14:06 MST 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.11 10:14:06 MST
acknowledgement: ack-nhfb
rawbooktitle: Proceedings of the International Symposium on Supercomputing: Fukuoka, Japan, November 6--8, 1991
raweditor: Anonymous
rawtitle: Proceedings of the International Symposium on Supercomputing: Fukuoka, Japan, November 6--8, 1991
entry:
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  booktitle =    "Proceedings of the International Symposium on
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  title =        "Proceedings of the International Symposium on
                 Supercomputing: Fukuoka, Japan, November 6--8, 1991",
  publisher =    "Kyushu University Press",
  address =      "Fukuoka, Japan",
  pages =        "iv + 261",
  year =         "1991",
  ISBN =         "4-87378-284-8",
  ISBN-13 =      "978-4-87378-284-3",
  LCCN =         "QA76.88.I 1991",
  bibdate =      "Sat Jan 11 10:14:06 MST 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
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bibtype: proceedings
filename: elefunt.bib
label: Bowers:1991:CCI
editor: K. L. (Kenneth L.) Bowers and J. (John) Lund
volume: 11
publisher: pub-BIRKHAUSER
address: pub-BIRKHAUSER:adr
pages: 369
year: 1991
ISBN: 0-8176-3611-0 OR 0817636110
ISBN13: 978-0-8176-3611-1 OR 9780817636111
LCCN: TA329 .C644 1991
bibdate: Wed May 9 08:56:08 MDT 2007
bibtimestamp: 2007.05.09 08:56:08 MDT
series: Progress in systems and control theory
keywords: convergence acceleration
subject: Engineering mathematics; Congresses; Feedback control systems
acknowledgement: ack-nhfb
raweditor: K. L. (Kenneth L.) Bowers and J. (John) Lund
booktitle:
Computation and control II: proceedings of the second Bozeman conference, Bozeman, Montana, August 1--7, 1990

title:
Computation and control II: proceedings of the second Bozeman conference, Bozeman, Montana, August 1--7, 1990

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager

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rawtitle:
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  title =        "{Computation and control II: proceedings of the second
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  volume =       "11",
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bibtype: proceedings
filename: elefunt.bib
label: IEEE:1991:PSA
editor: IEEE
booktitle: Proceedings, Supercomputing '91: Albuquerque, New Mexico, November 18--22, 1991
title: Proceedings, Supercomputing '91: Albuquerque, New Mexico, November 18--22, 1991
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xxiii + 917
year: 1991
LCCN: QA76.5 .S894 1991
bibdate: Fri Aug 30 08:01:51 MDT 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; University of California MELVYL catalog.
bibtimestamp: 1996.08.30 08:01:51 MDT
acknowledgement: ack-nhfb
rawbooktitle: Proceedings, Supercomputing '91: Albuquerque, New Mexico, November 18--22, 1991
raweditor: {IEEE}
rawtitle: Proceedings, Supercomputing '91: Albuquerque, New Mexico, November 18--22, 1991
ISBN:
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978-0-8186-9158-4 (IEEE case), 978-0-8186-2158-1 (IEEE paper), 978-0-8186-6158-7 (IEEE microfiche), 978-0-89791-459-8 (ACM) OR 9780818691584 (IEEE case), 9780818621581 (IEEE paper), 9780818661587 (IEEE microfiche), 9780897914598 (ACM)

note:
ACM order number 415913. IEEE Computer Society Press order number 2158. IEEE catalog number 91CH3058-5.

keywords:
combinatorial algorithms; data dependence; distributed memory code generation; high school environment; latency tolerance; memory access; numerical algorithms; parallel processing; parallel programming; performance evaluation; performance tools; processor design; program analysis; storage hierarchy optimization; supercomputer benchmarks; supercomputer congresses; supercomputing; system issues

rawnote:
ACM order number 415913. IEEE Computer Society Press order number 2158. IEEE catalog number 91CH3058-5.

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bibtype: proceedings
filename: elefunt.bib
label: Koopman:1991:PST
editor: Philip J. Koopman, Jr.
publisher: pub-ACM
address: pub-ACM:adr
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year: 1991
ISBN: 0-89791-462-7 OR 0897914627
ISBN13: 978-0-89791-462-8 OR 9780897914628
LCCN: QA 76.73 F24 S53 1991
bibdate: Tue May 04 07:39:28 1999
bibtimestamp: 1999.05.04 07:39:28 ???
note: ACM order number 817911.
acknowledgement: ack-nhfb
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rawnote: ACM order number 817911.
booktitle:
The proceedings of the second and third annual workshops for the ACM Special Interest Group on Forth: SIGForth '90, February 16--18, 1990, Dallas, Texas ldots SIGForth '91, March 7--9, 1991, San Antonio, Texas

title:
The proceedings of the second and third annual workshops for the ACM Special Interest Group on Forth: SIGForth '90, February 16--18, 1990, Dallas, Texas ldots SIGForth '91, March 7--9, 1991, San Antonio, Texas

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  title =        "{The proceedings of the second and third annual
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bibtype: proceedings
filename: elefunt.bib
label: Kornerup:1991:PIS
editor: Peter Kornerup and David W. Matula
booktitle: Proceedings: 10th IEEE Symposium on Computer Arithmetic: June 26--28, 1991, Grenoble, France
title: Proceedings: 10th IEEE Symposium on Computer Arithmetic: June 26--28, 1991, Grenoble, France
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xiii + 282
year: 1991
LCCN: QA76.9.C62 S95 1991
bibdate: Thu Sep 01 23:18:52 1994
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1994.09.01 23:18:52 ???
acknowledgement: ack-nhfb
rawbooktitle: Proceedings: 10th {IEEE} Symposium on Computer Arithmetic: June 26--28, 1991, Grenoble, France
raweditor: Peter Kornerup and David W. Matula
rawtitle: Proceedings: 10th {IEEE} Symposium on Computer Arithmetic: June 26--28, 1991, Grenoble, France
ISBN:
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  editor =       "Peter Kornerup and David W. Matula",
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  title =        "Proceedings: 10th {IEEE} Symposium on Computer
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  publisher =    pub-IEEE,
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bibtype: book
filename: elefunt.bib
label: Lewin:1991:SPP
editor: Leonard Lewin
booktitle: Structural Properties of Polylogarithms
title: Structural Properties of Polylogarithms
volume: 37
publisher: pub-AMS
address: pub-AMS:adr
pages: xviii + 412
year: 1991
ISBN: 0-8218-1634-9, 1-4704-1264-0 (e-book) OR 0821816349, 1470412640 (ebook)
ISBN13: 978-0-8218-1634-9, 978-1-4704-1264-7 (e-book) OR 9780821816349, 9781470412647 (ebook)
ISSN: 0076-5376 OR 00765376
MRclass: 33E20, 00B15, 11-02, 11F67, 11R70, 11R42, 19F27, 33-02, 33-06, 33B99
bibdate: Fri Jun 16 14:03:50 MDT 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2023.06.16 14:03:50 MDT
series: Mathematical surveys and monographs
acknowledgement: ack-nhfb
rawbooktitle: Structural Properties of Polylogarithms
raweditor: Leonard Lewin
rawtitle: Structural Properties of Polylogarithms
subject:
Logarithmic functions; Fonctions logarithmes; Mathematics; Algebra; Intermediate; Logarithmic functions; Fonctions logarithmes

TOC:
Preface / xiii Acknowledgments / xv List of Contributors / xvii 1: The Evolution of the Ladder Concept / L. Lewin / 1 1.1 Early History / 1 1.2 Functional Equations / 2 1.3 More Recent Numerical Results / 4 1.4 Current Developments / 6 1.5 Base on the Unit Circle and Clausen Function Ladders / 8 References / 9 2: Dilogarithmic Ladders / L. Lewin / 11 2.1 Derivation from Kummer's Functional Equation / 11 2.2 Relation to Clausen's Function / 15 2.3 A Three-Variable Dilogarithmic Functional Equation / 17 2.4 Functional Equations in the Complex Plane / 18 2.5 Cyclotomic Equations and Rogers' Function / 20 2.6 Accessible and Analytic Ladders / 21 2.7 Inaccessible Ladders / 23 References / 25 3: Polylogarithmic Ladders / M. Abouzahra and L. Lewin / 27 3.1 Kummer's Function and its Relation to the Polylogarithm / 27 3.2 Functional Equations for the Polylogarithm / 28 3.3 A Generalization of Rogers' Function to the $n$th Order / 31 3.4 Ladder Order-Independence on Reduction of Order / 33 3.5 Generic Ladders for the Base Equation $u^p + u^q = 1$ / 34 3.6 Examples of Ladders for $n < 3$ / 40 3.7 Examples of Ladders for $n < 4$ / 44 3.8 Examples of Ladders for $n < 5$ / 45 3.9 Polynomial Relations for Ladders / 46 References / 47 4: Ladders in the Trans-Kummer Region / M. Abouzahra and L. Lewin / 49 4.1 Ladder Results to $n = 9$ for the Base p / 49 4.2 Ladder Results to $n = 9$ for the Base co / 53 4.3 Ladder Results to $n = 6$ for the Base 6 / 62 4.4 The Nonexistence of Functional Equations at $n = 6$ with Arguments Limited to $pm z^m (1 - z)^r (1 + z)^s$ / 65 References / 67 5: Supemumary Ladders / M. Abouzahra and L. Lewin / 69 5.1 The Concept of Supemumary Results / 69 5.2 Supemumary Results for $p = 4$ / 71 5.3 Supemumary Results for $p = 5$ / 76 5.4 Supemumary Results for $p = 6$ / 78 5.5 Supemumary Results for the Equation-family $u^6m + 1 u^6r - 1$ = 1 / 80 5.6 Supemumary Results for an Irreducible Quintic / 82 5.7 Supemumary Ladders from a 15-Term Functional Equation / 84 5.8 Supemumary Ladders on the Unit Circle / 90 References 6: Functional Equations and Ladders / L. Lewin / 97 6.1 New Categories of Functional Equations / 97 6.2 The $rho $-family of Equations / 100 6.3 The $omega $-family of Equations / 109 6.4 The $theta $-family of Equations / 115 Acknowledgements / 121 References / 121 7: Multivariable Polylogarithm Identities / G. A. Ray / 123 7.0 Introduction / 123 7.1 A General Identity for the Dilogarithm / 123 7.2 A General Identity for the Bloch-Wigner Function / 135 7.3 A General Identity for the Trilogarithm and $D_3(z)$ / 141 7.4 Linear Power Relations among Dilogarithms / 147 7.5 Cyclotomic Equations and Bases for Polylogarithm Relations / 154 7.6 Mahler's Measure and Salem/Pisot Numbers / 160 7.7 Recent Results for Supemumary Ladders / 165 References / 168 8: Functional Equations of Hyperlogarithms / G. Wechsung / 171 8.1 Hyperlogarithms / 171 8.2 Logarithmic Singularities / 172 8.3 The Linear Spaces LI$_n$ and PLI$_n$ / 176 8.4 Functional Equations of Hyperlogarithms / 177 8.5 A Reduction Problem / 181 References / 184 9: Kummer-Type Functional Equations of Polylogarithms / G. Wechsung / 185 9.1 Automorphic Functions / 185 9.2 Kummer-Type Functional Equations / 186 9.3 A Method to Construct Functional Equations / 191 9.4 The Nonexistence of a Kummer-Type Functional Equation for $Li _6$ / 197 References / 203 10: The Basic Structure of Polylogarithmic Equations / Z. Wojtkowiak / 205 10.1 Introduction / 205 10.2 Canonical Unipotent Connection on $P^1(mathbb C)a_1, ldots , a_n+1$ / 211 10.3 Horizontal Sections / 213 10.4 Easy Lemmas about Monodromy / 215 10.5 Functional Equations / 216 10.6 Functional Equations of Polylogarithms / 218 10.7 Functional Equations of Lower Degree Polylogarithms / 223 10.8 Generalized Bloch Groups / 228 Acknowledgements / 231 References / 231 11: $K$-Theory, Cyclotomic Equations and Clausen's Function / J. Browkin / 233 11.1 Algebraic Background / 233 11.2 Analytic Background / 238 11.3 $K$-theoretic Background / 248 11.4 Examples / 251 11.5 Problems and Conjectures / 270 References / 272 12: Function Theory of Polylogarithms / S. Bloch / 275 13: Partition Identities and the Dilogarithm / J. H. Loxton / 287 13.1 Introduction / 287 13.2 Cyclotomic Equations / 290 13.3 Accessible Relations / 291 13.4 Partition Identities / 292 13.5 Generalisations and Extensions / 297 References / 299 14: The Dilogarithm and Volumes of Hyperbolic Polytopes / R. Kellerhals / 301 14.0 Introduction / 301 14.1 A Particular Class of Hyperbolic Polytopes / 303 14.2 The Volume of a rf-Truncated Orthoscheme / 309 14.3 Applications / 321 14.4 Further Aspects / 328 References / 335 15: Introduction to Higher Logarithms / R. M. Hain and R. MacPherson / 337 15.1 The Problem of Generalizing the Logarithm and the Dilogarithm / 337 15.2 The Quest for Higher Logarithms / 340 15.3 Higher Logarithms / 341 15.4 The Higher Logarithm Bicomplex / 343 15.5 Multivalued Deligne Cohomology / 346 15.6 Higher Logarithms as Deligne Cohomology Classes / 350 Acknowledgements 3 / 51 References / 352 16: Some Miscellaneous Results / L. Lewin / 355 16.1 Clausen's Function and the Di-Gamma Function for Rational Arguments / 355 16.2 An Infinite Integral of a Product of Two Polylogarithms / 359 16.3 Cyclotomic and Polylogarithmic Equations for a Salem Number / 364 16.4 New Functional Equations / 373 References / 374 Appendix A. Special Values and Functional Equations of Polylogarithms / D. Zagier / 377 0. Introduction / 377 1. The Basic Algebraic Relation and the Definition of $mathcal A_m(F)$ / 378 2. Examples of Dilogarithm Relations / 383 3. Examples for Higher Order Polylogarithms / 385 4. Examples: Ladders / 387 5. Existence of Relations among Polylogarithm Values of Arbitrarily High Order / 390 6. A Conjecture on Linear Independence / 391 7. Functional Equations / 392 References / 399 Appendix B. Summary of the Informal Polylogarithm Workshop, November 17--18, 1990, MIT, Cambridge, Massachusetts / 401 R. MacPherson and H. Sah / List of Participants / 401 Abbreviated Summary / 402 Bibliography / 405 Index / 409

rawTOC:
Preface / xiii \\ Acknowledgments / xv \\ List of Contributors / xvii \\ \\ 1: The Evolution of the Ladder Concept / L. Lewin / 1 \\ 1.1 Early History / 1 \\ 1.2 Functional Equations / 2 \\ 1.3 More Recent Numerical Results / 4 \\ 1.4 Current Developments / 6 \\ 1.5 Base on the Unit Circle and Clausen Function Ladders / 8 \\ References / 9 \\ \\ 2: Dilogarithmic Ladders / L. Lewin / 11 \\ 2.1 Derivation from Kummer's Functional Equation / 11 \\ 2.2 Relation to Clausen's Function / 15 \\ 2.3 A Three-Variable Dilogarithmic Functional Equation / 17 \\ 2.4 Functional Equations in the Complex Plane / 18 \\ 2.5 Cyclotomic Equations and Rogers' Function / 20 \\ 2.6 Accessible and Analytic Ladders / 21 \\ 2.7 Inaccessible Ladders / 23 \\ References / 25 \\ \\ 3: Polylogarithmic Ladders / M. Abouzahra and L. Lewin / 27 \\ 3.1 Kummer's Function and its Relation to the Polylogarithm / 27 \\ 3.2 Functional Equations for the Polylogarithm / 28 \\ 3.3 A Generalization of Rogers' Function to the $n$th Order / 31 \\ 3.4 Ladder Order-Independence on Reduction of Order / 33 \\ 3.5 Generic Ladders for the Base Equation $u^p + u^q = 1$ / 34 \\ 3.6 Examples of Ladders for $n < 3$ / 40 \\ 3.7 Examples of Ladders for $n < 4$ / 44 \\ 3.8 Examples of Ladders for $n < 5$ / 45 \\ 3.9 Polynomial Relations for Ladders / 46 \\ References / 47 \\ \\ 4: Ladders in the Trans-Kummer Region / M. Abouzahra and L. Lewin / 49 \\ 4.1 Ladder Results to $n = 9$ for the Base p / 49 \\ 4.2 Ladder Results to $n = 9$ for the Base co / 53 \\ 4.3 Ladder Results to $n = 6$ for the Base 6 / 62 \\ 4.4 The Nonexistence of Functional Equations at $n = 6$ with Arguments Limited to $\pm z^m (1 - z)^r (1 + z)^s$ / 65 \\ References / 67 \\ \\ 5: Supemumary Ladders / M. Abouzahra and L. Lewin / 69 \\ 5.1 The Concept of Supemumary Results / 69 \\ 5.2 Supemumary Results for $p = 4$ / 71 \\ 5.3 Supemumary Results for $p = 5$ / 76 \\ 5.4 Supemumary Results for $p = 6$ / 78 \\ 5.5 Supemumary Results for the Equation-family $u^{6m + 1} u^{6r - 1}$ = 1 / 80 \\ 5.6 Supemumary Results for an Irreducible Quintic / 82 \\ 5.7 Supemumary Ladders from a 15-Term Functional Equation / 84 \\ 5.8 Supemumary Ladders on the Unit Circle / 90 \\ References \\ 6: Functional Equations and Ladders / L. Lewin / 97 \\ 6.1 New Categories of Functional Equations / 97 \\ 6.2 The $\rho$-family of Equations / 100 \\ 6.3 The $\omega$-family of Equations / 109 \\ 6.4 The $\theta$-family of Equations / 115 \\ Acknowledgements / 121 \\ References / 121 \\ \\ 7: Multivariable Polylogarithm Identities / G. A. Ray / 123 \\ 7.0 Introduction / 123 \\ 7.1 A General Identity for the Dilogarithm / 123 \\ 7.2 A General Identity for the Bloch-Wigner Function / 135 \\ 7.3 A General Identity for the Trilogarithm and $D_3(z)$ / 141 \\ 7.4 Linear Power Relations among Dilogarithms / 147 \\ 7.5 Cyclotomic Equations and Bases for Polylogarithm Relations / 154 \\ 7.6 Mahler's Measure and Salem/Pisot Numbers / 160 \\ 7.7 Recent Results for Supemumary Ladders / 165 \\ References / 168 \\ \\ 8: Functional Equations of Hyperlogarithms / G. Wechsung / 171 \\ 8.1 Hyperlogarithms / 171 \\ 8.2 Logarithmic Singularities / 172 \\ 8.3 The Linear Spaces LI$_n$ and PLI$_n$ / 176 \\ 8.4 Functional Equations of Hyperlogarithms / 177 \\ 8.5 A Reduction Problem / 181 \\ References / 184 \\ \\ 9: Kummer-Type Functional Equations of Polylogarithms / G. Wechsung / 185 \\ 9.1 Automorphic Functions / 185 \\ 9.2 Kummer-Type Functional Equations / 186 \\ 9.3 A Method to Construct Functional Equations / 191 \\ 9.4 The Nonexistence of a Kummer-Type Functional Equation for $\Li_6$ / 197 \\ References / 203 \\ \\ 10: The Basic Structure of Polylogarithmic Equations / Z. Wojtkowiak / 205 \\ 10.1 Introduction / 205 \\ 10.2 Canonical Unipotent Connection on $P^1(\mathbb{C})\{a_1, \ldots{}, a_{n+1}\}$ / 211 \\ 10.3 Horizontal Sections / 213 \\ 10.4 Easy Lemmas about Monodromy / 215 \\ 10.5 Functional Equations / 216 \\ 10.6 Functional Equations of Polylogarithms / 218 \\ 10.7 Functional Equations of Lower Degree Polylogarithms / 223 \\ 10.8 Generalized Bloch Groups / 228 \\ Acknowledgements / 231 \\ References / 231 \\ \\ 11: $K$-Theory, Cyclotomic Equations and Clausen's Function / J. Browkin / 233 \\ 11.1 Algebraic Background / 233 \\ 11.2 Analytic Background / 238 \\ 11.3 $K$-theoretic Background / 248 \\ 11.4 Examples / 251 \\ 11.5 Problems and Conjectures / 270 \\ References / 272 \\ \\ 12: Function Theory of Polylogarithms / S. Bloch / 275 \\ \\ 13: Partition Identities and the Dilogarithm / J. H. Loxton / 287 \\ 13.1 Introduction / 287 \\ 13.2 Cyclotomic Equations / 290 \\ 13.3 Accessible Relations / 291 \\ 13.4 Partition Identities / 292 \\ 13.5 Generalisations and Extensions / 297 \\ References / 299 \\ \\ 14: The Dilogarithm and Volumes of Hyperbolic Polytopes / R. Kellerhals / 301 \\ 14.0 Introduction / 301 \\ 14.1 A Particular Class of Hyperbolic Polytopes / 303 \\ 14.2 The Volume of a rf-Truncated Orthoscheme / 309 \\ 14.3 Applications / 321 \\ 14.4 Further Aspects / 328 \\ References / 335 \\ \\ 15: Introduction to Higher Logarithms / R. M. Hain and R. MacPherson / 337 \\ 15.1 The Problem of Generalizing the Logarithm and the Dilogarithm / 337 \\ 15.2 The Quest for Higher Logarithms / 340 \\ 15.3 Higher Logarithms / 341 \\ 15.4 The Higher Logarithm Bicomplex / 343 \\ 15.5 Multivalued Deligne Cohomology / 346 \\ 15.6 Higher Logarithms as Deligne Cohomology Classes / 350 \\ Acknowledgements 3 / 51 \\ References / 352 \\ \\ 16: Some Miscellaneous Results / L. Lewin / 355 \\ 16.1 Clausen's Function and the Di-Gamma Function for Rational Arguments / 355 \\ 16.2 An Infinite Integral of a Product of Two Polylogarithms / 359 \\ 16.3 Cyclotomic and Polylogarithmic Equations for a Salem Number / 364 \\ 16.4 New Functional Equations / 373 \\ References / 374 \\ \\ Appendix A. Special Values and Functional Equations of Polylogarithms / D. Zagier / 377 \\ 0. Introduction / 377 \\ 1. The Basic Algebraic Relation and the Definition of $\mathcal{A}_m(F)$ / 378 \\ 2. Examples of Dilogarithm Relations / 383 \\ 3. Examples for Higher Order Polylogarithms / 385 \\ 4. Examples: Ladders / 387 \\ 5. Existence of Relations among Polylogarithm Values of Arbitrarily High Order / 390 \\ 6. A Conjecture on Linear Independence / 391 \\ 7. Functional Equations / 392 \\ References / 399 \\ \\ Appendix B. Summary of the Informal Polylogarithm Workshop, November 17--18, 1990, MIT, Cambridge, Massachusetts / 401 \\ R. MacPherson and H. Sah / List of Participants / 401 \\ Abbreviated Summary / 402 \\ Bibliography / 405 \\ Index / 409

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@Book{Lewin:1991:SPP,
  editor =       "Leonard Lewin",
  booktitle =    "Structural Properties of Polylogarithms",
  title =        "Structural Properties of Polylogarithms",
  volume =       "37",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "xviii + 412",
  year =         "1991",
  ISBN =         "0-8218-1634-9, 1-4704-1264-0 (e-book)",
  ISBN-13 =      "978-0-8218-1634-9, 978-1-4704-1264-7 (e-book)",
  ISSN =         "0076-5376",
  MRclass =      "33E20, 00B15, 11-02, 11F67, 11R70, 11R42, 19F27,
                 33-02, 33-06, 33B99",
  bibdate =      "Fri Jun 16 14:03:50 MDT 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Mathematical surveys and monographs",
  acknowledgement = ack-nhfb,
  editor-dates = "22-Jul-1919--13-Aug-2007",
  editor-url =   "https://en.wikipedia.org/wiki/Leonard_Lewin_(telecommunications_engineer)",
  subject =      "Logarithmic functions; Fonctions logarithmes;
                 Mathematics; Algebra; Intermediate; Logarithmic
                 functions; Fonctions logarithmes",
  tableofcontents = "Preface / xiii \\
                 Acknowledgments / xv \\
                 List of Contributors / xvii \\
                 \\
                 1: The Evolution of the Ladder Concept / L. Lewin / 1
                 \\
                 1.1 Early History / 1 \\
                 1.2 Functional Equations / 2 \\
                 1.3 More Recent Numerical Results / 4 \\
                 1.4 Current Developments / 6 \\
                 1.5 Base on the Unit Circle and Clausen Function
                 Ladders / 8 \\
                 References / 9 \\
                 \\
                 2: Dilogarithmic Ladders / L. Lewin / 11 \\
                 2.1 Derivation from Kummer's Functional Equation / 11
                 \\
                 2.2 Relation to Clausen's Function / 15 \\
                 2.3 A Three-Variable Dilogarithmic Functional Equation
                 / 17 \\
                 2.4 Functional Equations in the Complex Plane / 18 \\
                 2.5 Cyclotomic Equations and Rogers' Function / 20 \\
                 2.6 Accessible and Analytic Ladders / 21 \\
                 2.7 Inaccessible Ladders / 23 \\
                 References / 25 \\
                 \\
                 3: Polylogarithmic Ladders / M. Abouzahra and L. Lewin
                 / 27 \\
                 3.1 Kummer's Function and its Relation to the
                 Polylogarithm / 27 \\
                 3.2 Functional Equations for the Polylogarithm / 28 \\
                 3.3 A Generalization of Rogers' Function to the $n$th
                 Order / 31 \\
                 3.4 Ladder Order-Independence on Reduction of Order /
                 33 \\
                 3.5 Generic Ladders for the Base Equation $u^p + u^q =
                 1$ / 34 \\
                 3.6 Examples of Ladders for $n < 3$ / 40 \\
                 3.7 Examples of Ladders for $n < 4$ / 44 \\
                 3.8 Examples of Ladders for $n < 5$ / 45 \\
                 3.9 Polynomial Relations for Ladders / 46 \\
                 References / 47 \\
                 \\
                 4: Ladders in the Trans-Kummer Region / M. Abouzahra
                 and L. Lewin / 49 \\
                 4.1 Ladder Results to $n = 9$ for the Base p / 49 \\
                 4.2 Ladder Results to $n = 9$ for the Base co / 53 \\
                 4.3 Ladder Results to $n = 6$ for the Base 6 / 62 \\
                 4.4 The Nonexistence of Functional Equations at $n = 6$
                 with Arguments Limited to $\pm z^m (1 - z)^r (1 + z)^s$
                 / 65 \\
                 References / 67 \\
                 \\
                 5: Supemumary Ladders / M. Abouzahra and L. Lewin / 69
                 \\
                 5.1 The Concept of Supemumary Results / 69 \\
                 5.2 Supemumary Results for $p = 4$ / 71 \\
                 5.3 Supemumary Results for $p = 5$ / 76 \\
                 5.4 Supemumary Results for $p = 6$ / 78 \\
                 5.5 Supemumary Results for the Equation-family $u^{6m +
                 1} u^{6r - 1}$ = 1 / 80 \\
                 5.6 Supemumary Results for an Irreducible Quintic / 82
                 \\
                 5.7 Supemumary Ladders from a 15-Term Functional
                 Equation / 84 \\
                 5.8 Supemumary Ladders on the Unit Circle / 90 \\
                 References \\
                 6: Functional Equations and Ladders / L. Lewin / 97 \\
                 6.1 New Categories of Functional Equations / 97 \\
                 6.2 The $\rho$-family of Equations / 100 \\
                 6.3 The $\omega$-family of Equations / 109 \\
                 6.4 The $\theta$-family of Equations / 115 \\
                 Acknowledgements / 121 \\
                 References / 121 \\
                 \\
                 7: Multivariable Polylogarithm Identities / G. A. Ray /
                 123 \\
                 7.0 Introduction / 123 \\
                 7.1 A General Identity for the Dilogarithm / 123 \\
                 7.2 A General Identity for the Bloch-Wigner Function /
                 135 \\
                 7.3 A General Identity for the Trilogarithm and
                 $D_3(z)$ / 141 \\
                 7.4 Linear Power Relations among Dilogarithms / 147 \\
                 7.5 Cyclotomic Equations and Bases for Polylogarithm
                 Relations / 154 \\
                 7.6 Mahler's Measure and Salem/Pisot Numbers / 160 \\
                 7.7 Recent Results for Supemumary Ladders / 165 \\
                 References / 168 \\
                 \\
                 8: Functional Equations of Hyperlogarithms / G.
                 Wechsung / 171 \\
                 8.1 Hyperlogarithms / 171 \\
                 8.2 Logarithmic Singularities / 172 \\
                 8.3 The Linear Spaces LI$_n$ and PLI$_n$ / 176 \\
                 8.4 Functional Equations of Hyperlogarithms / 177 \\
                 8.5 A Reduction Problem / 181 \\
                 References / 184 \\
                 \\
                 9: Kummer-Type Functional Equations of Polylogarithms /
                 G. Wechsung / 185 \\
                 9.1 Automorphic Functions / 185 \\
                 9.2 Kummer-Type Functional Equations / 186 \\
                 9.3 A Method to Construct Functional Equations / 191
                 \\
                 9.4 The Nonexistence of a Kummer-Type Functional
                 Equation for $\Li_6$ / 197 \\
                 References / 203 \\
                 \\
                 10: The Basic Structure of Polylogarithmic Equations /
                 Z. Wojtkowiak / 205 \\
                 10.1 Introduction / 205 \\
                 10.2 Canonical Unipotent Connection on
                 $P^1(\mathbb{C})\{a_1, \ldots{}, a_{n+1}\}$ / 211 \\
                 10.3 Horizontal Sections / 213 \\
                 10.4 Easy Lemmas about Monodromy / 215 \\
                 10.5 Functional Equations / 216 \\
                 10.6 Functional Equations of Polylogarithms / 218 \\
                 10.7 Functional Equations of Lower Degree
                 Polylogarithms / 223 \\
                 10.8 Generalized Bloch Groups / 228 \\
                 Acknowledgements / 231 \\
                 References / 231 \\
                 \\
                 11: $K$-Theory, Cyclotomic Equations and Clausen's
                 Function / J. Browkin / 233 \\
                 11.1 Algebraic Background / 233 \\
                 11.2 Analytic Background / 238 \\
                 11.3 $K$-theoretic Background / 248 \\
                 11.4 Examples / 251 \\
                 11.5 Problems and Conjectures / 270 \\
                 References / 272 \\
                 \\
                 12: Function Theory of Polylogarithms / S. Bloch / 275
                 \\
                 \\
                 13: Partition Identities and the Dilogarithm / J. H.
                 Loxton / 287 \\
                 13.1 Introduction / 287 \\
                 13.2 Cyclotomic Equations / 290 \\
                 13.3 Accessible Relations / 291 \\
                 13.4 Partition Identities / 292 \\
                 13.5 Generalisations and Extensions / 297 \\
                 References / 299 \\
                 \\
                 14: The Dilogarithm and Volumes of Hyperbolic Polytopes
                 / R. Kellerhals / 301 \\
                 14.0 Introduction / 301 \\
                 14.1 A Particular Class of Hyperbolic Polytopes / 303
                 \\
                 14.2 The Volume of a rf-Truncated Orthoscheme / 309 \\
                 14.3 Applications / 321 \\
                 14.4 Further Aspects / 328 \\
                 References / 335 \\
                 \\
                 15: Introduction to Higher Logarithms / R. M. Hain and
                 R. MacPherson / 337 \\
                 15.1 The Problem of Generalizing the Logarithm and the
                 Dilogarithm / 337 \\
                 15.2 The Quest for Higher Logarithms / 340 \\
                 15.3 Higher Logarithms / 341 \\
                 15.4 The Higher Logarithm Bicomplex / 343 \\
                 15.5 Multivalued Deligne Cohomology / 346 \\
                 15.6 Higher Logarithms as Deligne Cohomology Classes /
                 350 \\
                 Acknowledgements 3 / 51 \\
                 References / 352 \\
                 \\
                 16: Some Miscellaneous Results / L. Lewin / 355 \\
                 16.1 Clausen's Function and the Di-Gamma Function for
                 Rational Arguments / 355 \\
                 16.2 An Infinite Integral of a Product of Two
                 Polylogarithms / 359 \\
                 16.3 Cyclotomic and Polylogarithmic Equations for a
                 Salem Number / 364 \\
                 16.4 New Functional Equations / 373 \\
                 References / 374 \\
                 \\
                 Appendix A. Special Values and Functional Equations of
                 Polylogarithms / D. Zagier / 377 \\
                 0. Introduction / 377 \\
                 1. The Basic Algebraic Relation and the Definition of
                 $\mathcal{A}_m(F)$ / 378 \\
                 2. Examples of Dilogarithm Relations / 383 \\
                 3. Examples for Higher Order Polylogarithms / 385 \\
                 4. Examples: Ladders / 387 \\
                 5. Existence of Relations among Polylogarithm Values of
                 Arbitrarily High Order / 390 \\
                 6. A Conjecture on Linear Independence / 391 \\
                 7. Functional Equations / 392 \\
                 References / 399 \\
                 \\
                 Appendix B. Summary of the Informal Polylogarithm
                 Workshop, November 17--18, 1990, MIT, Cambridge,
                 Massachusetts / 401 \\
                 R. MacPherson and H. Sah / List of Participants / 401
                 \\
                 Abbreviated Summary / 402 \\
                 Bibliography / 405 \\
                 Index / 409",
}


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filename: elefunt.bib
label: EC2:1992:DJN
publisher: EC2
address: Nanterre Cedex, France
pages: 384
year: 1992
ISBN: 2-906899-78-X OR 290689978X
ISBN13: 978-2-906899-78-0 OR 9782906899780
bibdate: Wed Jan 10 07:40:53 1996
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1996.01.10 07:40:53 ???
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key: AEF'92
booktitle:
Deuxiemes journees nationales: Les applications des ensembles flous, en l'honneur du Professeur A. Kaufmann, Nimes, 2--3 novembre 1992, conference scientifique (English: Second national conference: Application of Fuzzy Sets, in honor of Professor A. Kaufman, Nimes, 2--3 November 1992, scientific conference)

title:
Deuxiemes journees nationales: Les applications des ensembles flous, en l'honneur du Professeur A. Kaufmann, Nimes, 2--3 novembre 1992, conference scientifique (English: Second national conference: Application of Fuzzy Sets, in honor of Professor A. Kaufman, Nimes, 2--3 November 1992, scientific conference)

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bibtype: proceedings
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label: Richards:1992:HFD
editor: Donald St P. Richards
volume: 138
publisher: pub-AMS
address: pub-AMS:adr
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LCCN: QA353.H9 H97 1992
bibdate: Sat Oct 30 21:12:24 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
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series: Contemporary mathematics
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booktitle:
Hypergeometric functions on domains of positivity, Jack polynomials, and applications: proceedings of an AMS Special Session held March 22--23, 1991 in Tampa, Florida

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publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
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ISBN13: 978-0-12-044210-2 OR 9780120442102
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bibdate: Mon Jan 13 09:58:58 1997
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Contributors Preface Acknowledgements Introduction Part I. Language and Programming Support for Verified Scientific Computation 1. PASCAL-XSC, New Concepts for Scientific Computation and Numerical Data Processing 2. ACRITH-XSC, A Fortran-like Language for Verified Scientific Computing 3. C-XSC, A Programming Environment for Verified Scientific Computing and Numerical Data Processing 4. Proposal for Accurate Floating-Point Vector Arithmetic

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                 1. PASCAL-XSC, New Concepts for Scientific Computation
                 and Numerical Data Processing \\
                 2. ACRITH-XSC, A Fortran-like Language for Verified
                 Scientific Computing \\
                 3. C-XSC, A Programming Environment for Verified
                 Scientific Computing and Numerical Data Processing \\
                 4. Proposal for Accurate Floating-Point Vector
                 Arithmetic",
}


bibtype: proceedings
filename: elefunt.bib
label: Albrecht:1993:VNT
editor: R. Albrecht and G. Alefeld and H. J. Stetter
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publisher: pub-SPRINGER-WIEN
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LCCN: QA297 .V27 1993
bibdate: Wed Oct 13 18:45:11 1999
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Proceedings of the International Joint Symposium on Special Functions and Artificial Intelligence, (1993: Turin, Italy)

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Proceedings of the International Joint Symposium on Special Functions and Artificial Intelligence, (1993: Turin, Italy)

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bibtype: proceedings
filename: elefunt.bib
label: Sincovec:1993:PSS
editor: Richard F. Sincovec and David E. Keyes and Michael R. Leuze
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bibdate: Tue Oct 11 12:21:40 1994
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booktitle:
Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, held March 22--24, 1993, in Norfolk, VA, USA

title:
Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, held March 22--24, 1993, in Norfolk, VA, USA

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bibtype: proceedings
filename: elefunt.bib
label: Swartzlander:1993:SCA
editor: Earl Swartzlander, Jr. and Mary Jane Irwin and Graham Jullien
booktitle: Proceedings: 11th Symposium on Computer Arithmetic, June 29--July 2, 1993, Windsor, Ontario
title: Proceedings: 11th Symposium on Computer Arithmetic, June 29--July 2, 1993, Windsor, Ontario
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xii + 284
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bibdate: Thu Sep 01 22:58:49 1994
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note: IEEE Transactions on Computers bf 43(8), 1994
acknowledgement: ack-nhfb
rawbooktitle: Proceedings: 11th Symposium on Computer Arithmetic, June 29--July 2, 1993, Windsor, Ontario
raweditor: Earl {Swartzlander, Jr.} and Mary Jane Irwin and Graham Jullien
rawnote: IEEE Transactions on Computers {\bf 43(8)}, 1994
rawtitle: Proceedings: 11th Symposium on Computer Arithmetic, June 29--July 2, 1993, Windsor, Ontario
ISBN:
0-7803-1401-8 (softbound), 0-8186-3862-1 (casebound), 0-8186-3861-3 (microfiche) OR 0780314018 (softbound), 0818638621 (casebound), 0818638613 (microfiche)

ISBN13:
978-0-7803-1401-6 (softbound), 978-0-8186-3862-6 (casebound), 978-0-8186-3861-9 (microfiche) OR 9780780314016 (softbound), 9780818638626 (casebound), 9780818638619 (microfiche)

entry:
@Proceedings{Swartzlander:1993:SCA,
  editor =       "Earl {Swartzlander, Jr.} and Mary Jane Irwin and
                 Graham Jullien",
  booktitle =    "Proceedings: 11th Symposium on Computer Arithmetic,
                 June 29--July 2, 1993, Windsor, Ontario",
  title =        "Proceedings: 11th Symposium on Computer Arithmetic,
                 June 29--July 2, 1993, Windsor, Ontario",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 284",
  year =         "1993",
  ISBN =         "0-7803-1401-8 (softbound), 0-8186-3862-1 (casebound),
                 0-8186-3861-3 (microfiche)",
  ISBN-13 =      "978-0-7803-1401-6 (softbound), 978-0-8186-3862-6
                 (casebound), 978-0-8186-3861-9 (microfiche)",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  LCCN =         "QA 76.9 C62 S95 1993",
  bibdate =      "Thu Sep 01 22:58:49 1994",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE Transactions on Computers {\bf 43(8)}, 1994",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Brown:1994:PCL
editor: J. David Brown and Moody T. Chu and Donald C. Ellison and Robert J. Plemmons
volume: 73
publisher: pub-SIAM
address: pub-SIAM:adr
pages: lxv + 644
year: 1994
ISBN: 0-89871-339-0 OR 0898713390
ISBN13: 978-0-89871-339-8 OR 9780898713398
LCCN: QC19.2 .C67 1993
bibdate: Wed Jun 8 14:42:43 MDT 2011
bibtimestamp: 2011.06.08 14:42:43 MDT
series: Proceedings in Applied Mathematics
acknowledgement: ack-nhfb
subjectdates: 1893--1974
raweditor: J. David Brown and Moody T. Chu and Donald C. Ellison and Robert J. Plemmons
booktitle:
Proceedings of the Cornelius Lanczos International Centenary Conference, Raleigh, North Carolina, December 12--17, 1993

title:
Proceedings of the Cornelius Lanczos International Centenary Conference, Raleigh, North Carolina, December 12--17, 1993

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib; https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib; https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib; https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib; https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib; https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib; https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib; https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/einstein.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager

subject:
Mathematical physics; Congresses; Astrophysics; Mathematics; Lanczos, Cornelius; Physicists; Hungary; Biography; Mathematicians

TOC:
The Life and Works of Cornelius Lanczos A Photographic Essay / / xvii Cornelius Lanczos: A Biographical Essay / Barbara Gellai / xxi Cornelius Lanczos (1893-1974), and the Hungarian Phenomenon in Science and Mathematics / Peter D. Lax / xlix The Roots of Cornelius Lanczos / George Marx / liii Reminiscences of Cornelius Lanczos / Jon Todd / lviii Published Papers and Books of Cornelius Lanczos / / lx Plenary Presentations: Computational Mathematics Lanczos and the FFT: A Discovery Before its Time / James W. Cooley / 3 Lanczos Algorithms for Large Scale Symmetric and Nonsymmetric Matrix Eigenvalue Problems / Jane K. Cullum / 11 The Look-Ahead Lanczos Process for Nonsymmetric Matrices and its Applications / Roland W Freund / 33 The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic / Anne Greenbaum / 49 The Lanczos Process and Pade Approximation / Martin H. Gutknecht / 61 The Tau Method and the Numerical Solution of Differential Equations: Past Research and Recent Research / Eduardo L. Ortiz / 77 Krylov Subspace Processes, Krylov Subspace Methods, and Iteration Polynomials / C. C. Paige / 83 Do We Fully Understand the Symmetric Lanczos Algorithm Yet? / Beresford N. Parlett / 93 On Generalized Band Matrices and Their Inverses / Pal Rosa, Francesco Romani, and Roberto Bevilacqua / 109 Theoretical Error Bounds and General Analysis of a Few Lanczos-Type Algorithms / Youcef Saad / 123 Lanczos and Linear Systems / G. W. Stewart / 135 Plenary Presentations: Theoretical Physics and Astrophysics Integration on the Space of Connections Modulo Gauge Transformations / Abbay Ashtekar, Donald Marolf, and Jose Mourdo / 143 Quasiclassical Domains in a Quantum Universe / James B. Hartle / 161 Gauge Invariant Energy-Momentum Tensor in Spinar Electrodynamics / D. Petiot and Y. Takahashi / 173 $gamma $-Ray Bursts and Neutron Star Mergers / Tsvi Piran / 187 Lanczos's Early Contributions to Relativity and His Relationship with Einstein / John Stachel / 201 Topological Roots of Black Hole Entropy / Claudio Teitelboim / 223 Variational Principles, Local Symmetries, and Black Hole Entropy / Robert M. Wald / 231 Mathematics Minisymposia Eigenvalue Computations: Theory and Algorithms / / 241 Eigenvalue Computations: Applications / / 249 Moments in Numerical Analysis / / 265 Iterative Methods for Linear Systems / / 277 Least Squares / / 301 Software for Lanczos-based Algorithms / / 311 Tau Method / / 335 Chebyshev Polynomials / / 357 Lanczos Methods in Control and Signal Processing / / 375 Development of the FFT / / 393 The FFT in Signal Processing / / 399 Wavelets / / 411 Physics Minisymposia Computational Magnetohydrodynamics in Astrophysics / / 431 Numerical Simulations of Collisionless Space Plasmas / / 453 Detection of Gravitational Radiation from Astrophysical Sources / / 477 Lanczos $H$-tensor / / 489 Cosmic Censorship / / 513 Cauchy Problem of General Relativity / / 527 Black Hole Evaporation and Thermodynamics / / 543 The Problem of Time in Quantum Gravity / / 555 New Variables and Loop Quantization / / 571 Decoherence and the Foundations of Quantum Mechanics / / 589 Open Questions in Particle Theory / / 603 Supercollider Physics / / 621 Symplectic Methods in Physics / / 633

rawbooktitle:
{Proceedings of the Cornelius Lanczos International Centenary Conference, Raleigh, North Carolina, December 12--17, 1993}

rawtitle:
{Proceedings of the Cornelius Lanczos International Centenary Conference, Raleigh, North Carolina, December 12--17, 1993}

rawTOC:
The Life and Works of Cornelius Lanczos \\ \\ A Photographic Essay / / xvii \\ Cornelius Lanczos: A Biographical Essay / Barbara Gellai / xxi \\ Cornelius Lanczos (1893-1974), and the Hungarian Phenomenon in Science and Mathematics / Peter D. Lax / xlix \\ The Roots of Cornelius Lanczos / George Marx / liii \\ Reminiscences of Cornelius Lanczos / Jon Todd / lviii \\ Published Papers and Books of Cornelius Lanczos / / lx \\ \\ Plenary Presentations: Computational Mathematics \\ \\ Lanczos and the FFT: A Discovery Before its Time / James W. Cooley / 3 \\ Lanczos Algorithms for Large Scale Symmetric and Nonsymmetric Matrix Eigenvalue Problems / Jane K. Cullum / 11 \\ The Look-Ahead Lanczos Process for Nonsymmetric Matrices and its Applications / Roland W Freund / 33 \\ The Lanczos and Conjugate Gradient Algorithms in Finite Precision Arithmetic / Anne Greenbaum / 49 \\ The Lanczos Process and Pade Approximation / Martin H. Gutknecht / 61 \\ The Tau Method and the Numerical Solution of Differential Equations: Past Research and Recent Research / Eduardo L. Ortiz / 77 \\ Krylov Subspace Processes, Krylov Subspace Methods, and Iteration Polynomials / C. C. Paige / 83 \\ Do We Fully Understand the Symmetric Lanczos Algorithm Yet? / Beresford N. Parlett / 93 \\ On Generalized Band Matrices and Their Inverses / P{\'a}l R{\'o}sa, Francesco Romani, and Roberto Bevilacqua / 109 \\ Theoretical Error Bounds and General Analysis of a Few Lanczos-Type Algorithms / Youcef Saad / 123 \\ Lanczos and Linear Systems / G. W. Stewart / 135 \\ \\ Plenary Presentations: Theoretical Physics and Astrophysics \\ \\ Integration on the Space of Connections Modulo Gauge Transformations / Abbay Ashtekar, Donald Marolf, and Jose Mourdo / 143 \\ Quasiclassical Domains in a Quantum Universe / James B. Hartle / 161 \\ Gauge Invariant Energy-Momentum Tensor in Spinar Electrodynamics / D. Petiot and Y. Takahashi / 173 \\ $\gamma$-Ray Bursts and Neutron Star Mergers / Tsvi Piran / 187 \\ Lanczos's Early Contributions to Relativity and His Relationship with Einstein / John Stachel / 201 \\ Topological Roots of Black Hole Entropy / Claudio Teitelboim / 223 \\ Variational Principles, Local Symmetries, and Black Hole Entropy / Robert M. Wald / 231 \\ \\ Mathematics Minisymposia \\ \\ Eigenvalue Computations: Theory and Algorithms / / 241 \\ Eigenvalue Computations: Applications / / 249 \\ Moments in Numerical Analysis / / 265 \\ Iterative Methods for Linear Systems / / 277 \\ Least Squares / / 301 \\ Software for Lanczos-based Algorithms / / 311 \\ Tau Method / / 335 \\ Chebyshev Polynomials / / 357 \\ Lanczos Methods in Control and Signal Processing / / 375 \\ Development of the FFT / / 393 \\ The FFT in Signal Processing / / 399 \\ Wavelets / / 411 \\ \\ Physics Minisymposia \\ \\ Computational Magnetohydrodynamics in Astrophysics / / 431 \\ Numerical Simulations of Collisionless Space Plasmas / / 453 \\ Detection of Gravitational Radiation from Astrophysical Sources / / 477 \\ Lanczos $H$-tensor / / 489 \\ Cosmic Censorship / / 513 \\ Cauchy Problem of General Relativity / / 527 \\ Black Hole Evaporation and Thermodynamics / / 543 \\ The Problem of Time in Quantum Gravity / / 555 \\ New Variables and Loop Quantization / / 571 \\ Decoherence and the Foundations of Quantum Mechanics / / 589 \\ Open Questions in Particle Theory / / 603 \\ Supercollider Physics / / 621 \\ Symplectic Methods in Physics / / 633

entry:
@Proceedings{Brown:1994:PCL,
  editor =       "J. David Brown and Moody T. Chu and Donald C. Ellison
                 and Robert J. Plemmons",
  booktitle =    "{Proceedings of the Cornelius Lanczos International
                 Centenary Conference, Raleigh, North Carolina, December
                 12--17, 1993}",
  title =        "{Proceedings of the Cornelius Lanczos International
                 Centenary Conference, Raleigh, North Carolina, December
                 12--17, 1993}",
  volume =       "73",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "lxv + 644",
  year =         "1994",
  ISBN =         "0-89871-339-0",
  ISBN-13 =      "978-0-89871-339-8",
  LCCN =         "QC19.2 .C67 1993",
  bibdate =      "Wed Jun 8 14:42:43 MDT 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/golub-gene-h.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/heisenberg-werner.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/l/lanczos-cornelius.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/saad-yousef.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stewart-gilbert-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/t/tukey-john-w.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/vandervorst-henk-a.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/y/young-david-m.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/einstein.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Proceedings in Applied Mathematics",
  acknowledgement = ack-nhfb,
  meetingname =  "Cornelius Lanczos International Centenary Conference
                 (1993:Raleigh, NC)",
  subject =      "Mathematical physics; Congresses; Astrophysics;
                 Mathematics; Lanczos, Cornelius; Physicists; Hungary;
                 Biography; Mathematicians",
  subject-dates = "1893--1974",
  tableofcontents = "The Life and Works of Cornelius Lanczos \\
                 \\
                 A Photographic Essay / / xvii \\
                 Cornelius Lanczos: A Biographical Essay / Barbara
                 Gellai / xxi \\
                 Cornelius Lanczos (1893-1974), and the Hungarian
                 Phenomenon in Science and Mathematics / Peter D. Lax /
                 xlix \\
                 The Roots of Cornelius Lanczos / George Marx / liii \\
                 Reminiscences of Cornelius Lanczos / Jon Todd / lviii
                 \\
                 Published Papers and Books of Cornelius Lanczos / / lx
                 \\
                 \\
                 Plenary Presentations: Computational Mathematics \\
                 \\
                 Lanczos and the FFT: A Discovery Before its Time /
                 James W. Cooley / 3 \\
                 Lanczos Algorithms for Large Scale Symmetric and
                 Nonsymmetric Matrix Eigenvalue Problems / Jane K.
                 Cullum / 11 \\
                 The Look-Ahead Lanczos Process for Nonsymmetric
                 Matrices and its Applications / Roland W Freund / 33
                 \\
                 The Lanczos and Conjugate Gradient Algorithms in Finite
                 Precision Arithmetic / Anne Greenbaum / 49 \\
                 The Lanczos Process and Pade Approximation / Martin H.
                 Gutknecht / 61 \\
                 The Tau Method and the Numerical Solution of
                 Differential Equations: Past Research and Recent
                 Research / Eduardo L. Ortiz / 77 \\
                 Krylov Subspace Processes, Krylov Subspace Methods, and
                 Iteration Polynomials / C. C. Paige / 83 \\
                 Do We Fully Understand the Symmetric Lanczos Algorithm
                 Yet? / Beresford N. Parlett / 93 \\
                 On Generalized Band Matrices and Their Inverses /
                 P{\'a}l R{\'o}sa, Francesco Romani, and Roberto
                 Bevilacqua / 109 \\
                 Theoretical Error Bounds and General Analysis of a Few
                 Lanczos-Type Algorithms / Youcef Saad / 123 \\
                 Lanczos and Linear Systems / G. W. Stewart / 135 \\
                 \\
                 Plenary Presentations: Theoretical Physics and
                 Astrophysics \\
                 \\
                 Integration on the Space of Connections Modulo Gauge
                 Transformations / Abbay Ashtekar, Donald Marolf, and
                 Jose Mourdo / 143 \\
                 Quasiclassical Domains in a Quantum Universe / James B.
                 Hartle / 161 \\
                 Gauge Invariant Energy-Momentum Tensor in Spinar
                 Electrodynamics / D. Petiot and Y. Takahashi / 173 \\
                 $\gamma$-Ray Bursts and Neutron Star Mergers / Tsvi
                 Piran / 187 \\
                 Lanczos's Early Contributions to Relativity and His
                 Relationship with Einstein / John Stachel / 201 \\
                 Topological Roots of Black Hole Entropy / Claudio
                 Teitelboim / 223 \\
                 Variational Principles, Local Symmetries, and Black
                 Hole Entropy / Robert M. Wald / 231 \\
                 \\
                 Mathematics Minisymposia \\
                 \\
                 Eigenvalue Computations: Theory and Algorithms / / 241
                 \\
                 Eigenvalue Computations: Applications / / 249 \\
                 Moments in Numerical Analysis / / 265 \\
                 Iterative Methods for Linear Systems / / 277 \\
                 Least Squares / / 301 \\
                 Software for Lanczos-based Algorithms / / 311 \\
                 Tau Method / / 335 \\
                 Chebyshev Polynomials / / 357 \\
                 Lanczos Methods in Control and Signal Processing / /
                 375 \\
                 Development of the FFT / / 393 \\
                 The FFT in Signal Processing / / 399 \\
                 Wavelets / / 411 \\
                 \\
                 Physics Minisymposia \\
                 \\
                 Computational Magnetohydrodynamics in Astrophysics / /
                 431 \\
                 Numerical Simulations of Collisionless Space Plasmas /
                 / 453 \\
                 Detection of Gravitational Radiation from Astrophysical
                 Sources / / 477 \\
                 Lanczos $H$-tensor / / 489 \\
                 Cosmic Censorship / / 513 \\
                 Cauchy Problem of General Relativity / / 527 \\
                 Black Hole Evaporation and Thermodynamics / / 543 \\
                 The Problem of Time in Quantum Gravity / / 555 \\
                 New Variables and Loop Quantization / / 571 \\
                 Decoherence and the Foundations of Quantum Mechanics /
                 / 589 \\
                 Open Questions in Particle Theory / / 603 \\
                 Supercollider Physics / / 621 \\
                 Symplectic Methods in Physics / / 633",
}


bibtype: proceedings
filename: elefunt.bib
label: Cuyt:1994:NNM
editor: Annie Cuyt
booktitle: Nonlinear numerical methods and rational approximation II
title: Nonlinear numerical methods and rational approximation II
volume: 296
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: xviii + 446
year: 1994
ISBN: 0-7923-2967-8 OR 0792329678
ISBN13: 978-0-7923-2967-1 OR 9780792329671
LCCN: QA297 .N642 1994
bibdate: Wed Nov 3 09:30:14 MST 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.11.03 09:30:14 MST
series: Mathematics and its applications
keywords: approximation theory -- congresses; numerical analysis -- congresses
acknowledgement: ack-nhfb
rawbooktitle: Nonlinear numerical methods and rational approximation {II}
raweditor: Annie Cuyt
rawtitle: Nonlinear numerical methods and rational approximation {II}
note:
Proceedings of an international conference held at the University of Antwerp, Belgium, Sept. 5--11, 1993.

rawnote:
Proceedings of an international conference held at the University of Antwerp, Belgium, Sept. 5--11, 1993.

entry:
@Proceedings{Cuyt:1994:NNM,
  editor =       "Annie Cuyt",
  booktitle =    "Nonlinear numerical methods and rational approximation
                 {II}",
  title =        "Nonlinear numerical methods and rational approximation
                 {II}",
  volume =       "296",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "xviii + 446",
  year =         "1994",
  ISBN =         "0-7923-2967-8",
  ISBN-13 =      "978-0-7923-2967-1",
  LCCN =         "QA297 .N642 1994",
  bibdate =      "Wed Nov 3 09:30:14 MST 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of an international conference held at the
                 University of Antwerp, Belgium, Sept. 5--11, 1993.",
  series =       "Mathematics and its applications",
  acknowledgement = ack-nhfb,
  keywords =     "approximation theory -- congresses; numerical analysis
                 -- congresses",
}


bibtype: proceedings
filename: elefunt.bib
label: Gautschi:1994:MCH
editor: Walter Gautschi
volume: 48
publisher: pub-AMS
address: pub-AMS:adr
pages: xix + 643
year: 1994
ISSN: 0160-7634 OR 01607634
LCCN: QA1 .A56 v.48 1994; QA297.M385 1993
MRclass: 00B25 (11-06 65-06)
MRnumber: 95j:00014
bibdate: Mon Oct 24 11:37:20 2011
bibtimestamp: 2011.10.24 11:37:20 ???
note: See also SIAM Review, September 1995, bf 37(3), p. 483.
series: Proceedings of Symposia in Applied Mathematics
acknowledgement: ack-nhfb
authordates: Frank William John Olver (15 December 1924--23 April 2013)
raweditor: Walter Gautschi
rawnote: See also SIAM Review, September 1995, {\bf 37}(3), p. 483.
booktitle:
Mathematics of computation, 1943--1993: a half-century of computational mathematics: Mathematics of Computation 50th Anniversary Symposium, August 9--13, 1993, Vancouver, British Columbia

title:
Mathematics of computation, 1943--1993: a half-century of computational mathematics: Mathematics of Computation 50th Anniversary Symposium, August 9--13, 1993, Vancouver, British Columbia

ISBN:
0-8218-0291-7, 0-8218-0353-0 (pt. 1), 0-8218-0354-9 (pt. 2) OR 0821802917, 0821803530 (pt. 1), 0821803549 (pt. 2)

ISBN13:
978-0-8218-0291-5, 978-0-8218-0353-0 (pt. 1), 978-0-8218-0354-7 (pt. 2) OR 9780821802915, 9780821803530 (pt. 1), 9780821803547 (pt. 2)

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib; https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib; https://www.math.utah.edu/pub/bibnet/authors/l/lehmer-derrick-henry.bib; https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib; https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib; https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1940.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib; https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib

TOC:
Preface / xi Mathematics of Computation: A brief history / Eugene Isaacson / xvii Part I. Symposium on Numerical Analysis Invited Papers On the development of multigrid methods and their analysis / James H. Bramble / 5 An introduction to inverse problems / Margaret Cheney / 21 Algorithms for unconstrained optimization: A review of recent developments / Donald Goldfarb / 33 A survey of componentwise perturbation theory in numerical linear algebra / Nicholas J. Higham / 49 Numerical evaluation of special functions / D. W. Lozier and F. W. J. Olver / 79 A survey of numerical cubature over triangles / J. N. Lyness and Ronald Cools / 127 New trends in the use and analysis of integral equations / J. C. Nedelec / 151 Applications of multivariate splines / Larry L. Schumaker / 177 Initial value problems for ordinary differential equations: Development of ideas, techniques, and implementation / Hans J. Stetter / 205 Multiresolution methods for partial differential equations / Roger Temam / 225 Contributed Papers A comparison of techniques for solving ill-conditioned problems arising from the immersed boundary method / Loyce Adams and Zhiyun Yang / 243 A mixed spectral-collocation and operator splitting method for the Wigner-Poisson equation / Anton Arnold / 249 Finite volume methods for irregular one-dimensional grids / M. J. Berger, R. J. Leveque, and L. G. Stern / 255 Linear rational interpolation of continuous functions over an interval / Jean-Paul Berrut / 261 A von Neumann reflection for the 2-D Burgers equation / M. Brio and J. K. Hunter / 265 Slow evolution from the boundary: A new stabilizing constraint in ill-posed continuation problems / Alfred S. Carasso / 269 A finite element method for the 2D drift-diffusion semiconductor model / Zhangxin Chen / 275 Splitting functions and numerical analysis of WR-type methods for evolutionary and stationary problems / S. De Marchi, M. Vianello, and R. Zanovello / 281 Error estimates for a quadrature rule for Cauchy principal value integrals / Kai Diethelm / 287 A numerical radius approach to stable difference schemes for parabolic systems / Moshe Goldberg / 293 An extension of the Olver-Sookne method for the solution of second-order linear difference equations / Takemitsu Hasegawa and Tatsuo Torii / 297 The Faber polynomials for circular arcs / Matthew He / 301 Finite element approximation for optimal control of electrically conducting fluid flows / L. S. Hou and S. S. Ravindran / 305 ADI methods for heat equations with discontinuities along an arbitrary interface / Zhilin Li and Anita Mayo / 311 Eigenvalue approximation of Fredholm integral operators / E. B. Lin / 317 Spectral methods for singular perturbation problems / Wenbin Liu and Tao Tang / 323 A quaternion-Jacobi method for symmetric matrices / Niloufer Mackey / 327 On constructing Chebyshev series solutions of differential equations / Allan J. MacLeod / 333 Multiquadric collocation methods in the numerical solution of Volterra integral and integro-differential equations / Athena Makroglou / 337 Methods for solving large eigenvalue problems associated with configuration interaction electronic structure calculations / Kristyn J. Maschhoff / 343 Computing limiting normals to real surfaces / Donal O'Shea and Les Wilson / 349 Orthogonal spline collocation solution of nonlinear Schrodinger equations / Mark P. Robinson / 355 Who invented the computer? The debate from the viewpoint of computer architecture / Raul Rojas / 361 Locking and boundary layer effects in the finite element approximation of the Reissner--Mindlin plate model / Christoph Schwab and Manil Suri / 367 Efficient spectral Galerkin methods for some elliptic problems / Jie Shen / 373 Periodic solutions of higher-order difference equations in two independent variables / Qin Sheng and Ravi P. Agarwal / 377 Front tracking based on high-resolution wave propagation methods / Keh-Ming Shyue / 383 Time-splitting methods for nonhomogeneous conservation laws / Tao Tang and Zhen-Huan Teng / 389 Numerical aspects of uniform Airy-type asymptotic expansions / N. M. Temme / 395 Local dynamics and bifurcation consistencies of continuous-time dynamical systems and their numerical discretizations / Xin Wang, Edward K. Blum, and Qingnan Li / 399 Computing integrals of the complex error function / J. A. C. Weideman / 403 Quadratures for improper integrals and their applications in integral equations / Yuesheng Xu and Yunhe Zhao / 409 Spline harmonic analysis and wavelet bases / Valery A. Zheludev / 415 Part II. Minisymposium on Computational Number Theory Dedicated to the memory of Derrick Henry Lehmer Invited Papers Algorithms for quadratic orders / Ingrid Biehl and Johannes Buchmann / 425 Analytic computations in number theory / Andrew M. Odlyzko / 451 The number field sieve / Carl Pomerance / 465 Factoring integers before computers / H. C. Williams and J. O. Shallit / 481 Contributed Papers Explicit bounds for primes in residue classes / Eric Bach and Jonathan Sorenson / 535 Ramanujan and Euler's constant / Richard P. Brent / 541 Congruential sieves on FPGA computers / Nathan D. Bronson and Duncan A. Buell / 547 Lehmer pairs of zeros and the Riemann $xi $-function / George Csordas, Wayne Smith, and Richard S. Varga / 553 A record Aliquot sequence / Andrew W. P. Guy and Richard K. Guy / 557 Implications of computational mathematics for the philosophy of mathematics / Andrew J. Lazarus / 561 Square roots of products of algebraic numbers / Peter L. Montgomery / 567 A locally parameterized version of Lehmer's problem / Gary A. Ray / 573 A new method for finding amicable pairs / H. J. J. te Riele / 577 Generalized Fermat numbers / Hans Riesel and Anders Bjorn / 583 Evaluation of $zeta _K(2)$ for some totally real algebraic number fields K of degree 9 / Kisao Takeuchi / 589 The period of the Bell exponential integers modulo a prime / Samuel S. Wagstaff, Jr. / 595 Computing invariant polynomials of $p$-adic reflection groups / Changsheng Xu / 599 Author Index / 603 Subject Index / 619

rawbooktitle:
{Mathematics of computation, 1943--1993: a half-century of computational mathematics: Mathematics of Computation 50th Anniversary Symposium, August 9--13, 1993, Vancouver, British Columbia}

rawtitle:
{Mathematics of computation, 1943--1993: a half-century of computational mathematics: Mathematics of Computation 50th Anniversary Symposium, August 9--13, 1993, Vancouver, British Columbia}

rawTOC:
Preface / xi \\ Mathematics of Computation: A brief history / Eugene Isaacson / xvii \\ \\ Part I. Symposium on Numerical Analysis \\ \\ Invited Papers \\ \\ On the development of multigrid methods and their analysis / James H. Bramble / 5 \\ An introduction to inverse problems / Margaret Cheney / 21 \\ Algorithms for unconstrained optimization: A review of recent developments / Donald Goldfarb / 33 \\ A survey of componentwise perturbation theory in numerical linear algebra / Nicholas J. Higham / 49 \\ Numerical evaluation of special functions / D. W. Lozier and F. W. J. Olver / 79 \\ A survey of numerical cubature over triangles / J. N. Lyness and Ronald Cools / 127 \\ New trends in the use and analysis of integral equations / J. C. Nedelec / 151 \\ Applications of multivariate splines / Larry L. Schumaker / 177 \\ Initial value problems for ordinary differential equations: Development of ideas, techniques, and implementation / Hans J. Stetter / 205 \\ Multiresolution methods for partial differential equations / Roger Temam / 225 \\ \\ Contributed Papers \\ \\ A comparison of techniques for solving ill-conditioned problems arising from the immersed boundary method / Loyce Adams and Zhiyun Yang / 243 \\ A mixed spectral-collocation and operator splitting method for the Wigner-Poisson equation / Anton Arnold / 249 \\ Finite volume methods for irregular one-dimensional grids / M. J. Berger, R. J. Leveque, and L. G. Stern / 255 \\ Linear rational interpolation of continuous functions over an interval / Jean-Paul Berrut / 261 \\ A von Neumann reflection for the 2-D Burgers equation / M. Brio and J. K. Hunter / 265 \\ Slow evolution from the boundary: A new stabilizing constraint in ill-posed continuation problems / Alfred S. Carasso / 269 \\ A finite element method for the 2D drift-diffusion semiconductor model / Zhangxin Chen / 275 \\ Splitting functions and numerical analysis of WR-type methods for evolutionary and stationary problems / S. De Marchi, M. Vianello, and R. Zanovello / 281 \\ Error estimates for a quadrature rule for Cauchy principal value integrals / Kai Diethelm / 287 \\ A numerical radius approach to stable difference schemes for parabolic systems / Moshe Goldberg / 293 \\ An extension of the Olver-Sookne method for the solution of second-order linear difference equations / Takemitsu Hasegawa and Tatsuo Torii / 297 \\ The Faber polynomials for circular arcs / Matthew He / 301 \\ Finite element approximation for optimal control of electrically conducting fluid flows / L. S. Hou and S. S. Ravindran / 305 \\ ADI methods for heat equations with discontinuities along an arbitrary interface / Zhilin Li and Anita Mayo / 311 \\ Eigenvalue approximation of Fredholm integral operators / E. B. Lin / 317 \\ Spectral methods for singular perturbation problems / Wenbin Liu and Tao Tang / 323 \\ A quaternion-Jacobi method for symmetric matrices / Niloufer Mackey / 327 \\ On constructing Chebyshev series solutions of differential equations / Allan J. MacLeod / 333 \\ Multiquadric collocation methods in the numerical solution of Volterra integral and integro-differential equations / Athena Makroglou / 337 \\ Methods for solving large eigenvalue problems associated with configuration interaction electronic structure calculations / Kristyn J. Maschhoff / 343 \\ Computing limiting normals to real surfaces / Donal O'Shea and Les Wilson / 349 \\ Orthogonal spline collocation solution of nonlinear Schr{\"o}dinger equations / Mark P. Robinson / 355 \\ Who invented the computer? The debate from the viewpoint of computer architecture / Ra{\'u}l Rojas / 361 \\ Locking and boundary layer effects in the finite element approximation of the Reissner--Mindlin plate model / Christoph Schwab and Manil Suri / 367 \\ Efficient spectral Galerkin methods for some elliptic problems / Jie Shen / 373 \\ Periodic solutions of higher-order difference equations in two independent variables / Qin Sheng and Ravi P. Agarwal / 377 \\ Front tracking based on high-resolution wave propagation methods / Keh-Ming Shyue / 383 \\ Time-splitting methods for nonhomogeneous conservation laws / Tao Tang and Zhen-Huan Teng / 389 \\ Numerical aspects of uniform Airy-type asymptotic expansions / N. M. Temme / 395 \\ Local dynamics and bifurcation consistencies of continuous-time dynamical systems and their numerical discretizations / Xin Wang, Edward K. Blum, and Qingnan Li / 399 \\ Computing integrals of the complex error function / J. A. C. Weideman / 403 \\ Quadratures for improper integrals and their applications in integral equations / Yuesheng Xu and Yunhe Zhao / 409 \\ Spline harmonic analysis and wavelet bases / Valery A. Zheludev / 415 \\ \\ Part II. Minisymposium on Computational Number Theory Dedicated to the memory of Derrick Henry Lehmer \\ \\ Invited Papers \\ \\ Algorithms for quadratic orders / Ingrid Biehl and Johannes Buchmann / 425 \\ Analytic computations in number theory / Andrew M. Odlyzko / 451 \\ The number field sieve / Carl Pomerance / 465 \\ Factoring integers before computers / H. C. Williams and J. O. Shallit / 481 \\ \\ Contributed Papers \\ \\ Explicit bounds for primes in residue classes / Eric Bach and Jonathan Sorenson / 535 \\ Ramanujan and Euler's constant / Richard P. Brent / 541 \\ Congruential sieves on FPGA computers / Nathan D. Bronson and Duncan A. Buell / 547 \\ Lehmer pairs of zeros and the Riemann $\xi$-function / George Csordas, Wayne Smith, and Richard S. Varga / 553 \\ A record Aliquot sequence / Andrew W. P. Guy and Richard K. Guy / 557 \\ Implications of computational mathematics for the philosophy of mathematics / Andrew J. Lazarus / 561 \\ Square roots of products of algebraic numbers / Peter L. Montgomery / 567 \\ A locally parameterized version of Lehmer's problem / Gary A. Ray / 573 \\ A new method for finding amicable pairs / H. J. J. te Riele / 577 \\ Generalized Fermat numbers / Hans Riesel and Anders Bj{\"o}rn / 583 \\ Evaluation of $\zeta_K(2)$ for some totally real algebraic number fields K of degree 9 / Kisao Takeuchi / 589 \\ The period of the Bell exponential integers modulo a prime / Samuel S. Wagstaff, Jr. / 595 \\ Computing invariant polynomials of $p$-adic reflection groups / Changsheng Xu / 599 \\ Author Index / 603 \\ Subject Index / 619

entry:
@Proceedings{Gautschi:1994:MCH,
  editor =       "Walter Gautschi",
  booktitle =    "{Mathematics of computation, 1943--1993: a
                 half-century of computational mathematics: Mathematics
                 of Computation 50th Anniversary Symposium, August
                 9--13, 1993, Vancouver, British Columbia}",
  title =        "{Mathematics of computation, 1943--1993: a
                 half-century of computational mathematics: Mathematics
                 of Computation 50th Anniversary Symposium, August
                 9--13, 1993, Vancouver, British Columbia}",
  volume =       "48",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "xix + 643",
  year =         "1994",
  ISBN =         "0-8218-0291-7, 0-8218-0353-0 (pt. 1), 0-8218-0354-9
                 (pt. 2)",
  ISBN-13 =      "978-0-8218-0291-5, 978-0-8218-0353-0 (pt. 1),
                 978-0-8218-0354-7 (pt. 2)",
  ISSN =         "0160-7634",
  LCCN =         "QA1 .A56 v.48 1994; QA297.M385 1993",
  MRclass =      "00B25 (11-06 65-06)",
  MRnumber =     "95j:00014",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/g/gautschi-walter.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/h/higham-nicholas-john.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/l/lehmer-derrick-henry.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/o/olver-frank-w-j.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/v/varga-richard-steven.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/w/wigner-eugene.bib;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1940.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1950.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1960.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1970.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1980.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcomp1990.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib",
  note =         "See also SIAM Review, September 1995, {\bf 37}(3), p.
                 483.",
  series =       "Proceedings of Symposia in Applied Mathematics",
  acknowledgement = ack-nhfb,
  author-dates = "Frank William John Olver (15 December 1924--23 April
                 2013)",
  tableofcontents = "Preface / xi \\
                 Mathematics of Computation: A brief history / Eugene
                 Isaacson / xvii \\
                 \\
                 Part I. Symposium on Numerical Analysis \\
                 \\
                 Invited Papers \\
                 \\
                 On the development of multigrid methods and their
                 analysis / James H. Bramble / 5 \\
                 An introduction to inverse problems / Margaret Cheney /
                 21 \\
                 Algorithms for unconstrained optimization: A review of
                 recent developments / Donald Goldfarb / 33 \\
                 A survey of componentwise perturbation theory in
                 numerical linear algebra / Nicholas J. Higham / 49 \\
                 Numerical evaluation of special functions / D. W.
                 Lozier and F. W. J. Olver / 79 \\
                 A survey of numerical cubature over triangles / J. N.
                 Lyness and Ronald Cools / 127 \\
                 New trends in the use and analysis of integral
                 equations / J. C. Nedelec / 151 \\
                 Applications of multivariate splines / Larry L.
                 Schumaker / 177 \\
                 Initial value problems for ordinary differential
                 equations: Development of ideas, techniques, and
                 implementation / Hans J. Stetter / 205 \\
                 Multiresolution methods for partial differential
                 equations / Roger Temam / 225 \\
                 \\
                 Contributed Papers \\
                 \\
                 A comparison of techniques for solving ill-conditioned
                 problems arising from the immersed boundary method /
                 Loyce Adams and Zhiyun Yang / 243 \\
                 A mixed spectral-collocation and operator splitting
                 method for the Wigner-Poisson equation / Anton Arnold /
                 249 \\
                 Finite volume methods for irregular one-dimensional
                 grids / M. J. Berger, R. J. Leveque, and L. G. Stern /
                 255 \\
                 Linear rational interpolation of continuous functions
                 over an interval / Jean-Paul Berrut / 261 \\
                 A von Neumann reflection for the 2-D Burgers equation /
                 M. Brio and J. K. Hunter / 265 \\
                 Slow evolution from the boundary: A new stabilizing
                 constraint in ill-posed continuation problems / Alfred
                 S. Carasso / 269 \\
                 A finite element method for the 2D drift-diffusion
                 semiconductor model / Zhangxin Chen / 275 \\
                 Splitting functions and numerical analysis of WR-type
                 methods for evolutionary and stationary problems / S.
                 De Marchi, M. Vianello, and R. Zanovello / 281 \\
                 Error estimates for a quadrature rule for Cauchy
                 principal value integrals / Kai Diethelm / 287 \\
                 A numerical radius approach to stable difference
                 schemes for parabolic systems / Moshe Goldberg / 293
                 \\
                 An extension of the Olver-Sookne method for the
                 solution of second-order linear difference equations /
                 Takemitsu Hasegawa and Tatsuo Torii / 297 \\
                 The Faber polynomials for circular arcs / Matthew He /
                 301 \\
                 Finite element approximation for optimal control of
                 electrically conducting fluid flows / L. S. Hou and S.
                 S. Ravindran / 305 \\
                 ADI methods for heat equations with discontinuities
                 along an arbitrary interface / Zhilin Li and Anita Mayo
                 / 311 \\
                 Eigenvalue approximation of Fredholm integral operators
                 / E. B. Lin / 317 \\
                 Spectral methods for singular perturbation problems /
                 Wenbin Liu and Tao Tang / 323 \\
                 A quaternion-Jacobi method for symmetric matrices /
                 Niloufer Mackey / 327 \\
                 On constructing Chebyshev series solutions of
                 differential equations / Allan J. MacLeod / 333 \\
                 Multiquadric collocation methods in the numerical
                 solution of Volterra integral and integro-differential
                 equations / Athena Makroglou / 337 \\
                 Methods for solving large eigenvalue problems
                 associated with configuration interaction electronic
                 structure calculations / Kristyn J. Maschhoff / 343 \\
                 Computing limiting normals to real surfaces / Donal
                 O'Shea and Les Wilson / 349 \\
                 Orthogonal spline collocation solution of nonlinear
                 Schr{\"o}dinger equations / Mark P. Robinson / 355 \\
                 Who invented the computer? The debate from the
                 viewpoint of computer architecture / Ra{\'u}l Rojas /
                 361 \\
                 Locking and boundary layer effects in the finite
                 element approximation of the Reissner--Mindlin plate
                 model / Christoph Schwab and Manil Suri / 367 \\
                 Efficient spectral Galerkin methods for some elliptic
                 problems / Jie Shen / 373 \\
                 Periodic solutions of higher-order difference equations
                 in two independent variables / Qin Sheng and Ravi P.
                 Agarwal / 377 \\
                 Front tracking based on high-resolution wave
                 propagation methods / Keh-Ming Shyue / 383 \\
                 Time-splitting methods for nonhomogeneous conservation
                 laws / Tao Tang and Zhen-Huan Teng / 389 \\
                 Numerical aspects of uniform Airy-type asymptotic
                 expansions / N. M. Temme / 395 \\
                 Local dynamics and bifurcation consistencies of
                 continuous-time dynamical systems and their numerical
                 discretizations / Xin Wang, Edward K. Blum, and Qingnan
                 Li / 399 \\
                 Computing integrals of the complex error function / J.
                 A. C. Weideman / 403 \\
                 Quadratures for improper integrals and their
                 applications in integral equations / Yuesheng Xu and
                 Yunhe Zhao / 409 \\
                 Spline harmonic analysis and wavelet bases / Valery A.
                 Zheludev / 415 \\
                 \\
                 Part II. Minisymposium on Computational Number Theory
                 Dedicated to the memory of Derrick Henry Lehmer \\
                 \\
                 Invited Papers \\
                 \\
                 Algorithms for quadratic orders / Ingrid Biehl and
                 Johannes Buchmann / 425 \\
                 Analytic computations in number theory / Andrew M.
                 Odlyzko / 451 \\
                 The number field sieve / Carl Pomerance / 465 \\
                 Factoring integers before computers / H. C. Williams
                 and J. O. Shallit / 481 \\
                 \\
                 Contributed Papers \\
                 \\
                 Explicit bounds for primes in residue classes / Eric
                 Bach and Jonathan Sorenson / 535 \\
                 Ramanujan and Euler's constant / Richard P. Brent / 541
                 \\
                 Congruential sieves on FPGA computers / Nathan D.
                 Bronson and Duncan A. Buell / 547 \\
                 Lehmer pairs of zeros and the Riemann $\xi$-function /
                 George Csordas, Wayne Smith, and Richard S. Varga / 553
                 \\
                 A record Aliquot sequence / Andrew W. P. Guy and
                 Richard K. Guy / 557 \\
                 Implications of computational mathematics for the
                 philosophy of mathematics / Andrew J. Lazarus / 561 \\
                 Square roots of products of algebraic numbers / Peter
                 L. Montgomery / 567 \\
                 A locally parameterized version of Lehmer's problem /
                 Gary A. Ray / 573 \\
                 A new method for finding amicable pairs / H. J. J. te
                 Riele / 577 \\
                 Generalized Fermat numbers / Hans Riesel and Anders
                 Bj{\"o}rn / 583 \\
                 Evaluation of $\zeta_K(2)$ for some totally real
                 algebraic number fields K of degree 9 / Kisao Takeuchi
                 / 589 \\
                 The period of the Bell exponential integers modulo a
                 prime / Samuel S. Wagstaff, Jr. / 595 \\
                 Computing invariant polynomials of $p$-adic reflection
                 groups / Changsheng Xu / 599 \\
                 Author Index / 603 \\
                 Subject Index / 619",
}


bibtype: proceedings
filename: elefunt.bib
label: Mudge:1994:PTS
editor: Trevor N. Mudge and Bruce D. Shriver
publisher: pub-IEEE
address: pub-IEEE:adr
pages: various
year: 1994
ISBN: 0-8186-5050-8 (paper), 0-8186-5051-6 (microfiche) OR 0818650508 (paper), 0818650516 (microfiche)
bibdate: Mon Jan 13 10:02:18 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.13 10:02:18 ???
note: First of five volumes. IEEE Catalog No. 94TH0607-2.
acknowledgement: ack-nhfb
raweditor: Trevor N. Mudge and Bruce D. Shriver
rawnote: First of five volumes. IEEE Catalog No. 94TH0607-2.
booktitle:
Proceedings of the Twenty-Seventh Hawaii International Conference on System Sciences Vol. I: Architecture

title:
Proceedings of the Twenty-Seventh Hawaii International Conference on System Sciences Vol. I: Architecture

ISBN13:
978-0-8186-5050-5 (paper), 978-0-8186-5051-2 (microfiche) OR 9780818650505 (paper), 9780818650512 (microfiche)

rawbooktitle:
{Proceedings of the Twenty-Seventh Hawaii International Conference on System Sciences Vol. I: Architecture}

rawtitle:
{Proceedings of the Twenty-Seventh Hawaii International Conference on System Sciences Vol. I: Architecture}

entry:
@Proceedings{Mudge:1994:PTS,
  editor =       "Trevor N. Mudge and Bruce D. Shriver",
  booktitle =    "{Proceedings of the Twenty-Seventh Hawaii
                 International Conference on System Sciences Vol. I:
                 Architecture}",
  title =        "{Proceedings of the Twenty-Seventh Hawaii
                 International Conference on System Sciences Vol. I:
                 Architecture}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "various",
  year =         "1994",
  ISBN =         "0-8186-5050-8 (paper), 0-8186-5051-6 (microfiche)",
  ISBN-13 =      "978-0-8186-5050-5 (paper), 978-0-8186-5051-2
                 (microfiche)",
  LCCN =         "????",
  bibdate =      "Mon Jan 13 10:02:18 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "First of five volumes. IEEE Catalog No. 94TH0607-2.",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Zahar:1994:ACF
editor: R. V. M. (Ramsay Vincent Michael) Zahar
volume: 119
publisher: pub-BIRKHAUSER
address: pub-BIRKHAUSER:adr
pages: xlvi + 591
year: 1994
ISBN: 0-8176-3753-2 OR 0817637532
ISBN13: 978-0-8176-3753-8 OR 9780817637538
LCCN: QA221 .A634 1994
bibdate: Wed May 9 09:01:57 MDT 2007
bibtimestamp: 2007.05.09 09:01:57 MDT
series: International series of numerical mathematics
subject: Approximation theory; Congresses; Orthogonal polynomials; Numerical integration; Functions, Special
acknowledgement: ack-nhfb
raweditor: R. V. M. (Ramsay Vincent Michael) Zahar
booktitle:
Approximation and computation: a festschrift in honor of Walter Gautschi: proceedings of the Purdue conference, December 2--5, 1993

title:
Approximation and computation: a festschrift in honor of Walter Gautschi: proceedings of the Purdue conference, December 2--5, 1993

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib; https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager

rawbooktitle:
{Approximation and computation: a festschrift in honor of Walter Gautschi: proceedings of the Purdue conference, December 2--5, 1993}

rawtitle:
{Approximation and computation: a festschrift in honor of Walter Gautschi: proceedings of the Purdue conference, December 2--5, 1993}

entry:
@Proceedings{Zahar:1994:ACF,
  editor =       "R. V. M. (Ramsay Vincent Michael) Zahar",
  booktitle =    "{Approximation and computation: a festschrift in honor
                 of Walter Gautschi: proceedings of the Purdue
                 conference, December 2--5, 1993}",
  title =        "{Approximation and computation: a festschrift in honor
                 of Walter Gautschi: proceedings of the Purdue
                 conference, December 2--5, 1993}",
  volume =       "119",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "xlvi + 591",
  year =         "1994",
  ISBN =         "0-8176-3753-2",
  ISBN-13 =      "978-0-8176-3753-8",
  LCCN =         "QA221 .A634 1994",
  bibdate =      "Wed May 9 09:01:57 MDT 2007",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/r/rice-john-r.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "International series of numerical mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Approximation theory; Congresses; Orthogonal
                 polynomials; Numerical integration; Functions,
                 Special",
}


bibtype: proceedings
filename: elefunt.bib
label: Knowles:1995:PSC
editor: Simon Knowles and William H. McAllister
booktitle: Proceedings of the 12th Symposium on Computer Arithmetic, July 19--21, 1995, Bath, England
title: Proceedings of the 12th Symposium on Computer Arithmetic, July 19--21, 1995, Bath, England
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xvi + 252
year: 1995
LCCN: QA 76.9 C62 S95 1995
bibdate: Sun Mar 29 08:48:20 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.03.29 08:48:20 ???
acknowledgement: ack-nhfb
rawbooktitle: Proceedings of the 12th Symposium on Computer Arithmetic, July 19--21, 1995, Bath, England
raweditor: Simon Knowles and William H. McAllister
rawtitle: Proceedings of the 12th Symposium on Computer Arithmetic, July 19--21, 1995, Bath, England
ISBN:
0-8186-7089-4 (paperback), 0-8186-7089-4 (case), 0-8186-7149-1 (microfiche), 0-8186-7089-4 (softbound), 0-7803-2949-X (casebound) OR 0818670894 (paperback), 0818670894 (case), 0818671491 (microfiche), 0818670894 (softbound), 078032949X (casebound)

ISBN13:
978-0-8186-7089-3 (paperback), 978-0-8186-7089-3 (case), 978-0-8186-7149-4 (microfiche), 978-0-8186-7089-3 (softbound), 978-0-7803-2949-2 (casebound) OR 9780818670893 (paperback), 9780818670893 (case), 9780818671494 (microfiche), 9780818670893 (softbound), 9780780329492 (casebound)

entry:
@Proceedings{Knowles:1995:PSC,
  editor =       "Simon Knowles and William H. McAllister",
  booktitle =    "Proceedings of the 12th Symposium on Computer
                 Arithmetic, July 19--21, 1995, Bath, England",
  title =        "Proceedings of the 12th Symposium on Computer
                 Arithmetic, July 19--21, 1995, Bath, England",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xvi + 252",
  year =         "1995",
  ISBN =         "0-8186-7089-4 (paperback), 0-8186-7089-4 (case),
                 0-8186-7149-1 (microfiche), 0-8186-7089-4 (softbound),
                 0-7803-2949-X (casebound)",
  ISBN-13 =      "978-0-8186-7089-3 (paperback), 978-0-8186-7089-3
                 (case), 978-0-8186-7149-4 (microfiche),
                 978-0-8186-7089-3 (softbound), 978-0-7803-2949-2
                 (casebound)",
  LCCN =         "QA 76.9 C62 S95 1995",
  bibdate =      "Sun Mar 29 08:48:20 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Singh:1995:CRT
editor: Avtar Singh
publisher: pub-IEEE
address: pub-IEEE:adr
pages: various
year: 1995
ISBN: 0-8186-7370-2 OR 0818673702
ISBN13: 978-0-8186-7370-2 OR 9780818673702
LCCN: TK7801 .A83 1995
bibdate: Sun Mar 29 08:51:26 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.03.29 08:51:26 ???
note: Two volumes.
acknowledgement: ack-nhfb
raweditor: Avtar Singh
rawnote: Two volumes.
booktitle:
Conference record of the Twenty-Ninth Asilomar Conference on Signals, Systems & Computers: October 30--November 1, 1995 Pacific Grove, California

title:
Conference record of the Twenty-Ninth Asilomar Conference on Signals, Systems & Computers: October 30--November 1, 1995 Pacific Grove, California

rawbooktitle:
Conference record of the Twenty-Ninth Asilomar Conference on Signals, Systems \& Computers: October 30--November 1, 1995 Pacific Grove, California

rawtitle:
Conference record of the Twenty-Ninth Asilomar Conference on Signals, Systems \& Computers: October 30--November 1, 1995 Pacific Grove, California

entry:
@Proceedings{Singh:1995:CRT,
  editor =       "Avtar Singh",
  booktitle =    "Conference record of the Twenty-Ninth Asilomar
                 Conference on Signals, Systems \& Computers: October
                 30--November 1, 1995 Pacific Grove, California",
  title =        "Conference record of the Twenty-Ninth Asilomar
                 Conference on Signals, Systems \& Computers: October
                 30--November 1, 1995 Pacific Grove, California",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "various",
  year =         "1995",
  ISBN =         "0-8186-7370-2",
  ISBN-13 =      "978-0-8186-7370-2",
  LCCN =         "TK7801 .A83 1995",
  bibdate =      "Sun Mar 29 08:51:26 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: LakshmanYN:1996:IPI
editor: Lakshman Y.N.
publisher: pub-ACM
address: pub-ACM:adr
pages: xvii + 313
year: 1996
ISBN: 0-89791-796-0 OR 0897917960
ISBN13: 978-0-89791-796-4 OR 9780897917964
LCCN: QA 76.95 I59 1996
bibdate: Thu Mar 12 08:00:14 1998
bibtimestamp: 1998.03.12 08:00:14 ???
acknowledgement: ack-nhfb
raweditor: {Lakshman Y.N.}
booktitle:
ISSAC '96: Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation, July 24--26, 1996, Zurich, Switzerland

title:
ISSAC '96: Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation, July 24--26, 1996, Zurich, Switzerland

rawbooktitle:
{ISSAC '96: Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation, July 24--26, 1996, Zurich, Switzerland}

rawtitle:
{ISSAC '96: Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation, July 24--26, 1996, Zurich, Switzerland}

entry:
@Proceedings{LakshmanYN:1996:IPI,
  editor =       "{Lakshman Y.N.}",
  booktitle =    "{ISSAC '96: Proceedings of the 1996 International
                 Symposium on Symbolic and Algebraic Computation, July
                 24--26, 1996, Zurich, Switzerland}",
  title =        "{ISSAC '96: Proceedings of the 1996 International
                 Symposium on Symbolic and Algebraic Computation, July
                 24--26, 1996, Zurich, Switzerland}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "xvii + 313",
  year =         "1996",
  ISBN =         "0-89791-796-0",
  ISBN-13 =      "978-0-89791-796-4",
  LCCN =         "QA 76.95 I59 1996",
  bibdate =      "Thu Mar 12 08:00:14 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  sponsor =      "ACM; Special Interest Group in Symbolic and Algebraic
                 Manipulation (SIGSAM). ACM; Special Interest Group on
                 Numerical Mathematics (SIGNUM).",
}


bibtype: book
filename: elefunt.bib
label: Berggren:1997:PSB
editor: Lennart Berggren and Jonathan M. Borwein and Peter B. Borwein
booktitle: Pi, a source book
title: Pi, a source book
publisher: pub-SV
address: pub-SV:adr
pages: xix + 716
year: 1997
DOI: https://doi.org/10.1007/978-1-4757-2736-4
LCCN: QA484 .P5 1997
bibdate: Fri Sep 2 17:41:50 MDT 2022
bibtimestamp: 2022.09.02 17:41:50 MDT
subject: Pi; Pi (Le nombre); Pi.; Pi (le nombre)
acknowledgement: ack-nhfb
rawbooktitle: Pi, a source book
raweditor: Lennart Berggren and Jonathan M. Borwein and Peter B. Borwein
rawtitle: Pi, a source book
ORCID: Borwein, Jonathan/0000-0002-1263-0646
ISBN:
0-387-94924-0, 1-4757-2736-4 (e-book), 1-4757-2738-0 (print), 3-540-94924-0 OR 0387949240, 1475727364 (ebook), 1475727380 (print), 3540949240

ISBN13:
978-0-387-94924-6, 978-1-4757-2736-4 (e-book), 978-1-4757-2738-8 (print), 978-3-540-94924-4 OR 9780387949246, 9781475727364 (ebook), 9781475727388 (print), 9783540949244

bibsource:
fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib; z3950.loc.gov:7090/Voyager

abstract:
The aim of this book is to provide a complete history of pi from the dawn of mathematical time to the present. The story of pi reflects the most seminal, the most serious and sometimes the silliest aspects of mathematics, and a surprising amount of the most important mathematics and mathematicians have contributed to its unfolding. Pi is one of the few concepts in mathematics whose mention evokes a response of recognition and interest in those not concerned professionally with the subject. Yet, despite this, no source book on pi has been published. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet still accessible, mathematics. Mathematicians and historians of mathematics will find this book indispensable. Teachers at every level from the seventh grade onward will find here ample resources for anything from special topic courses to individual talks and special student projects. The literature on pi included in this source book falls into three classes: first a selection of the mathematical literature of four millennia, second a variety of historical studies or writings on the cultural meaning and significance of the number, and third, a number of treatments on pi that are fanciful, satirical and/or whimsical.

TOC:
Preface / v Acknowledgments / ix Introduction / xvii 1. The Rhind Mathematical Papyrus-Problem 50 ($approx $ 1650 B.C.) / A problem dealing with the area of a round field of given diameter / 1 2. Engels. Quadrature of the Circle in Ancient Egypt (1977) / A conjectural explanation of how the mathematicians of ancient Egypt approximated the area of a circle / 3 3. Archimedes. Measurement of a Circle ($approx $ 250 BC) / The seminal work in which Archimedes presents the first true algorithm for $pi $ / 7 4. Phillips. Archimedes the Numerical Analyst (1981) / A summary of Archimedes' work on the computation of $pi $ using modern notation / 15 5. Lam and Ang. Circle Measurements in Ancient China (1986) / This paper discusses and contains a translation of Liu Hui's (3rd century) method for evaluating $pi $ and also examines values for $pi $ given by Zu Chongzhi (429--500) / 20 6. The Banu Musa: The Measurement of Plane and Solid Figures ($approx $ 850) / This extract gives an explicit statement and proof that the ratio of the circumference to the diameter is constant / 36 7. Madhava. The Power Series for Arctan and Pi ($approx $ 1400) / These theorems by a fifteenth century Indian mathematician give Gregory's series for arctan with remainder terms and Leibniz's series for $pi $ / 45 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van Ceulen (1938) / Correspondence about van Ceulen's tombstone in reference to it containing some digits of $pi $ / 51 9. Viete. Variorum de Rebus Mathematicis Reponsorum Liber VII (1593) / Two excerpts. One containing the first infinite expression of $pi $, obtained by relating the area of a regular $2n$-gon to that of a regular $n$-gon / 53 10. Wallis. Computation of $pi $ by Successive Interpolations (1655) / How Wallis derived the infinite product for $pi $ that bears his name / 68 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt including Prop. 189, 191 and an alternate form of the result that gives Wm. Brounker's continued fraction expression for $4/pi $ / 78 12. Huygens. De Circuli Magnitudine Inventa (1724) / Huygens's proof of W. Snell's discovery of improvements in Archimedes' method of estimating the lengths of circular arcs / 81 13. Gregory. Correspondence with John Collins (1671) / A letter to Collins in which he gives his series for arctangent, carried to the ninth power. / 87 14. Roy. The Discovery of the Series Formula for $pi $ by Leibniz, Gregory, and Nilakantha (1990) / A discussion of the discovery of the series $pi /4 = 1 - 1/3 + 1/5, cdots $ / 92 15. Jones. The First Use of $pi $ for the Circle Ratio (1706) / An excerpt from Jones' book, the Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics, London, 1706 / 108 16. Newton. Of the Method of Fluxions and Infinite Series (1737) / An excerpt giving Newton's calculation of $pi $ to 16 decimal places / 110 17. Euler. Chapter 10 of Introduction to Analysis of the Infinite (On the Use of the Discovered Fractions to Sum Infinite Series) (1748) / This includes many of Euler's infinite series for $pi $ and powers of $pi $ / 112 18. Lambert. Memoire Sur Quelques Proprietes Remarquables Des Quantites Transcendentes Circulaires et Logarithmiques (1761) / An excerpt from Lambert's original proof of the irrationality of $pi $ / 129 19. Lambert. Irrationality of $pi $ (1969) / A translation and Struik's discussion of Lambert's proof of the irrationality of $pi $ / 141 20. Shanks. Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals (1853) / Pages from Shank's report of his monumental hand calculation of $pi $ / 147 21. Hermite. Sur La Fonction Exponentielle (1873) / The first proof of the transcendence of $e$ / 162 22. Lindemann. Ueber die Zahl $pi $ (1882) / The first proof of the transcendence of $pi $ / 194 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die Ludolphsche Zahl'' (1885) / Weierstrass' proof of the transcendence of $pi $ / 207 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und $pi $ (1893) / Hilbert's short and elegant simplification of the transcendence proofs for $e$ and $pi $ / 226 25. Goodwin. Quadrature of the Circle (1894) / The dubious origin of the attempted legislation of the value of $pi $ in Indiana / 230 26. Edington. House Bill No. 246, Indiana State Legislature, 1897 (1935) / A summary of the action taken by the Indiana State Legislature to fix the value of $pi $ (including a copy of the actual bill that was proposed) / 231 27. Singmaster. The Legal Values of Pi (1985) / A history of the attempt by Indiana to legislate the value of $pi $ / 236 28. Ramanujan. Squaring the Circle (1913) / A geometric approximation to $pi $ / 240 29. Ramanujan. Modular Equations and Approximations to $pi $ (1914) / Ramanujan's seminal paper on $pi $ that includes a number of striking series and algebraic approximations / 241 30. Watson. The Marquis and the Land Agent: A Tale of the Eighteenth Century (1933) / A Presidential address to the Mathematical Association in which the author gives an account of ``some of the elementary work on arcs and ellipses and other curves which led up to the idea of inverting an elliptic integral, and so laying the foundations of elliptic functions and doubly periodic functions generally.'' / 258 31. Ballantine. The Best (?) Formula for Computing $pi $ to a Thousand Places (1939) / An early attempt to orchestrate the calculation of $pi $ more cleverly / 271 32. Birch. An Algorithm for Construction of Arctangent Relations (1946) / The object of this note is to express $pi / 4 $ as a sum of arctan relations in powers of 10 / 274 33. Niven. A Simple Proof that $pi $ Is Irrational (1947) / A very concise proof of the irrationality of $pi $ / 276 34. Reitwiesner. An ENIAC Determination of $pi $ and $e$ to 2000 Decimal Places (1950) / One of the first computer-based computations / 277 35. Schepler. The Chronology of Pi (1950) / A fairly reliable outline of the history of $pi $ from 3000 BC to 1949 / 282 36. Mahler. On the Approximation of $pi $ (1953) / ``The aim of this paper is to determine an explicit lower bound free of unknown constants for the distance of $pi $ from a given rational or algebraic number'' / 306 37. Wrench, Jr. The Evolution of Extended Decimal Approximations to $pi $ (1960) / A history of the calculation of the digits of $pi $ to 1960 38. Shanks and Wrench, Jr. Calculation of $pi $ to 100,000 Decimals (1962) / A landmark computation of $pi $ to more than 100,000 places / 326 39. Sweeny. On the Computation of Euler's Constant (1963) / The computation of Euler's constant to 3566 decimal places / 350 40. Baker. Approximations to the Logarithms of Certain Rational Numbers (1964) / The main purpose of this deep and fundamental paper is to ``deduce results concerning the accuracy with which the natural logarithms of certain rational numbers may be approximated by rational numbers, or, more generally, by algebraic numbers of bounded degree.'' / 359 41. Adams. Asymptotic Diophantine Approximations to $E$ (1966) / An asymptotic estimate for the rational approximation to $e$ which disproves the conjecture that $e$ behaves like almost all numbers in this respect / 368 42. Mahler. Applications of Some Formulae by Hermite to the Approximations of Exponentials of Logarithms (1967) / An important extension of Hilbert's approach to the study of transcendence / 372 43. Eves. In Mathematical Circles; A Selection of Mathematical Stories and Anecdotes (excerpt) (1969) / A collection of mathematical stories and anecdotes about $pi $ / 400 44. Eves. Mathematical Circles Revisited; A Second Collection of Mathematical Stories and Anecdotes (excerpt) (1971) / A further collection of mathematical stories and anecdotes about $pi $ / 402 45. Todd. The Lemniscate Constants (1975) / A unifying account of some of the methods used for computing the lemniscate constants / 412 46. Salamin. Computation of r Using Arithmetic-Geometric Mean (1976) / The first quadratically converging algorithm for $pi $ based on Gauss's AGM and on Legendre's relation for elliptic integrals / 418 47. Brent. Fast Multiple-Precision Evaluation of Elementary Functions (1976) / ``This paper contains the `Gauss-Legendre' method and some different algorithms for log and exp (using Landen transformations).'' / 424 48. Beukers. A Note on the Irrationality of $zeta (2)$ and $zetq (3)$ (1979) / A short and elegant recasting of Apery's proof of the irrationality of $zeta (3)$ (and $zeta (2)$) / 434 49. van der Poorten. A Proof that Euler Missed ldots Apery's Proof of the Irrationality of $zeta (3)$ (1979) / An illuminating account of Apery's astonishing proof of the irrationality of $zeta (3)$ / 439 50. Brent and McMillan. Some New Algorithms for High-Precision Computation of Euler's Constant (1980) / Several new algorithms for high precision calculation of Euler's constant, including one which was used to compute 30,100 decimal places / 448 51. Apostol. A Proof that Euler Missed: Evaluating $zeta (2)$ the Easy Way (1983) / This note shows that one of the double integrals considered by Beukers ([48] in the table of contents) can be used to establish directly that $zeta (2) = pi / 6$ / 456 52. O'Shaughnessy. Putting God Back in Math (1983) / An article about the Institute of Pi Research, an organization that ``pokes fun at creationists by pointing out that even the Bible makes mistakes.'' / 458 53. Stern. A Remarkable Approximation to $pi $ (1985) / Justification of the value of $pi $ in the Bible through numerological interpretations / 460 54. Newman and Shanks. On a Sequence Arising in Series for $pi $ (1984) / More connections between $pi $ and modular equations / 462 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984) / An extensive study of the complex analytic properties of the AGM / 481 56. Borwein and Borwein. The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions (1984) / The relationship between the AGM iteration and fast computation of elementary functions (one of the by-products is an algorithm for $pi $) / 537 57. Newman. A Simplified Version of the Fast Algorithms of Brent and Salamin (1984) / Elementary algorithms for evaluating $e^x$ and $pi $ using the Gauss AGM without explicit elliptic function theory / 553 58. Wagon. Is Pi Normal? (1985) / A discussion of the conjecture that $pi $ has randomly distributed digits / 557 59. Keith. Circle Digits: A Self-Referential Story (1986) / A mnemonic for the first 402 decimal places of $pi $ / 560 60. Bailey. The Computation of $pi $ to 29,360,000 Decimal Digits Using Borweins' Quartically Convergent Algorithm (1988) / The algorithms used, both for $pi $ and for performing the required multiple-precision arithmetic / 562 61. Kanada. Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of 1 Calculation (1988) / Details of the computation and statistical tests of the first 200 million digits of $pi $ / 576 62. Borwein and Borwein. Ramanujan and Pi (1988) / This article documents Ramanujan's life, his ingenious approach to calculating $pi $, and how his approach is now incorporated into modern computer algorithms / 588 63. Chudnovsky and Chudnovsky. Approximations and Complex Multiplication According to Ramanujan (1988) / This excerpt describes ``Ramanujan's original quadratic period--quasiperiod relations for elliptic curves with complex multiplication and their applications to representations of fractions of $pi $ and other logarithms in terms of rapidly convergent nearly integral (hypergeometric) series.'' / 596 64. Borwein, Borwein and Bailey. Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi (1989) / An exposition of the computation of $pi $ using mathematics rooted in Ramanujan's work / 623 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers, and Asymptotic Expansions (1989) / An explanation as to why the slowly convergent Gregory series for $pi $, truncated at 500,000 terms, gives $pi $ to 40 places with only the 6th, 17th, 18th, and 29th places being incorrect / 642 66. Beukers, Bezivin, and Robba. An Alternative Proof of the Lindemann--Weierstrass Theorem (1990) / The Lindemann--Weierstrass theorem as a by-product of a criterion for rationality of solutions of differential equations / 649 67. Webster. The Tail of Pi (1991) / Various anecdotes about $pi $ from the 14th annual IMO Lecture to the Royal Society / 654 68. Eco. An excerpt from Foucault's Pendulum (1993) / ``The unnumbered perfection of the circle itself.'' / 658 69. Keith. Pi Mnemonics and the Art of Constrained Writing (1996) / A mnemonic for $pi $ based on Edgar Allen Poe's poem ``The Raven.'' / 659 70. Bailey, Borwein, and Plouffe. On the Rapid Computation of Various Polylogarithmic Constants (1996) / A fast method for computing individual digits of $pi $ in base 2 / 663 Appendix I --- On the Early History of Pi / 677 Appendix II --- A Computational Chronology of Pi / 683 Appendix III --- Selected Formulae for Pi / 686 Bibliography / 690 Credits / 697 Index / 701

rawabstract:
The aim of this book is to provide a complete history of pi from the dawn of mathematical time to the present. The story of pi reflects the most seminal, the most serious and sometimes the silliest aspects of mathematics, and a surprising amount of the most important mathematics and mathematicians have contributed to its unfolding. Pi is one of the few concepts in mathematics whose mention evokes a response of recognition and interest in those not concerned professionally with the subject. Yet, despite this, no source book on pi has been published. One of the beauties of the literature on pi is that it allows for the inclusion of very modern, yet still accessible, mathematics. Mathematicians and historians of mathematics will find this book indispensable. Teachers at every level from the seventh grade onward will find here ample resources for anything from special topic courses to individual talks and special student projects. The literature on pi included in this source book falls into three classes: first a selection of the mathematical literature of four millennia, second a variety of historical studies or writings on the cultural meaning and significance of the number, and third, a number of treatments on pi that are fanciful, satirical and/or whimsical.

rawTOC:
Preface / v \\ \\ Acknowledgments / ix \\ \\ Introduction / xvii \\ \\ 1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$ 1650 B.C.) / A problem dealing with the area of a round field of given diameter / 1 \\ \\ 2. Engels. Quadrature of the Circle in Ancient Egypt (1977) / A conjectural explanation of how the mathematicians of ancient Egypt approximated the area of a circle / 3 \\ \\ 3. Archimedes. Measurement of a Circle ($\approx$ 250 BC) / The seminal work in which Archimedes presents the first true algorithm for $\pi$ / 7 \\ \\ 4. Phillips. Archimedes the Numerical Analyst (1981) / A summary of Archimedes' work on the computation of $\pi$ using modern notation / 15 \\ \\ 5. Lam and Ang. Circle Measurements in Ancient China (1986) / This paper discusses and contains a translation of Liu Hui's (3rd century) method for evaluating $\pi$ and also examines values for $\pi$ given by Zu Chongzhi (429--500) / 20 \\ \\ 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane and Solid Figures ($\approx$ 850) / This extract gives an explicit statement and proof that the ratio of the circumference to the diameter is constant / 36 \\ \\ 7. M{\=a}dhava. The Power Series for Arctan and Pi ($\approx$ 1400) / These theorems by a fifteenth century Indian mathematician give Gregory's series for arctan with remainder terms and Leibniz's series for $\pi$ / 45 \\ \\ 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van Ceulen (1938) / Correspondence about van Ceulen's tombstone in reference to it containing some digits of $\pi$ / 51 \\ \\ 9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum Liber VII (1593) / Two excerpts. One containing the first infinite expression of $\pi$, obtained by relating the area of a regular $2n$-gon to that of a regular $n$-gon / 53 \\ \\ 10. Wallis. Computation of $\pi$ by Successive Interpolations (1655) / How Wallis derived the infinite product for $\pi$ that bears his name / 68 \\ \\ 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt including Prop. 189, 191 and an alternate form of the result that gives Wm. Brounker's continued fraction expression for $4/\pi$ / 78 \\ \\ 12. Huygens. De Circuli Magnitudine Inventa (1724) / Huygens's proof of W. Snell's discovery of improvements in Archimedes' method of estimating the lengths of circular arcs / 81 \\ \\ 13. Gregory. Correspondence with John Collins (1671) / A letter to Collins in which he gives his series for arctangent, carried to the ninth power. / 87 \\ \\ 14. Roy. The Discovery of the Series Formula for $\pi$ by Leibniz, Gregory, and Nilakantha (1990) / A discussion of the discovery of the series $\pi/4 = 1 - 1/3 + 1/5, \cdots{}$ / 92 \\ \\ 15. Jones. The First Use of $\pi$ for the Circle Ratio (1706) / An excerpt from Jones' book, the Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics, London, 1706 / 108 \\ \\ 16. Newton. Of the Method of Fluxions and Infinite Series (1737) / An excerpt giving Newton's calculation of $\pi$ to 16 decimal places / 110 \\ \\ 17. Euler. Chapter 10 of Introduction to Analysis of the Infinite (On the Use of the Discovered Fractions to Sum Infinite Series) (1748) / This includes many of Euler's infinite series for $\pi$ and powers of $\pi$ / 112 \\ \\ 18. Lambert. M{\'e}moire Sur Quelques Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s Transcendentes Circulaires et Logarithmiques (1761) / An excerpt from Lambert's original proof of the irrationality of $\pi$ / 129 \\ \\ 19. Lambert. Irrationality of $\pi$ (1969) / A translation and Struik's discussion of Lambert's proof of the irrationality of $\pi$ / 141 \\ \\ 20. Shanks. Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals (1853) / Pages from Shank's report of his monumental hand calculation of $\pi$ / 147 \\ \\ 21. Hermite. Sur La Fonction Exponentielle (1873) / The first proof of the transcendence of $e$ / 162 \\ \\ 22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first proof of the transcendence of $\pi$ / 194 \\ \\ 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die Ludolphsche Zahl'' (1885) / Weierstrass' proof of the transcendence of $\pi$ / 207 \\ \\ 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und $\pi$ (1893) / Hilbert's short and elegant simplification of the transcendence proofs for $e$ and $\pi$ / 226 \\ \\ 25. Goodwin. Quadrature of the Circle (1894) / The dubious origin of the attempted legislation of the value of $\pi$ in Indiana / 230 \\ \\ 26. Edington. House Bill No. 246, Indiana State Legislature, 1897 (1935) / A summary of the action taken by the Indiana State Legislature to fix the value of $\pi$ (including a copy of the actual bill that was proposed) / 231 \\ \\ 27. Singmaster. The Legal Values of Pi (1985) / A history of the attempt by Indiana to legislate the value of $\pi$ / 236 \\ \\ 28. Ramanujan. Squaring the Circle (1913) / A geometric approximation to $\pi$ / 240 \\ \\ 29. Ramanujan. Modular Equations and Approximations to $\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that includes a number of striking series and algebraic approximations / 241 \\ \\ 30. Watson. The Marquis and the Land Agent: A Tale of the Eighteenth Century (1933) / A Presidential address to the Mathematical Association in which the author gives an account of ``some of the elementary work on arcs and ellipses and other curves which led up to the idea of inverting an elliptic integral, and so laying the foundations of elliptic functions and doubly periodic functions generally.'' / 258 \\ \\ 31. Ballantine. The Best (?) Formula for Computing $\pi$ to a Thousand Places (1939) / An early attempt to orchestrate the calculation of $\pi$ more cleverly / 271 \\ \\ 32. Birch. An Algorithm for Construction of Arctangent Relations (1946) / The object of this note is to express $\pi / 4 $ as a sum of arctan relations in powers of 10 / 274 \\ \\ 33. Niven. A Simple Proof that $\pi$ Is Irrational (1947) / A very concise proof of the irrationality of $\pi$ / 276 \\ \\ 34. Reitwiesner. An ENIAC Determination of $\pi$ and $e$ to 2000 Decimal Places (1950) / One of the first computer-based computations / 277 \\ \\ 35. Schepler. The Chronology of Pi (1950) / A fairly reliable outline of the history of $\pi$ from 3000 BC to 1949 / 282 \\ \\ 36. Mahler. On the Approximation of $\pi$ (1953) / ``The aim of this paper is to determine an explicit lower bound free of unknown constants for the distance of $\pi$ from a given rational or algebraic number'' / 306 \\ \\ 37. Wrench, Jr. The Evolution of Extended Decimal Approximations to $\pi$ (1960) / A history of the calculation of the digits of $\pi$ to 1960 \\ \\ 38. Shanks and Wrench, Jr. Calculation of $\pi$ to 100,000 Decimals (1962) / A landmark computation of $\pi$ to more than 100,000 places / 326 \\ \\ 39. Sweeny. On the Computation of Euler's Constant (1963) / The computation of Euler's constant to 3566 decimal places / 350 \\ \\ 40. Baker. Approximations to the Logarithms of Certain Rational Numbers (1964) / The main purpose of this deep and fundamental paper is to ``deduce results concerning the accuracy with which the natural logarithms of certain rational numbers may be approximated by rational numbers, or, more generally, by algebraic numbers of bounded degree.'' / 359 \\ \\ 41. Adams. Asymptotic Diophantine Approximations to $E$ (1966) / An asymptotic estimate for the rational approximation to $e$ which disproves the conjecture that $e$ behaves like almost all numbers in this respect / 368 \\ \\ 42. Mahler. Applications of Some Formulae by Hermite to the Approximations of Exponentials of Logarithms (1967) / An important extension of Hilbert's approach to the study of transcendence / 372 \\ \\ 43. Eves. In Mathematical Circles; A Selection of Mathematical Stories and Anecdotes (excerpt) (1969) / A collection of mathematical stories and anecdotes about $\pi$ / 400 \\ \\ 44. Eves. Mathematical Circles Revisited; A Second Collection of Mathematical Stories and Anecdotes (excerpt) (1971) / A further collection of mathematical stories and anecdotes about $\pi$ / 402 \\ \\ 45. Todd. The Lemniscate Constants (1975) / A unifying account of some of the methods used for computing the lemniscate constants / 412 \\ \\ 46. Salamin. Computation of r Using Arithmetic-Geometric Mean (1976) / The first quadratically converging algorithm for $\pi$ based on Gauss's AGM and on Legendre's relation for elliptic integrals / 418 \\ \\ 47. Brent. Fast Multiple-Precision Evaluation of Elementary Functions (1976) / ``This paper contains the `Gauss-Legendre' method and some different algorithms for log and exp (using Landen transformations).'' / 424 \\ \\ 48. Beukers. A Note on the Irrationality of $\zeta(2)$ and $\zetq(3)$ (1979) / A short and elegant recasting of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$ (and $\zeta(2)$) / 434 \\ \\ 49. van der Poorten. A Proof that Euler Missed \ldots{} Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$ (1979) / An illuminating account of Ap{\'e}ry's astonishing proof of the irrationality of $\zeta(3)$ / 439 \\ \\ 50. Brent and McMillan. Some New Algorithms for High-Precision Computation of Euler's Constant (1980) / Several new algorithms for high precision calculation of Euler's constant, including one which was used to compute 30,100 decimal places / 448 \\ \\ 51. Apostol. A Proof that Euler Missed: Evaluating $\zeta(2)$ the Easy Way (1983) / This note shows that one of the double integrals considered by Beukers ([48] in the table of contents) can be used to establish directly that $\zeta(2) = \pi / 6$ / 456 \\ \\ 52. O'Shaughnessy. Putting God Back in Math (1983) / An article about the Institute of Pi Research, an organization that ``pokes fun at creationists by pointing out that even the Bible makes mistakes.'' / 458 \\ \\ 53. Stern. A Remarkable Approximation to $\pi$ (1985) / Justification of the value of $\pi$ in the Bible through numerological interpretations / 460 \\ \\ 54. Newman and Shanks. On a Sequence Arising in Series for $\pi$ (1984) / More connections between $\pi$ and modular equations / 462 \\ \\ 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984) / An extensive study of the complex analytic properties of the AGM / 481 \\ \\ 56. Borwein and Borwein. The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions (1984) / The relationship between the AGM iteration and fast computation of elementary functions (one of the by-products is an algorithm for $\pi$) / 537 \\ \\ 57. Newman. A Simplified Version of the Fast Algorithms of Brent and Salamin (1984) / Elementary algorithms for evaluating $e^x$ and $\pi$ using the Gauss AGM without explicit elliptic function theory / 553 \\ \\ 58. Wagon. Is Pi Normal? (1985) / A discussion of the conjecture that $\pi$ has randomly distributed digits / 557 \\ \\ 59. Keith. Circle Digits: A Self-Referential Story (1986) / A mnemonic for the first 402 decimal places of $\pi$ / 560 \\ \\ 60. Bailey. The Computation of $\pi$ to 29,360,000 Decimal Digits Using Borweins' Quartically Convergent Algorithm (1988) / The algorithms used, both for $\pi$ and for performing the required multiple-precision arithmetic / 562 \\ \\ 61. Kanada. Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of 1 Calculation (1988) / Details of the computation and statistical tests of the first 200 million digits of $\pi$ / 576 \\ \\ 62. Borwein and Borwein. Ramanujan and Pi (1988) / This article documents Ramanujan's life, his ingenious approach to calculating $\pi$, and how his approach is now incorporated into modern computer algorithms / 588 \\ \\ 63. Chudnovsky and Chudnovsky. Approximations and Complex Multiplication According to Ramanujan (1988) / This excerpt describes ``Ramanujan's original quadratic period--quasiperiod relations for elliptic curves with complex multiplication and their applications to representations of fractions of $\pi$ and other logarithms in terms of rapidly convergent nearly integral (hypergeometric) series.'' / 596 \\ \\ 64. Borwein, Borwein and Bailey. Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi (1989) / An exposition of the computation of $\pi$ using mathematics rooted in Ramanujan's work / 623 \\ \\ 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers, and Asymptotic Expansions (1989) / An explanation as to why the slowly convergent Gregory series for $\pi$, truncated at 500,000 terms, gives $\pi$ to 40 places with only the 6th, 17th, 18th, and 29th places being incorrect / 642 \\ \\ 66. Beukers, B{\'e}zivin, and Robba. An Alternative Proof of the Lindemann--Weierstrass Theorem (1990) / The Lindemann--Weierstrass theorem as a by-product of a criterion for rationality of solutions of differential equations / 649 \\ \\ 67. Webster. The Tail of Pi (1991) / Various anecdotes about $\pi$ from the 14th annual IMO Lecture to the Royal Society / 654 \\ \\ 68. Eco. An excerpt from Foucault's Pendulum (1993) / ``The unnumbered perfection of the circle itself.'' / 658 \\ \\ 69. Keith. Pi Mnemonics and the Art of Constrained Writing (1996) / A mnemonic for $\pi$ based on Edgar Allen Poe's poem ``The Raven.'' / 659 \\ \\ 70. Bailey, Borwein, and Plouffe. On the Rapid Computation of Various Polylogarithmic Constants (1996) / A fast method for computing individual digits of $\pi$ in base 2 / 663 \\ Appendix I --- On the Early History of Pi / 677 \\ \\ Appendix II --- A Computational Chronology of Pi / 683 \\ \\ Appendix III --- Selected Formulae for Pi / 686 \\ \\ Bibliography / 690 \\ \\ Credits / 697 \\ \\ Index / 701

entry:
@Book{Berggren:1997:PSB,
  editor =       "Lennart Berggren and Jonathan M. Borwein and Peter B.
                 Borwein",
  booktitle =    "Pi, a source book",
  title =        "Pi, a source book",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xix + 716",
  year =         "1997",
  DOI =          "https://doi.org/10.1007/978-1-4757-2736-4",
  ISBN =         "0-387-94924-0, 1-4757-2736-4 (e-book), 1-4757-2738-0
                 (print), 3-540-94924-0",
  ISBN-13 =      "978-0-387-94924-6, 978-1-4757-2736-4 (e-book),
                 978-1-4757-2738-8 (print), 978-3-540-94924-4",
  LCCN =         "QA484 .P5 1997",
  bibdate =      "Fri Sep 2 17:41:50 MDT 2022",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib;
                 z3950.loc.gov:7090/Voyager",
  abstract =     "The aim of this book is to provide a complete history
                 of pi from the dawn of mathematical time to the
                 present. The story of pi reflects the most seminal, the
                 most serious and sometimes the silliest aspects of
                 mathematics, and a surprising amount of the most
                 important mathematics and mathematicians have
                 contributed to its unfolding. Pi is one of the few
                 concepts in mathematics whose mention evokes a response
                 of recognition and interest in those not concerned
                 professionally with the subject. Yet, despite this, no
                 source book on pi has been published. One of the
                 beauties of the literature on pi is that it allows for
                 the inclusion of very modern, yet still accessible,
                 mathematics. Mathematicians and historians of
                 mathematics will find this book indispensable. Teachers
                 at every level from the seventh grade onward will find
                 here ample resources for anything from special topic
                 courses to individual talks and special student
                 projects. The literature on pi included in this source
                 book falls into three classes: first a selection of the
                 mathematical literature of four millennia, second a
                 variety of historical studies or writings on the
                 cultural meaning and significance of the number, and
                 third, a number of treatments on pi that are fanciful,
                 satirical and/or whimsical.",
  acknowledgement = ack-nhfb,
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject =      "Pi; Pi (Le nombre); Pi.; Pi (le nombre)",
  tableofcontents = "Preface / v \\
                 \\
                 Acknowledgments / ix \\
                 \\
                 Introduction / xvii \\
                 \\
                 1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$
                 1650 B.C.) / A problem dealing with the area of a round
                 field of given diameter / 1 \\
                 \\
                 2. Engels. Quadrature of the Circle in Ancient Egypt
                 (1977) / A conjectural explanation of how the
                 mathematicians of ancient Egypt approximated the area
                 of a circle / 3 \\
                 \\
                 3. Archimedes. Measurement of a Circle ($\approx$ 250
                 BC) / The seminal work in which Archimedes presents the
                 first true algorithm for $\pi$ / 7 \\
                 \\
                 4. Phillips. Archimedes the Numerical Analyst (1981) /
                 A summary of Archimedes' work on the computation of
                 $\pi$ using modern notation / 15 \\
                 \\
                 5. Lam and Ang. Circle Measurements in Ancient China
                 (1986) / This paper discusses and contains a
                 translation of Liu Hui's (3rd century) method for
                 evaluating $\pi$ and also examines values for $\pi$
                 given by Zu Chongzhi (429--500) / 20 \\
                 \\
                 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
                 and Solid Figures ($\approx$ 850) / This extract gives
                 an explicit statement and proof that the ratio of the
                 circumference to the diameter is constant / 36 \\
                 \\
                 7. M{\=a}dhava. The Power Series for Arctan and Pi
                 ($\approx$ 1400) / These theorems by a fifteenth
                 century Indian mathematician give Gregory's series for
                 arctan with remainder terms and Leibniz's series for
                 $\pi$ / 45 \\
                 \\
                 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van
                 Ceulen (1938) / Correspondence about van Ceulen's
                 tombstone in reference to it containing some digits of
                 $\pi$ / 51 \\
                 \\
                 9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum
                 Liber VII (1593) / Two excerpts. One containing the
                 first infinite expression of $\pi$, obtained by
                 relating the area of a regular $2n$-gon to that of a
                 regular $n$-gon / 53 \\
                 \\
                 10. Wallis. Computation of $\pi$ by Successive
                 Interpolations (1655) / How Wallis derived the infinite
                 product for $\pi$ that bears his name / 68 \\
                 \\
                 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt
                 including Prop. 189, 191 and an alternate form of the
                 result that gives Wm. Brounker's continued fraction
                 expression for $4/\pi$ / 78 \\
                 \\
                 12. Huygens. De Circuli Magnitudine Inventa (1724) /
                 Huygens's proof of W. Snell's discovery of improvements
                 in Archimedes' method of estimating the lengths of
                 circular arcs / 81 \\
                 \\
                 13. Gregory. Correspondence with John Collins (1671) /
                 A letter to Collins in which he gives his series for
                 arctangent, carried to the ninth power. / 87 \\
                 \\
                 14. Roy. The Discovery of the Series Formula for $\pi$
                 by Leibniz, Gregory, and Nilakantha (1990) / A
                 discussion of the discovery of the series $\pi/4 = 1 -
                 1/3 + 1/5, \cdots{}$ / 92 \\
                 \\
                 15. Jones. The First Use of $\pi$ for the Circle Ratio
                 (1706) / An excerpt from Jones' book, the Synopsis
                 Palmariorum Matheseos: or, a New Introduction to the
                 Mathematics, London, 1706 / 108 \\
                 \\
                 16. Newton. Of the Method of Fluxions and Infinite
                 Series (1737) / An excerpt giving Newton's calculation
                 of $\pi$ to 16 decimal places / 110 \\
                 \\
                 17. Euler. Chapter 10 of Introduction to Analysis of
                 the Infinite (On the Use of the Discovered Fractions to
                 Sum Infinite Series) (1748) / This includes many of
                 Euler's infinite series for $\pi$ and powers of $\pi$ /
                 112 \\
                 \\
                 18. Lambert. M{\'e}moire Sur Quelques
                 Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
                 Transcendentes Circulaires et Logarithmiques (1761) /
                 An excerpt from Lambert's original proof of the
                 irrationality of $\pi$ / 129 \\
                 \\
                 19. Lambert. Irrationality of $\pi$ (1969) / A
                 translation and Struik's discussion of Lambert's proof
                 of the irrationality of $\pi$ / 141 \\
                 \\
                 20. Shanks. Contributions to Mathematics Comprising
                 Chiefly of the Rectification of the Circle to 607
                 Places of Decimals (1853) / Pages from Shank's report
                 of his monumental hand calculation of $\pi$ / 147 \\
                 \\
                 21. Hermite. Sur La Fonction Exponentielle (1873) / The
                 first proof of the transcendence of $e$ / 162 \\
                 \\
                 22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first
                 proof of the transcendence of $\pi$ / 194 \\
                 \\
                 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die
                 Ludolphsche Zahl'' (1885) / Weierstrass' proof of the
                 transcendence of $\pi$ / 207 \\
                 \\
                 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und
                 $\pi$ (1893) / Hilbert's short and elegant
                 simplification of the transcendence proofs for $e$ and
                 $\pi$ / 226 \\
                 \\
                 25. Goodwin. Quadrature of the Circle (1894) / The
                 dubious origin of the attempted legislation of the
                 value of $\pi$ in Indiana / 230 \\
                 \\
                 26. Edington. House Bill No. 246, Indiana State
                 Legislature, 1897 (1935) / A summary of the action
                 taken by the Indiana State Legislature to fix the value
                 of $\pi$ (including a copy of the actual bill that was
                 proposed) / 231 \\
                 \\
                 27. Singmaster. The Legal Values of Pi (1985) / A
                 history of the attempt by Indiana to legislate the
                 value of $\pi$ / 236 \\
                 \\
                 28. Ramanujan. Squaring the Circle (1913) / A geometric
                 approximation to $\pi$ / 240 \\
                 \\
                 29. Ramanujan. Modular Equations and Approximations to
                 $\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that
                 includes a number of striking series and algebraic
                 approximations / 241 \\
                 \\
                 30. Watson. The Marquis and the Land Agent: A Tale of
                 the Eighteenth Century (1933) / A Presidential address
                 to the Mathematical Association in which the author
                 gives an account of ``some of the elementary work on
                 arcs and ellipses and other curves which led up to the
                 idea of inverting an elliptic integral, and so laying
                 the foundations of elliptic functions and doubly
                 periodic functions generally.'' / 258 \\
                 \\
                 31. Ballantine. The Best (?) Formula for Computing
                 $\pi$ to a Thousand Places (1939) / An early attempt to
                 orchestrate the calculation of $\pi$ more cleverly /
                 271 \\
                 \\
                 32. Birch. An Algorithm for Construction of Arctangent
                 Relations (1946) / The object of this note is to
                 express $\pi / 4 $ as a sum of arctan relations in
                 powers of 10 / 274 \\
                 \\
                 33. Niven. A Simple Proof that $\pi$ Is Irrational
                 (1947) / A very concise proof of the irrationality of
                 $\pi$ / 276 \\
                 \\
                 34. Reitwiesner. An ENIAC Determination of $\pi$ and
                 $e$ to 2000 Decimal Places (1950) / One of the first
                 computer-based computations / 277 \\
                 \\
                 35. Schepler. The Chronology of Pi (1950) / A fairly
                 reliable outline of the history of $\pi$ from 3000 BC
                 to 1949 / 282 \\
                 \\
                 36. Mahler. On the Approximation of $\pi$ (1953) /
                 ``The aim of this paper is to determine an explicit
                 lower bound free of unknown constants for the distance
                 of $\pi$ from a given rational or algebraic number'' /
                 306 \\
                 \\
                 37. Wrench, Jr. The Evolution of Extended Decimal
                 Approximations to $\pi$ (1960) / A history of the
                 calculation of the digits of $\pi$ to 1960 \\
                 \\
                 38. Shanks and Wrench, Jr. Calculation of $\pi$ to
                 100,000 Decimals (1962) / A landmark computation of
                 $\pi$ to more than 100,000 places / 326 \\
                 \\
                 39. Sweeny. On the Computation of Euler's Constant
                 (1963) / The computation of Euler's constant to 3566
                 decimal places / 350 \\
                 \\
                 40. Baker. Approximations to the Logarithms of Certain
                 Rational Numbers (1964) / The main purpose of this deep
                 and fundamental paper is to ``deduce results concerning
                 the accuracy with which the natural logarithms of
                 certain rational numbers may be approximated by
                 rational numbers, or, more generally, by algebraic
                 numbers of bounded degree.'' / 359 \\
                 \\
                 41. Adams. Asymptotic Diophantine Approximations to $E$
                 (1966) / An asymptotic estimate for the rational
                 approximation to $e$ which disproves the conjecture
                 that $e$ behaves like almost all numbers in this
                 respect / 368 \\
                 \\
                 42. Mahler. Applications of Some Formulae by Hermite to
                 the Approximations of Exponentials of Logarithms (1967)
                 / An important extension of Hilbert's approach to the
                 study of transcendence / 372 \\
                 \\
                 43. Eves. In Mathematical Circles; A Selection of
                 Mathematical Stories and Anecdotes (excerpt) (1969) / A
                 collection of mathematical stories and anecdotes about
                 $\pi$ / 400 \\
                 \\
                 44. Eves. Mathematical Circles Revisited; A Second
                 Collection of Mathematical Stories and Anecdotes
                 (excerpt) (1971) / A further collection of mathematical
                 stories and anecdotes about $\pi$ / 402 \\
                 \\
                 45. Todd. The Lemniscate Constants (1975) / A unifying
                 account of some of the methods used for computing the
                 lemniscate constants / 412 \\
                 \\
                 46. Salamin. Computation of r Using
                 Arithmetic-Geometric Mean (1976) / The first
                 quadratically converging algorithm for $\pi$ based on
                 Gauss's AGM and on Legendre's relation for elliptic
                 integrals / 418 \\
                 \\
                 47. Brent. Fast Multiple-Precision Evaluation of
                 Elementary Functions (1976) / ``This paper contains the
                 `Gauss-Legendre' method and some different algorithms
                 for log and exp (using Landen transformations).'' / 424
                 \\
                 \\
                 48. Beukers. A Note on the Irrationality of $\zeta(2)$
                 and $\zetq(3)$ (1979) / A short and elegant recasting
                 of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$
                 (and $\zeta(2)$) / 434 \\
                 \\
                 49. van der Poorten. A Proof that Euler Missed \ldots{}
                 Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$
                 (1979) / An illuminating account of Ap{\'e}ry's
                 astonishing proof of the irrationality of $\zeta(3)$ /
                 439 \\
                 \\
                 50. Brent and McMillan. Some New Algorithms for
                 High-Precision Computation of Euler's Constant (1980) /
                 Several new algorithms for high precision calculation
                 of Euler's constant, including one which was used to
                 compute 30,100 decimal places / 448 \\
                 \\
                 51. Apostol. A Proof that Euler Missed: Evaluating
                 $\zeta(2)$ the Easy Way (1983) / This note shows that
                 one of the double integrals considered by Beukers ([48]
                 in the table of contents) can be used to establish
                 directly that $\zeta(2) = \pi / 6$ / 456 \\
                 \\
                 52. O'Shaughnessy. Putting God Back in Math (1983) / An
                 article about the Institute of Pi Research, an
                 organization that ``pokes fun at creationists by
                 pointing out that even the Bible makes mistakes.'' /
                 458 \\
                 \\
                 53. Stern. A Remarkable Approximation to $\pi$ (1985) /
                 Justification of the value of $\pi$ in the Bible
                 through numerological interpretations / 460 \\
                 \\
                 54. Newman and Shanks. On a Sequence Arising in Series
                 for $\pi$ (1984) / More connections between $\pi$ and
                 modular equations / 462 \\
                 \\
                 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984)
                 / An extensive study of the complex analytic properties
                 of the AGM / 481 \\
                 \\
                 56. Borwein and Borwein. The Arithmetic-Geometric Mean
                 and Fast Computation of Elementary Functions (1984) /
                 The relationship between the AGM iteration and fast
                 computation of elementary functions (one of the
                 by-products is an algorithm for $\pi$) / 537 \\
                 \\
                 57. Newman. A Simplified Version of the Fast Algorithms
                 of Brent and Salamin (1984) / Elementary algorithms for
                 evaluating $e^x$ and $\pi$ using the Gauss AGM without
                 explicit elliptic function theory / 553 \\
                 \\
                 58. Wagon. Is Pi Normal? (1985) / A discussion of the
                 conjecture that $\pi$ has randomly distributed digits /
                 557 \\
                 \\
                 59. Keith. Circle Digits: A Self-Referential Story
                 (1986) / A mnemonic for the first 402 decimal places of
                 $\pi$ / 560 \\
                 \\
                 60. Bailey. The Computation of $\pi$ to 29,360,000
                 Decimal Digits Using Borweins' Quartically Convergent
                 Algorithm (1988) / The algorithms used, both for $\pi$
                 and for performing the required multiple-precision
                 arithmetic / 562 \\
                 \\
                 61. Kanada. Vectorization of Multiple-Precision
                 Arithmetic Program and 201,326,000 Decimal Digits of 1
                 Calculation (1988) / Details of the computation and
                 statistical tests of the first 200 million digits of
                 $\pi$ / 576 \\
                 \\
                 62. Borwein and Borwein. Ramanujan and Pi (1988) / This
                 article documents Ramanujan's life, his ingenious
                 approach to calculating $\pi$, and how his approach is
                 now incorporated into modern computer algorithms / 588
                 \\
                 \\
                 63. Chudnovsky and Chudnovsky. Approximations and
                 Complex Multiplication According to Ramanujan (1988) /
                 This excerpt describes ``Ramanujan's original quadratic
                 period--quasiperiod relations for elliptic curves with
                 complex multiplication and their applications to
                 representations of fractions of $\pi$ and other
                 logarithms in terms of rapidly convergent nearly
                 integral (hypergeometric) series.'' / 596 \\
                 \\
                 64. Borwein, Borwein and Bailey. Ramanujan, Modular
                 Equations, and Approximations to Pi or How to Compute
                 One Billion Digits of Pi (1989) / An exposition of the
                 computation of $\pi$ using mathematics rooted in
                 Ramanujan's work / 623 \\
                 \\
                 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers,
                 and Asymptotic Expansions (1989) / An explanation as to
                 why the slowly convergent Gregory series for $\pi$,
                 truncated at 500,000 terms, gives $\pi$ to 40 places
                 with only the 6th, 17th, 18th, and 29th places being
                 incorrect / 642 \\
                 \\
                 66. Beukers, B{\'e}zivin, and Robba. An Alternative
                 Proof of the Lindemann--Weierstrass Theorem (1990) /
                 The Lindemann--Weierstrass theorem as a by-product of a
                 criterion for rationality of solutions of differential
                 equations / 649 \\
                 \\
                 67. Webster. The Tail of Pi (1991) / Various anecdotes
                 about $\pi$ from the 14th annual IMO Lecture to the
                 Royal Society / 654 \\
                 \\
                 68. Eco. An excerpt from Foucault's Pendulum (1993) /
                 ``The unnumbered perfection of the circle itself.'' /
                 658 \\
                 \\
                 69. Keith. Pi Mnemonics and the Art of Constrained
                 Writing (1996) / A mnemonic for $\pi$ based on Edgar
                 Allen Poe's poem ``The Raven.'' / 659 \\
                 \\
                 70. Bailey, Borwein, and Plouffe. On the Rapid
                 Computation of Various Polylogarithmic Constants (1996)
                 / A fast method for computing individual digits of
                 $\pi$ in base 2 / 663 \\
                 Appendix I --- On the Early History of Pi / 677 \\
                 \\
                 Appendix II --- A Computational Chronology of Pi / 683
                 \\
                 \\
                 Appendix III --- Selected Formulae for Pi / 686 \\
                 \\
                 Bibliography / 690 \\
                 \\
                 Credits / 697 \\
                 \\
                 Index / 701",
}


bibtype: proceedings
filename: elefunt.bib
label: Boisvert:1997:QNS
editor: Ronald F. Boisvert
publisher: pub-CHAPMAN-HALL
address: pub-CHAPMAN-HALL:adr
pages: vii + 384
year: 1997
ISBN: 0-412-80530-8 OR 0412805308
ISBN13: 978-0-412-80530-1 OR 9780412805301
LCCN: QA297 .I35 1996
bibdate: Fri Jul 09 05:58:30 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 05:58:30 ???
acknowledgement: ack-nhfb
raweditor: Ronald F. Boisvert
booktitle:
Quality of Numerical Software: Assessment and Enhancement. Proceedings of the IFIP TC2/WG2.5 Working Conference on the Quality of Numerical Software, Assessment and Enhancement, Oxford, United Kingdom, 8--12 July 1996

title:
Quality of Numerical Software: Assessment and Enhancement. Proceedings of the IFIP TC2/WG2.5 Working Conference on the Quality of Numerical Software, Assessment and Enhancement, Oxford, United Kingdom, 8--12 July 1996

rawbooktitle:
Quality of Numerical Software: Assessment and Enhancement. {Proceedings of the IFIP TC2/WG2.5 Working Conference on the Quality of Numerical Software, Assessment and Enhancement, Oxford, United Kingdom, 8--12 July 1996}

rawtitle:
Quality of Numerical Software: Assessment and Enhancement. {Proceedings of the IFIP TC2/WG2.5 Working Conference on the Quality of Numerical Software, Assessment and Enhancement, Oxford, United Kingdom, 8--12 July 1996}

entry:
@Proceedings{Boisvert:1997:QNS,
  editor =       "Ronald F. Boisvert",
  booktitle =    "Quality of Numerical Software: Assessment and
                 Enhancement. {Proceedings of the IFIP TC2/WG2.5 Working
                 Conference on the Quality of Numerical Software,
                 Assessment and Enhancement, Oxford, United Kingdom,
                 8--12 July 1996}",
  title =        "Quality of Numerical Software: Assessment and
                 Enhancement. {Proceedings of the IFIP TC2/WG2.5 Working
                 Conference on the Quality of Numerical Software,
                 Assessment and Enhancement, Oxford, United Kingdom,
                 8--12 July 1996}",
  publisher =    pub-CHAPMAN-HALL,
  address =      pub-CHAPMAN-HALL:adr,
  pages =        "vii + 384",
  year =         "1997",
  ISBN =         "0-412-80530-8",
  ISBN-13 =      "978-0-412-80530-1",
  LCCN =         "QA297 .I35 1996",
  bibdate =      "Fri Jul 09 05:58:30 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Lang:1997:ISC
editor: Tomas Lang and Jean-Michel Muller and Naofumi Takagi
booktitle: 13th IEEE Symposium on Computer Arithmetic: proceedings, July 6--9, 1997, Asilomar, California, USA
title: 13th IEEE Symposium on Computer Arithmetic: proceedings, July 6--9, 1997, Asilomar, California, USA
volume: 13
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xiii + 291
year: 1997
ISBN: 0-8186-7846-1, 0-8186-7847-X, 0-8186-7848-8 OR 0818678461, 081867847X, 0818678488
ISSN: 1063-6889 OR 10636889
LCCN: QA76.9.C62 S95 1997
bibdate: Fri Mar 27 09:56:17 MST 1998
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1998.03.27 09:56:17 MST
note: IEEE Computer Society order number PR07846. IEEE Order Plan catalog number 97CB36091.
series: Symposium on Computer Arithmetic
acknowledgement: ack-nhfb
raweditor: Tomas Lang and Jean-Michel Muller and Naofumi Takagi
rawnote: IEEE Computer Society order number PR07846. IEEE Order Plan catalog number 97CB36091.
ISBN13:
978-0-8186-7846-2, 978-0-8186-7847-9, 978-0-8186-7848-6 OR 9780818678462, 9780818678479, 9780818678486

rawbooktitle:
13th {IEEE} Symposium on Computer Arithmetic: proceedings, July 6--9, 1997, Asilomar, California, {USA}

rawtitle:
13th {IEEE} Symposium on Computer Arithmetic: proceedings, July 6--9, 1997, Asilomar, California, {USA}

entry:
@Proceedings{Lang:1997:ISC,
  editor =       "Tomas Lang and Jean-Michel Muller and Naofumi Takagi",
  booktitle =    "13th {IEEE} Symposium on Computer Arithmetic:
                 proceedings, July 6--9, 1997, Asilomar, California,
                 {USA}",
  title =        "13th {IEEE} Symposium on Computer Arithmetic:
                 proceedings, July 6--9, 1997, Asilomar, California,
                 {USA}",
  volume =       "13",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 291",
  year =         "1997",
  ISBN =         "0-8186-7846-1, 0-8186-7847-X, 0-8186-7848-8",
  ISBN-13 =      "978-0-8186-7846-2, 978-0-8186-7847-9,
                 978-0-8186-7848-6",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 1997",
  bibdate =      "Fri Mar 27 09:56:17 MST 1998",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "IEEE Computer Society order number PR07846. IEEE Order
                 Plan catalog number 97CB36091.",
  series =       "Symposium on Computer Arithmetic",
  acknowledgement = ack-nhfb,
  sponsor =      "IEEE.",
}


bibtype: proceedings
filename: elefunt.bib
label: Thiele:1997:IIC
editor: Lothar Thiele and others
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xii + 540
year: 1997
ISBN: 0-8186-7959-X, 0-8186-7960-3, 0-8186-7958-1 OR 081867959X, 0818679603, 0818679581
LCCN: TK7874.6 .I57 1997eb; TK7874.6 .I57 1997; TK7874.6 .I58 1997
bibdate: Sun Mar 4 21:13:29 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; melvyl.cdlib.org:210/CDL90
bibtimestamp: 2007.03.04 21:13:29 MST
remark: IEEE Computer Society Press order number PR07958. IEEE catalog number 97TB100177
acknowledgement: ack-nhfb
raweditor: Lothar Thiele and others
booktitle:
IEEE International Conference on Application-Specific Systems, Architectures and Processors: proceedings, July 14--16, 1997, Zurich, Switzerland

title:
IEEE International Conference on Application-Specific Systems, Architectures and Processors: proceedings, July 14--16, 1997, Zurich, Switzerland

ISBN13:
978-0-8186-7959-9, 978-0-8186-7960-5, 978-0-8186-7958-2 OR 9780818679599, 9780818679605, 9780818679582

subject:
Array processors; Congresses; Signal processing; Digital techniques; Application-specific integrated circuits

rawbooktitle:
{IEEE International Conference on Application-Specific Systems, Architectures and Processors: proceedings, July 14--16, 1997, Z{\"u}rich, Switzerland}

rawtitle:
{IEEE International Conference on Application-Specific Systems, Architectures and Processors: proceedings, July 14--16, 1997, Z{\"u}rich, Switzerland}

entry:
@Proceedings{Thiele:1997:IIC,
  editor =       "Lothar Thiele and others",
  booktitle =    "{IEEE International Conference on Application-Specific
                 Systems, Architectures and Processors: proceedings,
                 July 14--16, 1997, Z{\"u}rich, Switzerland}",
  title =        "{IEEE International Conference on Application-Specific
                 Systems, Architectures and Processors: proceedings,
                 July 14--16, 1997, Z{\"u}rich, Switzerland}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 540",
  year =         "1997",
  ISBN =         "0-8186-7959-X, 0-8186-7960-3, 0-8186-7958-1",
  ISBN-13 =      "978-0-8186-7959-9, 978-0-8186-7960-5,
                 978-0-8186-7958-2",
  LCCN =         "TK7874.6 .I57 1997eb; TK7874.6 .I57 1997; TK7874.6
                 .I58 1997",
  bibdate =      "Sun Mar 4 21:13:29 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Application-Specific
                 Systems, Architectures, and Processors (11th: 1997:
                 Z{\"u}rich, Switzerland)",
  remark =       "IEEE Computer Society Press order number PR07958. IEEE
                 catalog number 97TB100177",
  subject =      "Array processors; Congresses; Signal processing;
                 Digital techniques; Application-specific integrated
                 circuits",
}


bibtype: proceedings
filename: elefunt.bib
label: Rusev:1998:TMS
editor: Petur Rusev and I. Dimovski and Virginia Kiryakova
booktitle: Transformation methods and special functions, Varna '96: second international workshop: proceedings
title: Transformation methods and special functions, Varna '96: second international workshop: proceedings
publisher: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
address: Sofia, Bulgaria
pages: vi + 613
year: 1998
ISBN: 954-8986-05-1 OR 9548986051
ISBN13: 978-954-8986-05-2 OR 9789548986052
bibdate: Thu Dec 1 11:08:47 MST 2011
bibsource: fsz3950.oclc.org:210/WorldCat https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 11:08:47 MST
subject: Transformations (Mathematics); Differential equations; Integral equations
acknowledgement: ack-nhfb
raweditor: Petur Rusev and I. Dimovski and Virginia Kiryakova
remark:
``This second edition of the Workshops 'TM and SF' has been devoted to the 100th anniversary of the eminent Bulgarian mathematician Nikola Obreshkoff (1896-1963)''--T.p. verso.

TOC:
On a generalization of the theorem on two constants / G. Adamczyk On a construction of the solutions of some elliptic equations with generalized coefficients / A. Antonevich Some non-metrizable spaces of harmonic functions / G. Balikov, I. Dimitrov Duhamel-type representations of the solutions of non-local boundary value problems for the fractional diffusion-wave equation / E. Bazhlekova Pointwise convergence for Hankel transform / J. Betancour, L. Rodriguez-Mesa On fractional order continuity, integrability and derivability of real functions / B. Bonilla, J. Trujillo, M. Rivero On the root functions of a nonlocal Sturm--Liouville problem / N. Bozhinov Mellin transform theory and the role of its differential and integral operators / P. Butzer, S. Jansche Exact solution of some systems of non-selfadjoint partial differential equations / D. Callebaut Numerical computation of Lame functions / H.-J. Dobner, S. Ritter Some extremal problems for $p$-valent alpha-convex functions / J. Dziok Extension of a result on the convolution product of distributions / B. Fisher, A. Kilicman Simple algorithms for approximations of generalized elliptic-type integrals / M. A. El-Gabali, Shyam L. Kalla On Zernicke polynomials / H.-J. Glaeske Tomato salad problem in spherical stereology / R. Gorenflo On existence of solutions of ordinary differential equations of fractional order / N. Hayek ldots [et al.] Tauberian theorem for distributions / J. Jelinek Radiation field integrals and their evaluation techniques / Shyam L. Kalla, H. G. Khajah On the product of distributions / A. Kaminski On isotopies of algebras and triple systems / N. Kamiya Univalence criteria connected with arithmetic and geometric means: I / S. Kanas, A. Lecko Global and causal solutions of fractional linear differential equations / S. Kempfle, H. Beyer On the applications of Mikusinski's operational calculus to the controllability of dynamical systems / W. Kierat, K. Skornik Application of fractional calculus to solve Abel--Volterra nonlinear and linear integral equations / A. Kilbas, M. Saigo Note on linear operators and fractional calculus operators in the univalent function theory / Yong Chan Kim Application of the generalized Mikhaylov criterion / S. Krasinska On some classes of holomorphic functions in the half-plane / A. Lazinska Expansions in series of Legendre functions / E. R. Love, M. Hunter Intersections with Gronwall methods / W. Luh Applications of fractional calculus in mechanics / F. Mainardi Automorphisms in the commutant of the integration operator in spaces of Lebesgue integrable functions / S. Mincheva Applications of fractional calculus operators to univalent functions / S. Owa Application of orthogonal polynomials to solution of fractional integral equations / I. Podlubny Remark on Watson transform / A. Prudnikov, U. Skornik Generalized operators of fractional integro-differentiation in meaning of M. Saigo and their applications / O. Repin Fractional integrals and wavelet transformations / B. Rubin, D. Ryabogin, E. Shamir More generalization of fractional calculus / M. Saigo, N. Maeda On certain subclasses of analytic functions involving a linear operator / H. Saitoh On some sequence spaces / E. Savas Class of integro-differential equations via fractional calculus / N. Shawagfeh On some extreme points of the unit ball / J. Sokol, W. Szumny Hyper-Bessel operators, differential equations, functions, and integral transforms of 4th order / S. Spirova Some operational techniques in the theory of special functions / H. M. Srivastava Convolution in the theory of univalent functions / J. Stankiewicz Some extensions of the Rolle and Gauss--Lucas theorems / T. Stoyanov On infinitely divisible probability distributions and integral equations / K. Takano Generating functions related to pairs of inverse functions / R. Tremblay, B. J. Fugere Integral transforms connected with the group representations / N. Tretyakova On some integral operators in the clas of functions with negative coefficients / L. Trojnar-Spelina On a new generalized Taylor's formula / J. Trujillo, M. Rivero, B. Bonilla Some properties of the finite Laplace transform / M. Valbuena, L. Galue, I. Ali Airy integral transform and the Paley--Wiener theorem / Vu Kim Tuan On starlike functions related with hyperbolic regions / A. Wisniowska Editorial: Nikola Obreshkoff (1896--1963): biographical data and 100 selected papers of Acad. N. Obreshkoff Obreshkoff's generalization of Descartes rule / P. Rusev Obrechkoff's generalization of the Laplace and Meijer transformations: origins and recent developments / I. Dimovski, V. Kiryakova Longstanding conjecture failed? / V. Kiryakova Afterthoughts on interpretation of fractional derivatives and integrals / R. Gorenflo Modelling viscous damped oscillations by fractional differential operators / S. Kempfle Considerations on fractional calculus: interpretations and applications / F. Mainardi Introduction to the fractional calculus and some applications / K. Oldham

rawbooktitle:
{Transformation methods and special functions, Varna '96: second international workshop: proceedings}

rawtitle:
{Transformation methods and special functions, Varna '96: second international workshop: proceedings}

rawTOC:
On a generalization of the theorem on two constants / G. Adamczyk \\ On a construction of the solutions of some elliptic equations with generalized coefficients / A. Antonevich \\ Some non-metrizable spaces of harmonic functions / G. Balikov, I. Dimitrov \\ Duhamel-type representations of the solutions of non-local boundary value problems for the fractional diffusion-wave equation / E. Bazhlekova \\ Pointwise convergence for Hankel transform / J. Betancour, L. Rodr\'iguez-Mesa \\ On fractional order continuity, integrability and derivability of real functions / B. Bonilla, J. Trujillo, M. Rivero \\ On the root functions of a nonlocal Sturm--Liouville problem / N. Bozhinov \\ Mellin transform theory and the role of its differential and integral operators / P. Butzer, S. Jansche \\ Exact solution of some systems of non-selfadjoint partial differential equations / D. Callebaut \\ Numerical computation of Lame functions / H.-J. Dobner, S. Ritter \\ Some extremal problems for $p$-valent alpha-convex functions / J. Dziok \\ Extension of a result on the convolution product of distributions / B. Fisher, A. Kilicman \\ Simple algorithms for approximations of generalized elliptic-type integrals / M. A. El-Gabali, Shyam L. Kalla \\ On Zernicke polynomials / H.-J. Glaeske \\ Tomato salad problem in spherical stereology / R. Gorenflo \\ On existence of solutions of ordinary differential equations of fractional order / N. Hayek \ldots{} [et al.] \\ Tauberian theorem for distributions / J. Jel\'inek \\ Radiation field integrals and their evaluation techniques / Shyam L. Kalla, H. G. Khajah \\ On the product of distributions / A. Kami\'nski \\ On isotopies of algebras and triple systems / N. Kamiya \\ Univalence criteria connected with arithmetic and geometric means: I / S. Kanas, A. Lecko \\ Global and causal solutions of fractional linear differential equations / S. Kempfle, H. Beyer \\ On the applications of Mikusinski's operational calculus to the controllability of dynamical systems / W. Kierat, K. Sk\'ornik \\ Application of fractional calculus to solve Abel--Volterra nonlinear and linear integral equations / A. Kilbas, M. Saigo \\ Note on linear operators and fractional calculus operators in the univalent function theory / Yong Chan Kim \\ Application of the generalized Mikhaylov criterion / S. Krasinska \\ On some classes of holomorphic functions in the half-plane / A. Lazi{\'n}ska \\ Expansions in series of Legendre functions / E. R. Love, M. Hunter \\ Intersections with Gronwall methods / W. Luh \\ Applications of fractional calculus in mechanics / F. Mainardi \\ Automorphisms in the commutant of the integration operator in spaces of Lebesgue integrable functions / S. Mincheva \\ Applications of fractional calculus operators to univalent functions / S. Owa \\ Application of orthogonal polynomials to solution of fractional integral equations / I. Podlubny \\ Remark on Watson transform / A. Prudnikov, U. Sk\'ornik \\ Generalized operators of fractional integro-differentiation in meaning of M. Saigo and their applications / O. Repin \\ Fractional integrals and wavelet transformations / B. Rubin, D. Ryabogin, E. Shamir \\ More generalization of fractional calculus / M. Saigo, N. Maeda \\ On certain subclasses of analytic functions involving a linear operator / H. Saitoh \\ On some sequence spaces / E. Savas \\ Class of integro-differential equations via fractional calculus / N. Shawagfeh \\ On some extreme points of the unit ball / J. Sokol, W. Szumny \\ Hyper-Bessel operators, differential equations, functions, and integral transforms of 4th order / S. Spirova \\ Some operational techniques in the theory of special functions / H. M. Srivastava \\ Convolution in the theory of univalent functions / J. Stankiewicz \\ Some extensions of the Rolle and Gauss--Lucas theorems / T. Stoyanov \\ On infinitely divisible probability distributions and integral equations / K. Takano \\ Generating functions related to pairs of inverse functions / R. Tremblay, B. J. Fug\`ere \\ Integral transforms connected with the group representations / N. Tretyakova \\ On some integral operators in the clas of functions with negative coefficients / L. Trojnar-Spelina \\ On a new generalized Taylor's formula / J. Trujillo, M. Rivero, B. Bonilla \\ Some properties of the finite Laplace transform / M. Valbuena, L. Galue, I. Ali \\ Airy integral transform and the Paley--Wiener theorem / Vu Kim Tuan \\ On starlike functions related with hyperbolic regions / A. Wi{\'s}niowska \\ Editorial: Nikola Obreshkoff (1896--1963): biographical data and 100 selected papers of Acad. N. Obreshkoff \\ Obreshkoff's generalization of Descartes rule / P. Rusev \\ Obrechkoff's generalization of the Laplace and Meijer transformations: origins and recent developments / I. Dimovski, V. Kiryakova \\ Longstanding conjecture failed? / V. Kiryakova \\ Afterthoughts on interpretation of fractional derivatives and integrals / R. Gorenflo \\ Modelling viscous damped oscillations by fractional differential operators / S. Kempfle \\ Considerations on fractional calculus: interpretations and applications / F. Mainardi \\ Introduction to the fractional calculus and some applications / K. Oldham

entry:
@Proceedings{Rusev:1998:TMS,
  editor =       "Petur Rusev and I. Dimovski and Virginia Kiryakova",
  booktitle =    "{Transformation methods and special functions, Varna
                 '96: second international workshop: proceedings}",
  title =        "{Transformation methods and special functions, Varna
                 '96: second international workshop: proceedings}",
  publisher =    "Institute of Mathematics and Informatics, Bulgarian
                 Academy of Sciences",
  address =      "Sofia, Bulgaria",
  pages =        "vi + 613",
  year =         "1998",
  ISBN =         "954-8986-05-1",
  ISBN-13 =      "978-954-8986-05-2",
  LCCN =         "????",
  bibdate =      "Thu Dec 1 11:08:47 MST 2011",
  bibsource =    "fsz3950.oclc.org:210/WorldCat
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  meetingname =  "International Workshop ``Transform Methods and Special
                 Functions'' (2nd: 1996: Varna, Bulgaria)",
  remark =       "``This second edition of the Workshops 'TM and SF' has
                 been devoted to the 100th anniversary of the eminent
                 Bulgarian mathematician Nikola Obreshkoff
                 (1896-1963)''--T.p. verso.",
  subject =      "Transformations (Mathematics); Differential equations;
                 Integral equations",
  tableofcontents = "On a generalization of the theorem on two constants
                 / G. Adamczyk \\
                 On a construction of the solutions of some elliptic
                 equations with generalized coefficients / A. Antonevich
                 \\
                 Some non-metrizable spaces of harmonic functions / G.
                 Balikov, I. Dimitrov \\
                 Duhamel-type representations of the solutions of
                 non-local boundary value problems for the fractional
                 diffusion-wave equation / E. Bazhlekova \\
                 Pointwise convergence for Hankel transform / J.
                 Betancour, L. Rodr\'iguez-Mesa \\
                 On fractional order continuity, integrability and
                 derivability of real functions / B. Bonilla, J.
                 Trujillo, M. Rivero \\
                 On the root functions of a nonlocal Sturm--Liouville
                 problem / N. Bozhinov \\
                 Mellin transform theory and the role of its
                 differential and integral operators / P. Butzer, S.
                 Jansche \\
                 Exact solution of some systems of non-selfadjoint
                 partial differential equations / D. Callebaut \\
                 Numerical computation of Lame functions / H.-J. Dobner,
                 S. Ritter \\
                 Some extremal problems for $p$-valent alpha-convex
                 functions / J. Dziok \\
                 Extension of a result on the convolution product of
                 distributions / B. Fisher, A. Kilicman \\
                 Simple algorithms for approximations of generalized
                 elliptic-type integrals / M. A. El-Gabali, Shyam L.
                 Kalla \\
                 On Zernicke polynomials / H.-J. Glaeske \\
                 Tomato salad problem in spherical stereology / R.
                 Gorenflo \\
                 On existence of solutions of ordinary differential
                 equations of fractional order / N. Hayek \ldots{} [et
                 al.] \\
                 Tauberian theorem for distributions / J. Jel\'inek \\
                 Radiation field integrals and their evaluation
                 techniques / Shyam L. Kalla, H. G. Khajah \\
                 On the product of distributions / A. Kami\'nski \\
                 On isotopies of algebras and triple systems / N. Kamiya
                 \\
                 Univalence criteria connected with arithmetic and
                 geometric means: I / S. Kanas, A. Lecko \\
                 Global and causal solutions of fractional linear
                 differential equations / S. Kempfle, H. Beyer \\
                 On the applications of Mikusinski's operational
                 calculus to the controllability of dynamical systems /
                 W. Kierat, K. Sk\'ornik \\
                 Application of fractional calculus to solve
                 Abel--Volterra nonlinear and linear integral equations
                 / A. Kilbas, M. Saigo \\
                 Note on linear operators and fractional calculus
                 operators in the univalent function theory / Yong Chan
                 Kim \\
                 Application of the generalized Mikhaylov criterion / S.
                 Krasinska \\
                 On some classes of holomorphic functions in the
                 half-plane / A. Lazi{\'n}ska \\
                 Expansions in series of Legendre functions / E. R.
                 Love, M. Hunter \\
                 Intersections with Gronwall methods / W. Luh \\
                 Applications of fractional calculus in mechanics / F.
                 Mainardi \\
                 Automorphisms in the commutant of the integration
                 operator in spaces of Lebesgue integrable functions /
                 S. Mincheva \\
                 Applications of fractional calculus operators to
                 univalent functions / S. Owa \\
                 Application of orthogonal polynomials to solution of
                 fractional integral equations / I. Podlubny \\
                 Remark on Watson transform / A. Prudnikov, U. Sk\'ornik
                 \\
                 Generalized operators of fractional
                 integro-differentiation in meaning of M. Saigo and
                 their applications / O. Repin \\
                 Fractional integrals and wavelet transformations / B.
                 Rubin, D. Ryabogin, E. Shamir \\
                 More generalization of fractional calculus / M. Saigo,
                 N. Maeda \\
                 On certain subclasses of analytic functions involving a
                 linear operator / H. Saitoh \\
                 On some sequence spaces / E. Savas \\
                 Class of integro-differential equations via fractional
                 calculus / N. Shawagfeh \\
                 On some extreme points of the unit ball / J. Sokol, W.
                 Szumny \\
                 Hyper-Bessel operators, differential equations,
                 functions, and integral transforms of 4th order / S.
                 Spirova \\
                 Some operational techniques in the theory of special
                 functions / H. M. Srivastava \\
                 Convolution in the theory of univalent functions / J.
                 Stankiewicz \\
                 Some extensions of the Rolle and Gauss--Lucas theorems
                 / T. Stoyanov \\
                 On infinitely divisible probability distributions and
                 integral equations / K. Takano \\
                 Generating functions related to pairs of inverse
                 functions / R. Tremblay, B. J. Fug\`ere \\
                 Integral transforms connected with the group
                 representations / N. Tretyakova \\
                 On some integral operators in the clas of functions
                 with negative coefficients / L. Trojnar-Spelina \\
                 On a new generalized Taylor's formula / J. Trujillo, M.
                 Rivero, B. Bonilla \\
                 Some properties of the finite Laplace transform / M.
                 Valbuena, L. Galue, I. Ali \\
                 Airy integral transform and the Paley--Wiener theorem /
                 Vu Kim Tuan \\
                 On starlike functions related with hyperbolic regions /
                 A. Wi{\'s}niowska \\
                 Editorial: Nikola Obreshkoff (1896--1963): biographical
                 data and 100 selected papers of Acad. N. Obreshkoff \\
                 Obreshkoff's generalization of Descartes rule / P.
                 Rusev \\
                 Obrechkoff's generalization of the Laplace and Meijer
                 transformations: origins and recent developments / I.
                 Dimovski, V. Kiryakova \\
                 Longstanding conjecture failed? / V. Kiryakova \\
                 Afterthoughts on interpretation of fractional
                 derivatives and integrals / R. Gorenflo \\
                 Modelling viscous damped oscillations by fractional
                 differential operators / S. Kempfle \\
                 Considerations on fractional calculus: interpretations
                 and applications / F. Mainardi \\
                 Introduction to the fractional calculus and some
                 applications / K. Oldham",
}


bibtype: book
filename: elefunt.bib
label: Bultheel:1999:ORF
editor: Adhemar Bultheel and Pablo Gonzales-Vera and Erik Hendriksen and Olav Njastad
booktitle: Orthogonal Rational Functions
title: Orthogonal Rational Functions
volume: 5
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: xiv + 407
year: 1999
DOI: https://doi.org/10.1017/CBO9780511530050
ISBN: 0-521-65006-2 (hardcover) OR 0521650062 (hardcover)
ISBN13: 978-0-521-65006-9 (hardcover) OR 9780521650069 (hardcover)
LCCN: QA404.5 .O75 1999
bibdate: Tue Mar 24 21:04:21 MDT 2009
bibtimestamp: 2009.03.24 21:04:21 MDT
series: Cambridge monographs on applied and computational mathematics
subject: functions, orthogonal; functions of complex variables
acknowledgement: ack-nhfb
rawbooktitle: Orthogonal Rational Functions
raweditor: Adhemar Bultheel and Pablo Gonzales-Vera and Erik Hendriksen and Olav Njastad
rawtitle: Orthogonal Rational Functions
URL:
http://www.loc.gov/catdir/description/cam029/98011646.html; http://www.loc.gov/catdir/toc/cam024/98011646.html

TOC:
1. Preliminaries / 15--41 2. The fundamental spaces / 42--63 3. The kernel functions / 64--73 4. Recurrence and second kind functions / 74--105 5. Para-orthogonality and quadrature / 106--120 6. Interpolation / 121--148 7. Density of the rational functions / 149--160 8. Favard theorems / 161--172 9. Convergence / 173--238 10. Moment problems / 239--256 11. The boundary case / 257--341 12. Some applications / 342--388 Conclusion / 389--392 Bibliography/ 393--404 Index / 405--407

rawTOC:
1. Preliminaries / 15--41 \\ 2. The fundamental spaces / 42--63 \\ 3. The kernel functions / 64--73 \\ 4. Recurrence and second kind functions / 74--105 \\ 5. Para-orthogonality and quadrature / 106--120 \\ 6. Interpolation / 121--148 \\ 7. Density of the rational functions / 149--160 \\ 8. Favard theorems / 161--172 \\ 9. Convergence / 173--238 \\ 10. Moment problems / 239--256 \\ 11. The boundary case / 257--341 \\ 12. Some applications / 342--388 \\ Conclusion / 389--392 \\ Bibliography/ 393--404 \\ Index / 405--407

entry:
@Book{Bultheel:1999:ORF,
  editor =       "Adhemar Bultheel and Pablo Gonzales-Vera and Erik
                 Hendriksen and Olav Njastad",
  booktitle =    "Orthogonal Rational Functions",
  title =        "Orthogonal Rational Functions",
  volume =       "5",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xiv + 407",
  year =         "1999",
  DOI =          "https://doi.org/10.1017/CBO9780511530050",
  ISBN =         "0-521-65006-2 (hardcover)",
  ISBN-13 =      "978-0-521-65006-9 (hardcover)",
  LCCN =         "QA404.5 .O75 1999",
  bibdate =      "Tue Mar 24 21:04:21 MDT 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Cambridge monographs on applied and computational
                 mathematics",
  URL =          "http://www.loc.gov/catdir/description/cam029/98011646.html;
                 http://www.loc.gov/catdir/toc/cam024/98011646.html",
  acknowledgement = ack-nhfb,
  subject =      "functions, orthogonal; functions of complex
                 variables",
  tableofcontents = "1. Preliminaries / 15--41 \\
                 2. The fundamental spaces / 42--63 \\
                 3. The kernel functions / 64--73 \\
                 4. Recurrence and second kind functions / 74--105 \\
                 5. Para-orthogonality and quadrature / 106--120 \\
                 6. Interpolation / 121--148 \\
                 7. Density of the rational functions / 149--160 \\
                 8. Favard theorems / 161--172 \\
                 9. Convergence / 173--238 \\
                 10. Moment problems / 239--256 \\
                 11. The boundary case / 257--341 \\
                 12. Some applications / 342--388 \\
                 Conclusion / 389--392 \\
                 Bibliography/ 393--404 \\
                 Index / 405--407",
}


bibtype: proceedings
filename: elefunt.bib
label: IEEE:1999:PIF
editor: IEEE
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xi + 217
year: 1999
ISBN: 0-7695-0219-9 OR 0769502199
ISBN13: 978-0-7695-0219-9 OR 9780769502199
LCCN: ZA4080 .F67 1999
bibdate: Fri Jul 09 06:32:32 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:32:32 ???
acknowledgement: ack-nhfb
raweditor: IEEE
booktitle:
Proceedings of the IEEE Forum on Research and Technology Advances in Digital Libraries, May 19--21, 1999, Baltimore, Maryland

title:
Proceedings of the IEEE Forum on Research and Technology Advances in Digital Libraries, May 19--21, 1999, Baltimore, Maryland

rawbooktitle:
Proceedings of the {IEEE} Forum on Research and Technology Advances in Digital Libraries, May 19--21, 1999, Baltimore, Maryland

rawtitle:
Proceedings of the {IEEE} Forum on Research and Technology Advances in Digital Libraries, May 19--21, 1999, Baltimore, Maryland

entry:
@Proceedings{IEEE:1999:PIF,
  editor =       "IEEE",
  booktitle =    "Proceedings of the {IEEE} Forum on Research and
                 Technology Advances in Digital Libraries, May 19--21,
                 1999, Baltimore, Maryland",
  title =        "Proceedings of the {IEEE} Forum on Research and
                 Technology Advances in Digital Libraries, May 19--21,
                 1999, Baltimore, Maryland",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xi + 217",
  year =         "1999",
  ISBN =         "0-7695-0219-9",
  ISBN-13 =      "978-0-7695-0219-9",
  LCCN =         "ZA4080 .F67 1999",
  bibdate =      "Fri Jul 09 06:32:32 2004",
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filename: elefunt.bib
label: Koren:1999:ISC
editor: Israel Koren and Peter Kornerup
booktitle: 14th IEEE Symposium on Computer Arithmetic: proceedings: April 14--16, 1999, Adelaide, Australia
title: 14th IEEE Symposium on Computer Arithmetic: proceedings: April 14--16, 1999, Adelaide, Australia
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xi + 274
year: 1999
ISBN: 0-7803-5609-8, 0-7695-0116-8, 0-7695-0118-4 OR 0780356098, 0769501168, 0769501184
ISSN: 1063-6889 OR 10636889
LCCN: QA76.6 .S887 1999
bibdate: Mon Feb 7 07:28:26 MST 2000
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2000.02.07 07:28:26 MST
note: IEEE Computer Society Order Number PR00116. IEEE Order Plan Catalog Number 99CB36336.
URL: http://computer.org/conferen/home/arith/; http://www.ecs.umass.edu/ece/arith14/program.html
acknowledgement: ack-nhfb
annote: Also known as ARITH-14.
rawbooktitle: 14th {IEEE} Symposium on Computer Arithmetic: proceedings: April 14--16, 1999, Adelaide, Australia
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rawtitle: 14th {IEEE} Symposium on Computer Arithmetic: proceedings: April 14--16, 1999, Adelaide, Australia
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  title =        "14th {IEEE} Symposium on Computer Arithmetic:
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  note =         "IEEE Computer Society Order Number PR00116. IEEE Order
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bibtype: proceedings
filename: elefunt.bib
label: Luk:1999:PSA
editor: Franklin T. Luk
volume: 3807
publisher: pub-SPIE
address: pub-SPIE:adr
pages: ix + 648
year: 1999
ISBN: 0-8194-3293-8 OR 0819432938
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bibdate: Mon Mar 5 07:43:43 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; melvyl.cdlib.org:210/CDL90
bibtimestamp: 2007.03.05 07:43:43 MST
subject: Signal processing; Digital techniques; Congresses; Algorithms; Computer architecture
acknowledgement: ack-nhfb
raweditor: Franklin T. Luk
booktitle:
Proceedings of SPIE: Advanced signal processing algorithms, architectures, and implementations IX: 19--21 July, 1999, Denver, Colorado

title:
Proceedings of SPIE: Advanced signal processing algorithms, architectures, and implementations IX: 19--21 July, 1999, Denver, Colorado

rawbooktitle:
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Proceedings of {SPIE: Advanced signal processing algorithms, architectures, and implementations IX: 19--21 July, 1999, Denver, Colorado}

entry:
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  title =        "Proceedings of {SPIE: Advanced signal processing
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bibtype: book
filename: elefunt.bib
label: Berggren:2000:PSB
editor: Lennart Berggren and Jonathan Borwein and Peter Borwein
booktitle: Pi: a source book
title: Pi: a source book
publisher: pub-SV
address: pub-SV:adr
edition: Second
pages: xx + 736
year: 2000
DOI: https://doi.org/10.1007/978-1-4757-3240-5
ISBN: 0-387-98946-3 (hardcover) OR 0387989463 (hardcover)
ISBN13: 978-0-387-98946-4 (hardcover) OR 9780387989464 (hardcover)
LCCN: QA484 .P5 2000
MRclass: 11-00 (01A05 01A75 11-03)
MRnumber: 1746004
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
subject: Pi (mathematical constant)
acknowledgement: ack-nhfb
authordates: Jonathan Michael Borwein (20 May 1951--2 August 2016)
rawbooktitle: Pi: a source book
raweditor: Lennart Berggren and Jonathan Borwein and Peter Borwein
rawtitle: Pi: a source book
ORCID: Borwein, Jonathan/0000-0002-1263-0646
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/master.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; https://www.math.utah.edu/pub/tex/bib/pi.bib

TOC:
Preface / v Preface to the Second Edition / viii Acknowledgments / ix Introduction / xvii 1. The Rhind Mathematical Papyrus-Problem 50 ($approx $ 1650 B.C.) / A problem dealing with the area of a round field of given diameter / 1 2. Engels. Quadrature of the Circle in Ancient Egypt (1977) / A conjectural explanation of how the mathematicians of ancient Egypt approximated the area of a circle / 3 3. Archimedes. Measurement of a Circle ($approx $ 250 BC) / The seminal work in which Archimedes presents the first true algorithm for $pi $ / 7 4. Phillips. Archimedes the Numerical Analyst (1981) / A summary of Archimedes' work on the computation of $pi $ using modern notation / 15 5. Lam and Ang. Circle Measurements in Ancient China (1986) / This paper discusses and contains a translation of Liu Hui's (3rd century) method for evaluating $pi $ and also examines values for $pi $ given by Zu Chongzhi (429--500) / 20 6. The Banu Musa: The Measurement of Plane and Solid Figures ($approx $ 850) / This extract gives an explicit statement and proof that the ratio of the circumference to the diameter is constant / 36 7. Madhava. The Power Series for Arctan and Pi ($approx $ 1400) / These theorems by a fifteenth century Indian mathematician give Gregory's series for arctan with remainder terms and Leibniz's series for $pi $ / 45 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van Ceulen (1938) / Correspondence about van Ceulen's tombstone in reference to it containing some digits of $pi $ / 51 9. Viete. Variorum de Rebus Mathematicis Reponsorum Liber VII (1593) / Two excerpts. One containing the first infinite expression of $pi $, obtained by relating the area of a regular $2n$-gon to that of a regular $n$-gon / 53 10. Wallis. Computation of $pi $ by Successive Interpolations (1655) / How Wallis derived the infinite product for $pi $ that bears his name / 68 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt including Prop. 189, 191 and an alternate form of the result that gives Wm. Brounker's continued fraction expression for $4/pi $ / 78 12. Huygens. De Circuli Magnitudine Inventa (1724) / Huygens's proof of W. Snell's discovery of improvements in Archimedes' method of estimating the lengths of circular arcs / 81 13. Gregory. Correspondence with John Collins (1671) / A letter to Collins in which he gives his series for arctangent, carried to the ninth power. / 87 14. Roy. The Discovery of the Series Formula for $pi $ by Leibniz, Gregory, and Nilakantha (1990) / A discussion of the discovery of the series $pi /4 = 1 - 1/3 + 1/5, cdots $ / 92 15. Jones. The First Use of $pi $ for the Circle Ratio (1706) / An excerpt from Jones' book, the Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics, London, 1706 / 108 16. Newton. Of the Method of Fluxions and Infinite Series (1737) / An excerpt giving Newton's calculation of $pi $ to 16 decimal places / 110 17. Euler. Chapter 10 of Introduction to Analysis of the Infinite (On the Use of the Discovered Fractions to Sum Infinite Series) (1748) / This includes many of Euler's infinite series for $pi $ and powers of $pi $ / 112 18. Lambert. Memoire Sur Quelques Proprietes Remarquables Des Quantites Transcendentes Circulaires et Logarithmiques (1761) / An excerpt from Lambert's original proof of the irrationality of $pi $ / 129 19. Lambert. Irrationality of $pi $ (1969) / A translation and Struik's discussion of Lambert's proof of the irrationality of $pi $ / 141 20. Shanks. Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals (1853) / Pages from Shank's report of his monumental hand calculation of $pi $ / 147 21. Hermite. Sur La Fonction Exponentielle (1873) / The first proof of the transcendence of $e$ / 162 22. Lindemann. Ueber die Zahl $pi $ (1882) / The first proof of the transcendence of $pi $ / 194 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die Ludolphsche Zahl'' (1885) / Weierstrass' proof of the transcendence of $pi $ / 207 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und $pi $ (1893) / Hilbert's short and elegant simplification of the transcendence proofs for $e$ and $pi $ / 226 25. Goodwin. Quadrature of the Circle (1894) / The dubious origin of the attempted legislation of the value of $pi $ in Indiana / 230 26. Edington. House Bill No. 246, Indiana State Legislature, 1897 (1935) / A summary of the action taken by the Indiana State Legislature to fix the value of $pi $ (including a copy of the actual bill that was proposed) / 231 27. Singmaster. The Legal Values of Pi (1985) / A history of the attempt by Indiana to legislate the value of $pi $ / 236 28. Ramanujan. Squaring the Circle (1913) / A geometric approximation to $pi $ / 240 29. Ramanujan. Modular Equations and Approximations to $pi $ (1914) / Ramanujan's seminal paper on $pi $ that includes a number of striking series and algebraic approximations / 241 30. Watson. The Marquis and the Land Agent: A Tale of the Eighteenth Century (1933) / A Presidential address to the Mathematical Association in which the author gives an account of ``some of the elementary work on arcs and ellipses and other curves which led up to the idea of inverting an elliptic integral, and so laying the foundations of elliptic functions and doubly periodic functions generally.'' / 258 31. Ballantine. The Best (?) Formula for Computing $pi $ to a Thousand Places (1939) / An early attempt to orchestrate the calculation of $pi $ more cleverly / 271 32. Birch. An Algorithm for Construction of Arctangent Relations (1946) / The object of this note is to express $pi / 4 $ as a sum of arctan relations in powers of 10 / 274 33. Niven. A Simple Proof that $pi $ Is Irrational (1947) / A very concise proof of the irrationality of $pi $ / 276 34. Reitwiesner. An ENIAC Determination of $pi $ and $e$ to 2000 Decimal Places (1950) / One of the first computer-based computations / 277 35. Schepler. The Chronology of Pi (1950) / A fairly reliable outline of the history of $pi $ from 3000 BC to 1949 / 282 36. Mahler. On the Approximation of $pi $ (1953) / ``The aim of this paper is to determine an explicit lower bound free of unknown constants for the distance of $pi $ from a given rational or algebraic number'' / 306 37. Wrench, Jr. The Evolution of Extended Decimal Approximations to $pi $ (1960) / A history of the calculation of the digits of $pi $ to 1960 38. Shanks and Wrench, Jr. Calculation of $pi $ to 100,000 Decimals (1962) / A landmark computation of $pi $ to more than 100,000 places / 326 39. Sweeny. On the Computation of Euler's Constant (1963) / The computation of Euler's constant to 3566 decimal places / 350 40. Baker. Approximations to the Logarithms of Certain Rational Numbers (1964) / The main purpose of this deep and fundamental paper is to ``deduce results concerning the accuracy with which the natural logarithms of certain rational numbers may be approximated by rational numbers, or, more generally, by algebraic numbers of bounded degree.'' / 359 41. Adams. Asymptotic Diophantine Approximations to $E$ (1966) / An asymptotic estimate for the rational approximation to $e$ which disproves the conjecture that $e$ behaves like almost all numbers in this respect / 368 42. Mahler. Applications of Some Formulae by Hermite to the Approximations of Exponentials of Logarithms (1967) / An important extension of Hilbert's approach to the study of transcendence / 372 43. Eves. In Mathematical Circles; A Selection of Mathematical Stories and Anecdotes (excerpt) (1969) / A collection of mathematical stories and anecdotes about $pi $ / 400 44. Eves. Mathematical Circles Revisited; A Second Collection of Mathematical Stories and Anecdotes (excerpt) (1971) / A further collection of mathematical stories and anecdotes about $pi $ / 402 45. Todd. The Lemniscate Constants (1975) / A unifying account of some of the methods used for computing the lemniscate constants / 412 46. Salamin. Computation of r Using Arithmetic-Geometric Mean (1976) / The first quadratically converging algorithm for $pi $ based on Gauss's AGM and on Legendre's relation for elliptic integrals / 418 47. Brent. Fast Multiple-Precision Evaluation of Elementary Functions (1976) / ``This paper contains the `Gauss-Legendre' method and some different algorithms for log and exp (using Landen transformations).'' / 424 48. Beukers. A Note on the Irrationality of $zeta (2)$ and $zetq (3)$ (1979) / A short and elegant recasting of Apery's proof of the irrationality of $zeta (3)$ (and $zeta (2)$) / 434 49. van der Poorten. A Proof that Euler Missed ldots Apery's Proof of the Irrationality of $zeta (3)$ (1979) / An illuminating account of Apery's astonishing proof of the irrationality of $zeta (3)$ / 439 50. Brent and McMillan. Some New Algorithms for High-Precision Computation of Euler's Constant (1980) / Several new algorithms for high precision calculation of Euler's constant, including one which was used to compute 30,100 decimal places / 448 51. Apostol. A Proof that Euler Missed: Evaluating $zeta (2)$ the Easy Way (1983) / This note shows that one of the double integrals considered by Beukers ([48] in the table of contents) can be used to establish directly that $zeta (2) = pi / 6$ / 456 52. O'Shaughnessy. Putting God Back in Math (1983) / An article about the Institute of Pi Research, an organization that ``pokes fun at creationists by pointing out that even the Bible makes mistakes.'' / 458 53. Stern. A Remarkable Approximation to $pi $ (1985) / Justification of the value of $pi $ in the Bible through numerological interpretations / 460 54. Newman and Shanks. On a Sequence Arising in Series for $pi $ (1984) / More connections between $pi $ and modular equations / 462 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984) / An extensive study of the complex analytic properties of the AGM / 481 56. Borwein and Borwein. The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions (1984) / The relationship between the AGM iteration and fast computation of elementary functions (one of the by-products is an algorithm for $pi $) / 537 57. Newman. A Simplified Version of the Fast Algorithms of Brent and Salamin (1984) / Elementary algorithms for evaluating $e^x$ and $pi $ using the Gauss AGM without explicit elliptic function theory / 553 58. Wagon. Is Pi Normal? (1985) / A discussion of the conjecture that $pi $ has randomly distributed digits / 557 59. Keith. Circle Digits: A Self-Referential Story (1986) / A mnemonic for the first 402 decimal places of $pi $ / 560 60. Bailey. The Computation of $pi $ to 29,360,000 Decimal Digits Using Borweins' Quartically Convergent Algorithm (1988) / The algorithms used, both for $pi $ and for performing the required multiple-precision arithmetic / 562 61. Kanada. Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of 1 Calculation (1988) / Details of the computation and statistical tests of the first 200 million digits of $pi $ / 576 62. Borwein and Borwein. Ramanujan and Pi (1988) / This article documents Ramanujan's life, his ingenious approach to calculating $pi $, and how his approach is now incorporated into modern computer algorithms / 588 63. Chudnovsky and Chudnovsky. Approximations and Complex Multiplication According to Ramanujan (1988) / This excerpt describes ``Ramanujan's original quadratic period--quasiperiod relations for elliptic curves with complex multiplication and their applications to representations of fractions of $pi $ and other logarithms in terms of rapidly convergent nearly integral (hypergeometric) series.'' / 596 64. Borwein, Borwein and Bailey. Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi (1989) / An exposition of the computation of $pi $ using mathematics rooted in Ramanujan's work / 623 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers, and Asymptotic Expansions (1989) / An explanation as to why the slowly convergent Gregory series for $pi $, truncated at 500,000 terms, gives $pi $ to 40 places with only the 6th, 17th, 18th, and 29th places being incorrect / 642 66. Beukers, Bezivin, and Robba. An Alternative Proof of the Lindemann--Weierstrass Theorem (1990) / The Lindemann--Weierstrass theorem as a by-product of a criterion for rationality of solutions of differential equations / 649 67. Webster. The Tail of Pi (1991) / Various anecdotes about $pi $ from the 14th annual IMO Lecture to the Royal Society / 654 68. Eco. An excerpt from Foucault's Pendulum (1993) / ``The unnumbered perfection of the circle itself.'' / 658 69. Keith. Pi Mnemonics and the Art of Constrained Writing (1996) / A mnemonic for $pi $ based on Edgar Allen Poe's poem ``The Raven.'' / 659 70. Bailey, Borwein, and Plouffe. On the Rapid Computation of Various Polylogarithmic Constants (1996) / A fast method for computing individual digits of $pi $ in base 2 / 663 Appendix I --- On the Early History of Pi / 677 Appendix II --- A Computational Chronology of Pi / 683 Appendix III --- Selected Formulae for Pi / 686 Appendix IV --- Translations of Viete and Huygens / 690 Bibliography / 711 Credits / 717 Index / 721

rawTOC:
Preface / v \\ \\ Preface to the Second Edition / viii \\ Acknowledgments / ix \\ \\ Introduction / xvii \\ \\ 1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$ 1650 B.C.) / A problem dealing with the area of a round field of given diameter / 1 \\ \\ 2. Engels. Quadrature of the Circle in Ancient Egypt (1977) / A conjectural explanation of how the mathematicians of ancient Egypt approximated the area of a circle / 3 \\ \\ 3. Archimedes. Measurement of a Circle ($\approx$ 250 BC) / The seminal work in which Archimedes presents the first true algorithm for $\pi$ / 7 \\ \\ 4. Phillips. Archimedes the Numerical Analyst (1981) / A summary of Archimedes' work on the computation of $\pi$ using modern notation / 15 \\ \\ 5. Lam and Ang. Circle Measurements in Ancient China (1986) / This paper discusses and contains a translation of Liu Hui's (3rd century) method for evaluating $\pi$ and also examines values for $\pi$ given by Zu Chongzhi (429--500) / 20 \\ \\ 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane and Solid Figures ($\approx$ 850) / This extract gives an explicit statement and proof that the ratio of the circumference to the diameter is constant / 36 \\ \\ 7. M{\=a}dhava. The Power Series for Arctan and Pi ($\approx$ 1400) / These theorems by a fifteenth century Indian mathematician give Gregory's series for arctan with remainder terms and Leibniz's series for $\pi$ / 45 \\ \\ 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van Ceulen (1938) / Correspondence about van Ceulen's tombstone in reference to it containing some digits of $\pi$ / 51 \\ \\ 9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum Liber VII (1593) / Two excerpts. One containing the first infinite expression of $\pi$, obtained by relating the area of a regular $2n$-gon to that of a regular $n$-gon / 53 \\ \\ 10. Wallis. Computation of $\pi$ by Successive Interpolations (1655) / How Wallis derived the infinite product for $\pi$ that bears his name / 68 \\ \\ 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt including Prop. 189, 191 and an alternate form of the result that gives Wm. Brounker's continued fraction expression for $4/\pi$ / 78 \\ \\ 12. Huygens. De Circuli Magnitudine Inventa (1724) / Huygens's proof of W. Snell's discovery of improvements in Archimedes' method of estimating the lengths of circular arcs / 81 \\ \\ 13. Gregory. Correspondence with John Collins (1671) / A letter to Collins in which he gives his series for arctangent, carried to the ninth power. / 87 \\ \\ 14. Roy. The Discovery of the Series Formula for $\pi$ by Leibniz, Gregory, and Nilakantha (1990) / A discussion of the discovery of the series $\pi/4 = 1 - 1/3 + 1/5, \cdots{}$ / 92 \\ \\ 15. Jones. The First Use of $\pi$ for the Circle Ratio (1706) / An excerpt from Jones' book, the Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics, London, 1706 / 108 \\ \\ 16. Newton. Of the Method of Fluxions and Infinite Series (1737) / An excerpt giving Newton's calculation of $\pi$ to 16 decimal places / 110 \\ \\ 17. Euler. Chapter 10 of Introduction to Analysis of the Infinite (On the Use of the Discovered Fractions to Sum Infinite Series) (1748) / This includes many of Euler's infinite series for $\pi$ and powers of $\pi$ / 112 \\ \\ 18. Lambert. M{\'e}moire Sur Quelques Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s Transcendentes Circulaires et Logarithmiques (1761) / An excerpt from Lambert's original proof of the irrationality of $\pi$ / 129 \\ \\ 19. Lambert. Irrationality of $\pi$ (1969) / A translation and Struik's discussion of Lambert's proof of the irrationality of $\pi$ / 141 \\ \\ 20. Shanks. Contributions to Mathematics Comprising Chiefly of the Rectification of the Circle to 607 Places of Decimals (1853) / Pages from Shank's report of his monumental hand calculation of $\pi$ / 147 \\ \\ 21. Hermite. Sur La Fonction Exponentielle (1873) / The first proof of the transcendence of $e$ / 162 \\ \\ 22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first proof of the transcendence of $\pi$ / 194 \\ \\ 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die Ludolphsche Zahl'' (1885) / Weierstrass' proof of the transcendence of $\pi$ / 207 \\ \\ 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und $\pi$ (1893) / Hilbert's short and elegant simplification of the transcendence proofs for $e$ and $\pi$ / 226 \\ \\ 25. Goodwin. Quadrature of the Circle (1894) / The dubious origin of the attempted legislation of the value of $\pi$ in Indiana / 230 \\ \\ 26. Edington. House Bill No. 246, Indiana State Legislature, 1897 (1935) / A summary of the action taken by the Indiana State Legislature to fix the value of $\pi$ (including a copy of the actual bill that was proposed) / 231 \\ \\ 27. Singmaster. The Legal Values of Pi (1985) / A history of the attempt by Indiana to legislate the value of $\pi$ / 236 \\ \\ 28. Ramanujan. Squaring the Circle (1913) / A geometric approximation to $\pi$ / 240 \\ \\ 29. Ramanujan. Modular Equations and Approximations to $\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that includes a number of striking series and algebraic approximations / 241 \\ \\ 30. Watson. The Marquis and the Land Agent: A Tale of the Eighteenth Century (1933) / A Presidential address to the Mathematical Association in which the author gives an account of ``some of the elementary work on arcs and ellipses and other curves which led up to the idea of inverting an elliptic integral, and so laying the foundations of elliptic functions and doubly periodic functions generally.'' / 258 \\ \\ 31. Ballantine. The Best (?) Formula for Computing $\pi$ to a Thousand Places (1939) / An early attempt to orchestrate the calculation of $\pi$ more cleverly / 271 \\ \\ 32. Birch. An Algorithm for Construction of Arctangent Relations (1946) / The object of this note is to express $\pi / 4 $ as a sum of arctan relations in powers of 10 / 274 \\ \\ 33. Niven. A Simple Proof that $\pi$ Is Irrational (1947) / A very concise proof of the irrationality of $\pi$ / 276 \\ \\ 34. Reitwiesner. An ENIAC Determination of $\pi$ and $e$ to 2000 Decimal Places (1950) / One of the first computer-based computations / 277 \\ \\ 35. Schepler. The Chronology of Pi (1950) / A fairly reliable outline of the history of $\pi$ from 3000 BC to 1949 / 282 \\ \\ 36. Mahler. On the Approximation of $\pi$ (1953) / ``The aim of this paper is to determine an explicit lower bound free of unknown constants for the distance of $\pi$ from a given rational or algebraic number'' / 306 \\ \\ 37. Wrench, Jr. The Evolution of Extended Decimal Approximations to $\pi$ (1960) / A history of the calculation of the digits of $\pi$ to 1960 \\ \\ 38. Shanks and Wrench, Jr. Calculation of $\pi$ to 100,000 Decimals (1962) / A landmark computation of $\pi$ to more than 100,000 places / 326 \\ \\ 39. Sweeny. On the Computation of Euler's Constant (1963) / The computation of Euler's constant to 3566 decimal places / 350 \\ \\ 40. Baker. Approximations to the Logarithms of Certain Rational Numbers (1964) / The main purpose of this deep and fundamental paper is to ``deduce results concerning the accuracy with which the natural logarithms of certain rational numbers may be approximated by rational numbers, or, more generally, by algebraic numbers of bounded degree.'' / 359 \\ \\ 41. Adams. Asymptotic Diophantine Approximations to $E$ (1966) / An asymptotic estimate for the rational approximation to $e$ which disproves the conjecture that $e$ behaves like almost all numbers in this respect / 368 \\ \\ 42. Mahler. Applications of Some Formulae by Hermite to the Approximations of Exponentials of Logarithms (1967) / An important extension of Hilbert's approach to the study of transcendence / 372 \\ \\ 43. Eves. In Mathematical Circles; A Selection of Mathematical Stories and Anecdotes (excerpt) (1969) / A collection of mathematical stories and anecdotes about $\pi$ / 400 \\ \\ 44. Eves. Mathematical Circles Revisited; A Second Collection of Mathematical Stories and Anecdotes (excerpt) (1971) / A further collection of mathematical stories and anecdotes about $\pi$ / 402 \\ \\ 45. Todd. The Lemniscate Constants (1975) / A unifying account of some of the methods used for computing the lemniscate constants / 412 \\ \\ 46. Salamin. Computation of r Using Arithmetic-Geometric Mean (1976) / The first quadratically converging algorithm for $\pi$ based on Gauss's AGM and on Legendre's relation for elliptic integrals / 418 \\ \\ 47. Brent. Fast Multiple-Precision Evaluation of Elementary Functions (1976) / ``This paper contains the `Gauss-Legendre' method and some different algorithms for log and exp (using Landen transformations).'' / 424 \\ \\ 48. Beukers. A Note on the Irrationality of $\zeta(2)$ and $\zetq(3)$ (1979) / A short and elegant recasting of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$ (and $\zeta(2)$) / 434 \\ \\ 49. van der Poorten. A Proof that Euler Missed \ldots{} Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$ (1979) / An illuminating account of Ap{\'e}ry's astonishing proof of the irrationality of $\zeta(3)$ / 439 \\ \\ 50. Brent and McMillan. Some New Algorithms for High-Precision Computation of Euler's Constant (1980) / Several new algorithms for high precision calculation of Euler's constant, including one which was used to compute 30,100 decimal places / 448 \\ \\ 51. Apostol. A Proof that Euler Missed: Evaluating $\zeta(2)$ the Easy Way (1983) / This note shows that one of the double integrals considered by Beukers ([48] in the table of contents) can be used to establish directly that $\zeta(2) = \pi / 6$ / 456 \\ \\ 52. O'Shaughnessy. Putting God Back in Math (1983) / An article about the Institute of Pi Research, an organization that ``pokes fun at creationists by pointing out that even the Bible makes mistakes.'' / 458 \\ \\ 53. Stern. A Remarkable Approximation to $\pi$ (1985) / Justification of the value of $\pi$ in the Bible through numerological interpretations / 460 \\ \\ 54. Newman and Shanks. On a Sequence Arising in Series for $\pi$ (1984) / More connections between $\pi$ and modular equations / 462 \\ \\ 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984) / An extensive study of the complex analytic properties of the AGM / 481 \\ \\ 56. Borwein and Borwein. The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions (1984) / The relationship between the AGM iteration and fast computation of elementary functions (one of the by-products is an algorithm for $\pi$) / 537 \\ \\ 57. Newman. A Simplified Version of the Fast Algorithms of Brent and Salamin (1984) / Elementary algorithms for evaluating $e^x$ and $\pi$ using the Gauss AGM without explicit elliptic function theory / 553 \\ \\ 58. Wagon. Is Pi Normal? (1985) / A discussion of the conjecture that $\pi$ has randomly distributed digits / 557 \\ \\ 59. Keith. Circle Digits: A Self-Referential Story (1986) / A mnemonic for the first 402 decimal places of $\pi$ / 560 \\ \\ 60. Bailey. The Computation of $\pi$ to 29,360,000 Decimal Digits Using Borweins' Quartically Convergent Algorithm (1988) / The algorithms used, both for $\pi$ and for performing the required multiple-precision arithmetic / 562 \\ \\ 61. Kanada. Vectorization of Multiple-Precision Arithmetic Program and 201,326,000 Decimal Digits of 1 Calculation (1988) / Details of the computation and statistical tests of the first 200 million digits of $\pi$ / 576 \\ \\ 62. Borwein and Borwein. Ramanujan and Pi (1988) / This article documents Ramanujan's life, his ingenious approach to calculating $\pi$, and how his approach is now incorporated into modern computer algorithms / 588 \\ \\ 63. Chudnovsky and Chudnovsky. Approximations and Complex Multiplication According to Ramanujan (1988) / This excerpt describes ``Ramanujan's original quadratic period--quasiperiod relations for elliptic curves with complex multiplication and their applications to representations of fractions of $\pi$ and other logarithms in terms of rapidly convergent nearly integral (hypergeometric) series.'' / 596 \\ \\ 64. Borwein, Borwein and Bailey. Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi (1989) / An exposition of the computation of $\pi$ using mathematics rooted in Ramanujan's work / 623 \\ \\ 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers, and Asymptotic Expansions (1989) / An explanation as to why the slowly convergent Gregory series for $\pi$, truncated at 500,000 terms, gives $\pi$ to 40 places with only the 6th, 17th, 18th, and 29th places being incorrect / 642 \\ \\ 66. Beukers, B{\'e}zivin, and Robba. An Alternative Proof of the Lindemann--Weierstrass Theorem (1990) / The Lindemann--Weierstrass theorem as a by-product of a criterion for rationality of solutions of differential equations / 649 \\ \\ 67. Webster. The Tail of Pi (1991) / Various anecdotes about $\pi$ from the 14th annual IMO Lecture to the Royal Society / 654 \\ \\ 68. Eco. An excerpt from Foucault's Pendulum (1993) / ``The unnumbered perfection of the circle itself.'' / 658 \\ \\ 69. Keith. Pi Mnemonics and the Art of Constrained Writing (1996) / A mnemonic for $\pi$ based on Edgar Allen Poe's poem ``The Raven.'' / 659 \\ \\ 70. Bailey, Borwein, and Plouffe. On the Rapid Computation of Various Polylogarithmic Constants (1996) / A fast method for computing individual digits of $\pi$ in base 2 / 663 \\ Appendix I --- On the Early History of Pi / 677 \\ \\ Appendix II --- A Computational Chronology of Pi / 683 \\ \\ Appendix III --- Selected Formulae for Pi / 686 \\ \\ Appendix IV --- Translations of Vi{\`e}te and Huygens / 690 \\ Bibliography / 711 \\ \\ Credits / 717 \\ \\ Index / 721

entry:
@Book{Berggren:2000:PSB,
  editor =       "Lennart Berggren and Jonathan Borwein and Peter
                 Borwein",
  booktitle =    "Pi: a source book",
  title =        "Pi: a source book",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  edition =      "Second",
  pages =        "xx + 736",
  year =         "2000",
  DOI =          "https://doi.org/10.1007/978-1-4757-3240-5",
  ISBN =         "0-387-98946-3 (hardcover)",
  ISBN-13 =      "978-0-387-98946-4 (hardcover)",
  LCCN =         "QA484 .P5 2000",
  MRclass =      "11-00 (01A05 01A75 11-03)",
  MRnumber =     "1746004",
  bibdate =      "Wed Aug 10 11:09:47 2016",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/master.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 https://www.math.utah.edu/pub/tex/bib/pi.bib",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  libnote =      "Not yet in my library.",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  subject =      "Pi (mathematical constant)",
  tableofcontents = "Preface / v \\
                 \\
                 Preface to the Second Edition / viii \\
                 Acknowledgments / ix \\
                 \\
                 Introduction / xvii \\
                 \\
                 1. The Rhind Mathematical Papyrus-Problem 50 ($\approx$
                 1650 B.C.) / A problem dealing with the area of a round
                 field of given diameter / 1 \\
                 \\
                 2. Engels. Quadrature of the Circle in Ancient Egypt
                 (1977) / A conjectural explanation of how the
                 mathematicians of ancient Egypt approximated the area
                 of a circle / 3 \\
                 \\
                 3. Archimedes. Measurement of a Circle ($\approx$ 250
                 BC) / The seminal work in which Archimedes presents the
                 first true algorithm for $\pi$ / 7 \\
                 \\
                 4. Phillips. Archimedes the Numerical Analyst (1981) /
                 A summary of Archimedes' work on the computation of
                 $\pi$ using modern notation / 15 \\
                 \\
                 5. Lam and Ang. Circle Measurements in Ancient China
                 (1986) / This paper discusses and contains a
                 translation of Liu Hui's (3rd century) method for
                 evaluating $\pi$ and also examines values for $\pi$
                 given by Zu Chongzhi (429--500) / 20 \\
                 \\
                 6. The Ban{\=u} M{\=u}s{\=a}: The Measurement of Plane
                 and Solid Figures ($\approx$ 850) / This extract gives
                 an explicit statement and proof that the ratio of the
                 circumference to the diameter is constant / 36 \\
                 \\
                 7. M{\=a}dhava. The Power Series for Arctan and Pi
                 ($\approx$ 1400) / These theorems by a fifteenth
                 century Indian mathematician give Gregory's series for
                 arctan with remainder terms and Leibniz's series for
                 $\pi$ / 45 \\
                 \\
                 8. Hope-Jones. Ludolph (or Ludolff or Lucius) van
                 Ceulen (1938) / Correspondence about van Ceulen's
                 tombstone in reference to it containing some digits of
                 $\pi$ / 51 \\
                 \\
                 9. Vi{\'e}te. Variorum de Rebus Mathematicis Reponsorum
                 Liber VII (1593) / Two excerpts. One containing the
                 first infinite expression of $\pi$, obtained by
                 relating the area of a regular $2n$-gon to that of a
                 regular $n$-gon / 53 \\
                 \\
                 10. Wallis. Computation of $\pi$ by Successive
                 Interpolations (1655) / How Wallis derived the infinite
                 product for $\pi$ that bears his name / 68 \\
                 \\
                 11. Wallis. Arithmetica Infinitorum (1655) / An excerpt
                 including Prop. 189, 191 and an alternate form of the
                 result that gives Wm. Brounker's continued fraction
                 expression for $4/\pi$ / 78 \\
                 \\
                 12. Huygens. De Circuli Magnitudine Inventa (1724) /
                 Huygens's proof of W. Snell's discovery of improvements
                 in Archimedes' method of estimating the lengths of
                 circular arcs / 81 \\
                 \\
                 13. Gregory. Correspondence with John Collins (1671) /
                 A letter to Collins in which he gives his series for
                 arctangent, carried to the ninth power. / 87 \\
                 \\
                 14. Roy. The Discovery of the Series Formula for $\pi$
                 by Leibniz, Gregory, and Nilakantha (1990) / A
                 discussion of the discovery of the series $\pi/4 = 1 -
                 1/3 + 1/5, \cdots{}$ / 92 \\
                 \\
                 15. Jones. The First Use of $\pi$ for the Circle Ratio
                 (1706) / An excerpt from Jones' book, the Synopsis
                 Palmariorum Matheseos: or, a New Introduction to the
                 Mathematics, London, 1706 / 108 \\
                 \\
                 16. Newton. Of the Method of Fluxions and Infinite
                 Series (1737) / An excerpt giving Newton's calculation
                 of $\pi$ to 16 decimal places / 110 \\
                 \\
                 17. Euler. Chapter 10 of Introduction to Analysis of
                 the Infinite (On the Use of the Discovered Fractions to
                 Sum Infinite Series) (1748) / This includes many of
                 Euler's infinite series for $\pi$ and powers of $\pi$ /
                 112 \\
                 \\
                 18. Lambert. M{\'e}moire Sur Quelques
                 Propri{\'e}t{\'e}s Remarquables Des Quantit{\'e}s
                 Transcendentes Circulaires et Logarithmiques (1761) /
                 An excerpt from Lambert's original proof of the
                 irrationality of $\pi$ / 129 \\
                 \\
                 19. Lambert. Irrationality of $\pi$ (1969) / A
                 translation and Struik's discussion of Lambert's proof
                 of the irrationality of $\pi$ / 141 \\
                 \\
                 20. Shanks. Contributions to Mathematics Comprising
                 Chiefly of the Rectification of the Circle to 607
                 Places of Decimals (1853) / Pages from Shank's report
                 of his monumental hand calculation of $\pi$ / 147 \\
                 \\
                 21. Hermite. Sur La Fonction Exponentielle (1873) / The
                 first proof of the transcendence of $e$ / 162 \\
                 \\
                 22. Lindemann. Ueber die Zahl $\pi$ (1882) / The first
                 proof of the transcendence of $\pi$ / 194 \\
                 \\
                 23. Weierstrass. Zu Lindemann's Abhandlung ``Uber die
                 Ludolphsche Zahl'' (1885) / Weierstrass' proof of the
                 transcendence of $\pi$ / 207 \\
                 \\
                 24. Hilbert. Ueber die Trancendenz der Zahlen $e$ und
                 $\pi$ (1893) / Hilbert's short and elegant
                 simplification of the transcendence proofs for $e$ and
                 $\pi$ / 226 \\
                 \\
                 25. Goodwin. Quadrature of the Circle (1894) / The
                 dubious origin of the attempted legislation of the
                 value of $\pi$ in Indiana / 230 \\
                 \\
                 26. Edington. House Bill No. 246, Indiana State
                 Legislature, 1897 (1935) / A summary of the action
                 taken by the Indiana State Legislature to fix the value
                 of $\pi$ (including a copy of the actual bill that was
                 proposed) / 231 \\
                 \\
                 27. Singmaster. The Legal Values of Pi (1985) / A
                 history of the attempt by Indiana to legislate the
                 value of $\pi$ / 236 \\
                 \\
                 28. Ramanujan. Squaring the Circle (1913) / A geometric
                 approximation to $\pi$ / 240 \\
                 \\
                 29. Ramanujan. Modular Equations and Approximations to
                 $\pi$ (1914) / Ramanujan's seminal paper on $\pi$ that
                 includes a number of striking series and algebraic
                 approximations / 241 \\
                 \\
                 30. Watson. The Marquis and the Land Agent: A Tale of
                 the Eighteenth Century (1933) / A Presidential address
                 to the Mathematical Association in which the author
                 gives an account of ``some of the elementary work on
                 arcs and ellipses and other curves which led up to the
                 idea of inverting an elliptic integral, and so laying
                 the foundations of elliptic functions and doubly
                 periodic functions generally.'' / 258 \\
                 \\
                 31. Ballantine. The Best (?) Formula for Computing
                 $\pi$ to a Thousand Places (1939) / An early attempt to
                 orchestrate the calculation of $\pi$ more cleverly /
                 271 \\
                 \\
                 32. Birch. An Algorithm for Construction of Arctangent
                 Relations (1946) / The object of this note is to
                 express $\pi / 4 $ as a sum of arctan relations in
                 powers of 10 / 274 \\
                 \\
                 33. Niven. A Simple Proof that $\pi$ Is Irrational
                 (1947) / A very concise proof of the irrationality of
                 $\pi$ / 276 \\
                 \\
                 34. Reitwiesner. An ENIAC Determination of $\pi$ and
                 $e$ to 2000 Decimal Places (1950) / One of the first
                 computer-based computations / 277 \\
                 \\
                 35. Schepler. The Chronology of Pi (1950) / A fairly
                 reliable outline of the history of $\pi$ from 3000 BC
                 to 1949 / 282 \\
                 \\
                 36. Mahler. On the Approximation of $\pi$ (1953) /
                 ``The aim of this paper is to determine an explicit
                 lower bound free of unknown constants for the distance
                 of $\pi$ from a given rational or algebraic number'' /
                 306 \\
                 \\
                 37. Wrench, Jr. The Evolution of Extended Decimal
                 Approximations to $\pi$ (1960) / A history of the
                 calculation of the digits of $\pi$ to 1960 \\
                 \\
                 38. Shanks and Wrench, Jr. Calculation of $\pi$ to
                 100,000 Decimals (1962) / A landmark computation of
                 $\pi$ to more than 100,000 places / 326 \\
                 \\
                 39. Sweeny. On the Computation of Euler's Constant
                 (1963) / The computation of Euler's constant to 3566
                 decimal places / 350 \\
                 \\
                 40. Baker. Approximations to the Logarithms of Certain
                 Rational Numbers (1964) / The main purpose of this deep
                 and fundamental paper is to ``deduce results concerning
                 the accuracy with which the natural logarithms of
                 certain rational numbers may be approximated by
                 rational numbers, or, more generally, by algebraic
                 numbers of bounded degree.'' / 359 \\
                 \\
                 41. Adams. Asymptotic Diophantine Approximations to $E$
                 (1966) / An asymptotic estimate for the rational
                 approximation to $e$ which disproves the conjecture
                 that $e$ behaves like almost all numbers in this
                 respect / 368 \\
                 \\
                 42. Mahler. Applications of Some Formulae by Hermite to
                 the Approximations of Exponentials of Logarithms (1967)
                 / An important extension of Hilbert's approach to the
                 study of transcendence / 372 \\
                 \\
                 43. Eves. In Mathematical Circles; A Selection of
                 Mathematical Stories and Anecdotes (excerpt) (1969) / A
                 collection of mathematical stories and anecdotes about
                 $\pi$ / 400 \\
                 \\
                 44. Eves. Mathematical Circles Revisited; A Second
                 Collection of Mathematical Stories and Anecdotes
                 (excerpt) (1971) / A further collection of mathematical
                 stories and anecdotes about $\pi$ / 402 \\
                 \\
                 45. Todd. The Lemniscate Constants (1975) / A unifying
                 account of some of the methods used for computing the
                 lemniscate constants / 412 \\
                 \\
                 46. Salamin. Computation of r Using
                 Arithmetic-Geometric Mean (1976) / The first
                 quadratically converging algorithm for $\pi$ based on
                 Gauss's AGM and on Legendre's relation for elliptic
                 integrals / 418 \\
                 \\
                 47. Brent. Fast Multiple-Precision Evaluation of
                 Elementary Functions (1976) / ``This paper contains the
                 `Gauss-Legendre' method and some different algorithms
                 for log and exp (using Landen transformations).'' / 424
                 \\
                 \\
                 48. Beukers. A Note on the Irrationality of $\zeta(2)$
                 and $\zetq(3)$ (1979) / A short and elegant recasting
                 of Ap{\'e}ry's proof of the irrationality of $\zeta(3)$
                 (and $\zeta(2)$) / 434 \\
                 \\
                 49. van der Poorten. A Proof that Euler Missed \ldots{}
                 Ap{\'e}ry's Proof of the Irrationality of $\zeta(3)$
                 (1979) / An illuminating account of Ap{\'e}ry's
                 astonishing proof of the irrationality of $\zeta(3)$ /
                 439 \\
                 \\
                 50. Brent and McMillan. Some New Algorithms for
                 High-Precision Computation of Euler's Constant (1980) /
                 Several new algorithms for high precision calculation
                 of Euler's constant, including one which was used to
                 compute 30,100 decimal places / 448 \\
                 \\
                 51. Apostol. A Proof that Euler Missed: Evaluating
                 $\zeta(2)$ the Easy Way (1983) / This note shows that
                 one of the double integrals considered by Beukers ([48]
                 in the table of contents) can be used to establish
                 directly that $\zeta(2) = \pi / 6$ / 456 \\
                 \\
                 52. O'Shaughnessy. Putting God Back in Math (1983) / An
                 article about the Institute of Pi Research, an
                 organization that ``pokes fun at creationists by
                 pointing out that even the Bible makes mistakes.'' /
                 458 \\
                 \\
                 53. Stern. A Remarkable Approximation to $\pi$ (1985) /
                 Justification of the value of $\pi$ in the Bible
                 through numerological interpretations / 460 \\
                 \\
                 54. Newman and Shanks. On a Sequence Arising in Series
                 for $\pi$ (1984) / More connections between $\pi$ and
                 modular equations / 462 \\
                 \\
                 55. Cox. The Arithmetic-Geometric Mean of Gauss (1984)
                 / An extensive study of the complex analytic properties
                 of the AGM / 481 \\
                 \\
                 56. Borwein and Borwein. The Arithmetic-Geometric Mean
                 and Fast Computation of Elementary Functions (1984) /
                 The relationship between the AGM iteration and fast
                 computation of elementary functions (one of the
                 by-products is an algorithm for $\pi$) / 537 \\
                 \\
                 57. Newman. A Simplified Version of the Fast Algorithms
                 of Brent and Salamin (1984) / Elementary algorithms for
                 evaluating $e^x$ and $\pi$ using the Gauss AGM without
                 explicit elliptic function theory / 553 \\
                 \\
                 58. Wagon. Is Pi Normal? (1985) / A discussion of the
                 conjecture that $\pi$ has randomly distributed digits /
                 557 \\
                 \\
                 59. Keith. Circle Digits: A Self-Referential Story
                 (1986) / A mnemonic for the first 402 decimal places of
                 $\pi$ / 560 \\
                 \\
                 60. Bailey. The Computation of $\pi$ to 29,360,000
                 Decimal Digits Using Borweins' Quartically Convergent
                 Algorithm (1988) / The algorithms used, both for $\pi$
                 and for performing the required multiple-precision
                 arithmetic / 562 \\
                 \\
                 61. Kanada. Vectorization of Multiple-Precision
                 Arithmetic Program and 201,326,000 Decimal Digits of 1
                 Calculation (1988) / Details of the computation and
                 statistical tests of the first 200 million digits of
                 $\pi$ / 576 \\
                 \\
                 62. Borwein and Borwein. Ramanujan and Pi (1988) / This
                 article documents Ramanujan's life, his ingenious
                 approach to calculating $\pi$, and how his approach is
                 now incorporated into modern computer algorithms / 588
                 \\
                 \\
                 63. Chudnovsky and Chudnovsky. Approximations and
                 Complex Multiplication According to Ramanujan (1988) /
                 This excerpt describes ``Ramanujan's original quadratic
                 period--quasiperiod relations for elliptic curves with
                 complex multiplication and their applications to
                 representations of fractions of $\pi$ and other
                 logarithms in terms of rapidly convergent nearly
                 integral (hypergeometric) series.'' / 596 \\
                 \\
                 64. Borwein, Borwein and Bailey. Ramanujan, Modular
                 Equations, and Approximations to Pi or How to Compute
                 One Billion Digits of Pi (1989) / An exposition of the
                 computation of $\pi$ using mathematics rooted in
                 Ramanujan's work / 623 \\
                 \\
                 65. Borwein, Borwein and Dilcher. Pi, Euler Numbers,
                 and Asymptotic Expansions (1989) / An explanation as to
                 why the slowly convergent Gregory series for $\pi$,
                 truncated at 500,000 terms, gives $\pi$ to 40 places
                 with only the 6th, 17th, 18th, and 29th places being
                 incorrect / 642 \\
                 \\
                 66. Beukers, B{\'e}zivin, and Robba. An Alternative
                 Proof of the Lindemann--Weierstrass Theorem (1990) /
                 The Lindemann--Weierstrass theorem as a by-product of a
                 criterion for rationality of solutions of differential
                 equations / 649 \\
                 \\
                 67. Webster. The Tail of Pi (1991) / Various anecdotes
                 about $\pi$ from the 14th annual IMO Lecture to the
                 Royal Society / 654 \\
                 \\
                 68. Eco. An excerpt from Foucault's Pendulum (1993) /
                 ``The unnumbered perfection of the circle itself.'' /
                 658 \\
                 \\
                 69. Keith. Pi Mnemonics and the Art of Constrained
                 Writing (1996) / A mnemonic for $\pi$ based on Edgar
                 Allen Poe's poem ``The Raven.'' / 659 \\
                 \\
                 70. Bailey, Borwein, and Plouffe. On the Rapid
                 Computation of Various Polylogarithmic Constants (1996)
                 / A fast method for computing individual digits of
                 $\pi$ in base 2 / 663 \\
                 Appendix I --- On the Early History of Pi / 677 \\
                 \\
                 Appendix II --- A Computational Chronology of Pi / 683
                 \\
                 \\
                 Appendix III --- Selected Formulae for Pi / 686 \\
                 \\
                 Appendix IV --- Translations of Vi{\`e}te and Huygens /
                 690 \\
                 Bibliography / 711 \\
                 \\
                 Credits / 717 \\
                 \\
                 Index / 721",
}


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filename: elefunt.bib
label: Cocolicchio:2000:ASF
editor: Decio Cocolicchio and G. Dattoli and H. M. Srivastava
volume: 1
publisher: Aracne
address: Roma, Italy
edition: 1.
pages: 336
year: 2000
ISBN: 88-7999-265-X OR 887999265X
ISBN13: 978-88-7999-265-7 OR 9788879992657
LCCN: QA351 .A38 2000
bibdate: Sat Oct 30 19:16:34 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 19:16:34 MDT
series: Proceedings of the Melfi school on advanced topics in mathematics and physics
subject: Functions, Special; Congresses
acknowledgement: ack-nhfb
raweditor: Decio Cocolicchio and G. Dattoli and H. M. Srivastava
booktitle:
Advanced special functions and applications: proceedings of the workshop: Melfi (PZ), Italy, 9--12 May 1999

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  editor =       "Decio Cocolicchio and G. Dattoli and H. M.
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  booktitle =    "{Advanced special functions and applications:
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  title =        "{Advanced special functions and applications:
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                 May 1999}",
  volume =       "1",
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  bibdate =      "Sat Oct 30 19:16:34 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
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  series =       "Proceedings of the Melfi school on advanced topics in
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  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Congresses",
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filename: elefunt.bib
label: Dunkl:2000:PIW
editor: Charles Dunkl and Mourad Ismail and Roderick Wong
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title: Proceedings of the international workshop, special functions: Hong Kong, 21--25 June 1999
publisher: pub-WORLD-SCI
address: pub-WORLD-SCI:adr
pages: xi + 438
year: 2000
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rawbooktitle: {Proceedings of the international workshop, special functions: Hong Kong, 21--25 June 1999}
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  editor =       "Charles Dunkl and Mourad Ismail and Roderick Wong",
  booktitle =    "{Proceedings of the international workshop, special
                 functions: Hong Kong, 21--25 June 1999}",
  title =        "{Proceedings of the international workshop, special
                 functions: Hong Kong, 21--25 June 1999}",
  publisher =    pub-WORLD-SCI,
  address =      pub-WORLD-SCI:adr,
  pages =        "xi + 438",
  year =         "2000",
  ISBN =         "981-02-4393-6",
  ISBN-13 =      "978-981-02-4393-7",
  LCCN =         "QA351 .P76 2000",
  bibdate =      "Fri Jul 09 06:30:25 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Sprague:2000:PAH
editor: Ralph H. Sprague
publisher: pub-IEEE
address: pub-IEEE:adr
pages: liv + 259
year: 2000
ISBN: 0-7695-0493-0, 0-7695-0494-9, 0-7695-0495-7 OR 0769504930, 0769504949, 0769504957
LCCN: TA168 .H37 2000; TA168 .H37 2000xeb; TA168
bibdate: Sun Mar 4 21:23:42 MST 2007
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; melvyl.cdlib.org:210/CDL90
bibtimestamp: 2007.03.04 21:23:42 MST
remark: IEEE Computer Society Order Number: PR00493
subject: Systems engineering; Congresses; Information theory; Electronic data processing; System design
acknowledgement: ack-nhfb
raweditor: Ralph H. Sprague
booktitle:
Proceedings of the 33rd Annual Hawaii International Conference on System Sciences: abstracts and CD-ROM of full papers: January 4--7, 2000, Maui, Hawaii

title:
Proceedings of the 33rd Annual Hawaii International Conference on System Sciences: abstracts and CD-ROM of full papers: January 4--7, 2000, Maui, Hawaii

ISBN13:
978-0-7695-0493-3, 978-0-7695-0494-0, 978-0-7695-0495-7 OR 9780769504933, 9780769504940, 9780769504957

rawbooktitle:
{Proceedings of the 33rd Annual Hawaii International Conference on System Sciences: abstracts and CD-ROM of full papers: January 4--7, 2000, Maui, Hawaii}

rawtitle:
{Proceedings of the 33rd Annual Hawaii International Conference on System Sciences: abstracts and CD-ROM of full papers: January 4--7, 2000, Maui, Hawaii}

entry:
@Proceedings{Sprague:2000:PAH,
  editor =       "Ralph H. Sprague",
  booktitle =    "{Proceedings of the 33rd Annual Hawaii International
                 Conference on System Sciences: abstracts and CD-ROM of
                 full papers: January 4--7, 2000, Maui, Hawaii}",
  title =        "{Proceedings of the 33rd Annual Hawaii International
                 Conference on System Sciences: abstracts and CD-ROM of
                 full papers: January 4--7, 2000, Maui, Hawaii}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "liv + 259",
  year =         "2000",
  ISBN =         "0-7695-0493-0, 0-7695-0494-9, 0-7695-0495-7",
  ISBN-13 =      "978-0-7695-0493-3, 978-0-7695-0494-0,
                 978-0-7695-0495-7",
  LCCN =         "TA168 .H37 2000; TA168 .H37 2000xeb; TA168",
  bibdate =      "Sun Mar 4 21:23:42 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "Hawaii International Conference on System Sciences
                 (33rd: 2000: Maui, Hawaii)",
  remark =       "IEEE Computer Society Order Number: PR00493",
  subject =      "Systems engineering; Congresses; Information theory;
                 Electronic data processing; System design",
}


bibtype: proceedings
filename: elefunt.bib
label: Banerji:2001:SFS
editor: P. K. Banerji
address: Jodhpur, India
pages: 258
year: 2001
ISBN: 81-7233-267-X OR 817233267X
ISBN13: 978-81-7233-267-9 OR 9788172332679
LCCN: QA351 .S665 2001
bibdate: Sat Oct 30 19:13:10 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 19:13:10 MDT
subject: Functions, Special; Congresses
acknowledgement: ack-nhfb
raweditor: P. K. Banerji
booktitle:
Special functions: selected articles: proceedings of the First National Conference of the Society for Special Functions and their Applications, March 3--4, 2000, Jodhpur, India

title:
Special functions: selected articles: proceedings of the First National Conference of the Society for Special Functions and their Applications, March 3--4, 2000, Jodhpur, India

publisher:
Published by Scientific Publishers (India) for the Society for Special Functions and their Applications

rawbooktitle:
{Special functions: selected articles: proceedings of the First National Conference of the Society for Special Functions and their Applications, March 3--4, 2000, Jodhpur, India}

rawtitle:
{Special functions: selected articles: proceedings of the First National Conference of the Society for Special Functions and their Applications, March 3--4, 2000, Jodhpur, India}

entry:
@Proceedings{Banerji:2001:SFS,
  editor =       "P. K. Banerji",
  booktitle =    "{Special functions: selected articles: proceedings of
                 the First National Conference of the Society for
                 Special Functions and their Applications, March 3--4,
                 2000, Jodhpur, India}",
  title =        "{Special functions: selected articles: proceedings of
                 the First National Conference of the Society for
                 Special Functions and their Applications, March 3--4,
                 2000, Jodhpur, India}",
  publisher =    "Published by Scientific Publishers (India) for the
                 Society for Special Functions and their Applications",
  address =      "Jodhpur, India",
  pages =        "258",
  year =         "2001",
  ISBN =         "81-7233-267-X",
  ISBN-13 =      "978-81-7233-267-9",
  LCCN =         "QA351 .S665 2001",
  bibdate =      "Sat Oct 30 19:13:10 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Congresses",
}


bibtype: proceedings
filename: elefunt.bib
label: Burgess:2001:ISC
editor: N. Burgess and L. Ciminiera
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xii + 285
year: 2001
ISBN: 0-7695-1150-3; 0-7695-1152-X OR 0769511503; 076951152X
ISBN13: 978-0-7695-1150-4; 978-0-7695-1152-8 OR 9780769511504; 9780769511528
ISSN: 1063-6889 OR 10636889
LCCN: QA76.9.C62 S95 2001
bibdate: Fri May 03 14:20:49 2002
bibtimestamp: 2002.05.03 14:20:49 ???
note: IEEE order no. PR01150.
keywords: ARITH-15
acknowledgement: ack-nhfb
raweditor: N. Burgess and L. Ciminiera
rawnote: IEEE order no. PR01150.
booktitle:
15th IEEE Symposium on Computer Arithmetic: ARITH-15 2001: proceedings: Vail, Colorado, 11--13 June, 2001

title:
15th IEEE Symposium on Computer Arithmetic: ARITH-15 2001: proceedings: Vail, Colorado, 11--13 June, 2001

rawbooktitle:
{15th IEEE Symposium on Computer Arithmetic: ARITH-15 2001: proceedings: Vail, Colorado, 11--13 June, 2001}

rawtitle:
{15th IEEE Symposium on Computer Arithmetic: ARITH-15 2001: proceedings: Vail, Colorado, 11--13 June, 2001}

entry:
@Proceedings{Burgess:2001:ISC,
  editor =       "N. Burgess and L. Ciminiera",
  booktitle =    "{15th IEEE Symposium on Computer Arithmetic: ARITH-15
                 2001: proceedings: Vail, Colorado, 11--13 June, 2001}",
  title =        "{15th IEEE Symposium on Computer Arithmetic: ARITH-15
                 2001: proceedings: Vail, Colorado, 11--13 June, 2001}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 285",
  year =         "2001",
  ISBN =         "0-7695-1150-3; 0-7695-1152-X",
  ISBN-13 =      "978-0-7695-1150-4; 978-0-7695-1152-8",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62 S95 2001",
  bibdate =      "Fri May 03 14:20:49 2002",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "IEEE order no. PR01150.",
  price =        "US\$145",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-15",
  xxnote =       "Check dates: 11--13 or 11--17??",
  xxtitle =      "Computer Arithmetic: Papers presented at the {15th
                 IEEE Symposium on Computer Arithmetic (Arith-15 2001),
                 11--17 June, 2001, Vail, CO}",
}


bibtype: book
filename: elefunt.bib
label: Garvan:2001:SCN
editor: Frank (Frank G.) Garvan and Mourad Ismail
booktitle: Symbolic Computation, Number Theory, Special Functions, Physics, and Combinatorics
title: Symbolic Computation, Number Theory, Special Functions, Physics, and Combinatorics
volume: 4
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: x + 283
year: 2001
ISBN: 1-4020-0101-0 OR 1402001010
ISBN13: 978-1-4020-0101-7 OR 9781402001017
LCCN: QA295 .S86 2001
bibdate: Sat Oct 30 17:31:50 MDT 2010
bibtimestamp: 2010.10.30 17:31:50 MDT
series: Developments in mathematics
acknowledgement: ack-nhfb
rawbooktitle: Symbolic Computation, Number Theory, Special Functions, Physics, and Combinatorics
raweditor: Frank (Frank G.) Garvan and Mourad Ismail
rawtitle: Symbolic Computation, Number Theory, Special Functions, Physics, and Combinatorics
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager

subject:
q-series; Congresses; Algebra; Data processing; Number theory; Functions, Special; Mathematical physics; Combinatorial analysis

TOC:
Preface Participants Gaussian hypergeometric series and combinatorial congruences / Scott Ahlgren / 1--12 A double bounded key identity for Gollnitz's (BIG) partition theorem / Krishnaswami Alladi and Alexander Berkovich / 13--32 Engel expansions of q-series by computer algebra / George E. Andrews, Arnold Knopfmacher and Peter Paule / [and others] / 33--57 Sums of squares and the preservation of modularity under congruence restrictions / Paul T. Bateman, Boris A. Datskovsky and Marvin I. Knopp / 59--71 On the transformation formula for the Dedekind eta-function / Bruce C. Berndt and K. Venkatachaliengar / 73--77 Experiments and discoveries in q-trigonometry / R. Wm. Gosper / 79--105 Algebraic consequences of Jacobi's two- and four-square theorems / Michael D. Hirschhorn and James A. McGowan / 107--132 The Borweins' Cubic Theta Functions and q-Elliptic Functions / Richard Lewis, Zhi-Guo Liu / 133--145 Some Eisenstein Series Identities Associated with the Borwein Functions / Zhi-Guo Liu / 147--169 Hankel Determinants of Eisenstein Series / Stephen C. Milne / 171--188 Jacobi's Identity and Two K3-Surfaces / Maki Murata / 189--198 $q$-Random Matrix Ensembles / K. A. Muttalib, Y. Chen, M. E. H. Ismail / 199--221 Differential Endomorphisms for Modular Forms On $Gamma _0(4)$ / Ken Ono / 223--229 On the Asymptotics of Takeuchi Numbers / Thomas Prellberg / 231--242 Fine-Tuning Zeilberger's Algorithm / Axel Riese / 243--254 Gaussian Integrals and the Rogers--Ramanujan Identities / D. Stanton / 255--265 Some Remarks on a Product Expansion / M. V. Subbarao, A. Verma / 267--283 Back Matter / 285--285

rawTOC:
Preface \\ Participants \\ Gaussian hypergeometric series and combinatorial congruences / Scott Ahlgren / 1--12 \\ A double bounded key identity for Gollnitz's (BIG) partition theorem / Krishnaswami Alladi and Alexander Berkovich / 13--32 \\ Engel expansions of q-series by computer algebra / George E. Andrews, Arnold Knopfmacher and Peter Paule / [and others] / 33--57 \\ Sums of squares and the preservation of modularity under congruence restrictions / Paul T. Bateman, Boris A. Datskovsky and Marvin I. Knopp / 59--71 \\ On the transformation formula for the Dedekind eta-function / Bruce C. Berndt and K. Venkatachaliengar / 73--77 \\ Experiments and discoveries in q-trigonometry / R. Wm. Gosper / 79--105 \\ Algebraic consequences of Jacobi's two- and four-square theorems / Michael D. Hirschhorn and James A. McGowan / 107--132 \\ The Borweins' Cubic Theta Functions and q-Elliptic Functions / Richard Lewis, Zhi-Guo Liu / 133--145 \\ Some Eisenstein Series Identities Associated with the Borwein Functions / Zhi-Guo Liu / 147--169 \\ Hankel Determinants of Eisenstein Series / Stephen C. Milne / 171--188 \\ Jacobi's Identity and Two K3-Surfaces / Maki Murata / 189--198 \\ $q$-Random Matrix Ensembles / K. A. Muttalib, Y. Chen, M. E. H. Ismail / 199--221 \\ Differential Endomorphisms for Modular Forms On $\Gamma_0(4)$ / Ken Ono / 223--229 \\ On the Asymptotics of Takeuchi Numbers / Thomas Prellberg / 231--242 \\ Fine-Tuning Zeilberger's Algorithm / Axel Riese / 243--254 \\ Gaussian Integrals and the Rogers--Ramanujan Identities / D. Stanton / 255--265 \\ Some Remarks on a Product Expansion / M. V. Subbarao, A. Verma / 267--283 \\ Back Matter / 285--285

entry:
@Book{Garvan:2001:SCN,
  editor =       "Frank (Frank G.) Garvan and Mourad Ismail",
  booktitle =    "Symbolic Computation, Number Theory, Special
                 Functions, Physics, and Combinatorics",
  title =        "Symbolic Computation, Number Theory, Special
                 Functions, Physics, and Combinatorics",
  volume =       "4",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "x + 283",
  year =         "2001",
  ISBN =         "1-4020-0101-0",
  ISBN-13 =      "978-1-4020-0101-7",
  LCCN =         "QA295 .S86 2001",
  bibdate =      "Sat Oct 30 17:31:50 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/borwein-jonathan-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "Developments in mathematics",
  acknowledgement = ack-nhfb,
  subject =      "q-series; Congresses; Algebra; Data processing; Number
                 theory; Functions, Special; Mathematical physics;
                 Combinatorial analysis",
  tableofcontents = "Preface \\
                 Participants \\
                 Gaussian hypergeometric series and combinatorial
                 congruences / Scott Ahlgren / 1--12 \\
                 A double bounded key identity for Gollnitz's (BIG)
                 partition theorem / Krishnaswami Alladi and Alexander
                 Berkovich / 13--32 \\
                 Engel expansions of q-series by computer algebra /
                 George E. Andrews, Arnold Knopfmacher and Peter Paule /
                 [and others] / 33--57 \\
                 Sums of squares and the preservation of modularity
                 under congruence restrictions / Paul T. Bateman, Boris
                 A. Datskovsky and Marvin I. Knopp / 59--71 \\
                 On the transformation formula for the Dedekind
                 eta-function / Bruce C. Berndt and K. Venkatachaliengar
                 / 73--77 \\
                 Experiments and discoveries in q-trigonometry / R. Wm.
                 Gosper / 79--105 \\
                 Algebraic consequences of Jacobi's two- and four-square
                 theorems / Michael D. Hirschhorn and James A. McGowan /
                 107--132 \\
                 The Borweins' Cubic Theta Functions and q-Elliptic
                 Functions / Richard Lewis, Zhi-Guo Liu / 133--145 \\
                 Some Eisenstein Series Identities Associated with the
                 Borwein Functions / Zhi-Guo Liu / 147--169 \\
                 Hankel Determinants of Eisenstein Series / Stephen C.
                 Milne / 171--188 \\
                 Jacobi's Identity and Two K3-Surfaces / Maki Murata /
                 189--198 \\
                 $q$-Random Matrix Ensembles / K. A. Muttalib, Y. Chen,
                 M. E. H. Ismail / 199--221 \\
                 Differential Endomorphisms for Modular Forms On
                 $\Gamma_0(4)$ / Ken Ono / 223--229 \\
                 On the Asymptotics of Takeuchi Numbers / Thomas
                 Prellberg / 231--242 \\
                 Fine-Tuning Zeilberger's Algorithm / Axel Riese /
                 243--254 \\
                 Gaussian Integrals and the Rogers--Ramanujan Identities
                 / D. Stanton / 255--265 \\
                 Some Remarks on a Product Expansion / M. V. Subbarao,
                 A. Verma / 267--283 \\
                 Back Matter / 285--285",
}


