# bibtab

bibtype: proceedings
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 ???
acknowledgement: ack-nhfb
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)

rawbooktitle:
{Deuxi{\`e}mes journ{\'e}es 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)}

rawtitle:
{Deuxi{\`e}mes journ{\'e}es 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)}

entry:
@Proceedings{EC2:1992:DJN,
  key =          "AEF'92",
  booktitle =    "{Deuxi{\`e}mes journ{\'e}es 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 =        "{Deuxi{\`e}mes journ{\'e}es 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)}",
  publisher =    "EC2",
  address =      "Nanterre Cedex, France",
  pages =        "384",
  year =         "1992",
  ISBN =         "2-906899-78-X",
  ISBN-13 =      "978-2-906899-78-0",
  LCCN =         "????",
  bibdate =      "Wed Jan 10 07:40:53 1996",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Richards:1992:HFD
editor: Donald St P. Richards
volume: 138
publisher: pub-AMS
address: pub-AMS:adr
pages: x + 259
year: 1992
ISBN: 0-8218-5159-4 OR 0821851594
ISBN13: 978-0-8218-5159-3 OR 9780821851593
ISSN: 0271-4132 (print), 1098-3627 (electronic) OR 02714132 (print), 10983627 (electronic)
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
bibtimestamp: 2010.10.30 21:12:24 MDT
series: Contemporary mathematics
subject: Hypergeometric functions; Congresses
acknowledgement: ack-nhfb
raweditor: Donald St P. Richards
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

title:
Hypergeometric functions on domains of positivity, Jack polynomials, and applications: proceedings of an AMS Special Session held March 22--23, 1991 in Tampa, Florida

rawbooktitle:
{Hypergeometric functions on domains of positivity, Jack polynomials, and applications: proceedings of an AMS Special Session held March 22--23, 1991 in Tampa, Florida}

rawtitle:
{Hypergeometric functions on domains of positivity, Jack polynomials, and applications: proceedings of an AMS Special Session held March 22--23, 1991 in Tampa, Florida}

entry:
@Proceedings{Richards:1992:HFD,
  editor =       "Donald St P. Richards",
  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}",
  title =        "{Hypergeometric functions on domains of positivity,
                 Jack polynomials, and applications: proceedings of an
                 AMS Special Session held March 22--23, 1991 in Tampa,
                 Florida}",
  volume =       "138",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "x + 259",
  year =         "1992",
  ISBN =         "0-8218-5159-4",
  ISBN-13 =      "978-0-8218-5159-3",
  ISSN =         "0271-4132 (print), 1098-3627 (electronic)",
  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",
  series =       "Contemporary mathematics",
  acknowledgement = ack-nhfb,
  subject =      "Hypergeometric functions; Congresses",
}


bibtype: book
filename: elefunt.bib
label: Adams:1993:ACA
editor: E. Adams and U. Kulisch
booktitle: Scientific Computing with Automatic Result Verification
title: Scientific Computing with Automatic Result Verification
volume: 189
publisher: pub-ACADEMIC
address: pub-ACADEMIC:adr
pages: x + 612
year: 1993
ISBN: 0-12-044210-8 OR 0120442108
ISBN13: 978-0-12-044210-2 OR 9780120442102
LCCN: QA76.S368 1993
bibdate: Mon Jan 13 09:58:58 1997
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1997.01.13 09:58:58 ???
series: Mathematics in science and engineering
acknowledgement: ack-nhfb
rawbooktitle: Scientific Computing with Automatic Result Verification
raweditor: E. Adams and U. Kulisch
rawtitle: Scientific Computing with Automatic Result Verification
TOC:
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

rawTOC:
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

entry:
@Book{Adams:1993:ACA,
  editor =       "E. Adams and U. Kulisch",
  booktitle =    "Scientific Computing with Automatic Result
                 Verification",
  title =        "Scientific Computing with Automatic Result
                 Verification",
  volume =       "189",
  publisher =    pub-ACADEMIC,
  address =      pub-ACADEMIC:adr,
  pages =        "x + 612",
  year =         "1993",
  ISBN =         "0-12-044210-8",
  ISBN-13 =      "978-0-12-044210-2",
  LCCN =         "QA76.S368 1993",
  bibdate =      "Mon Jan 13 09:58:58 1997",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Mathematics in science and engineering",
  acknowledgement = ack-nhfb,
  tableofcontents = "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",
}


bibtype: proceedings
filename: elefunt.bib
label: Albrecht:1993:VNT
editor: R. Albrecht and G. Alefeld and H. J. Stetter
booktitle: Validation numerics: theory and applications
title: Validation numerics: theory and applications
volume: 9
publisher: pub-SPRINGER-WIEN
address: pub-SPRINGER-WIEN:adr
pages: 291
year: 1993
CODEN: COSPDM
ISBN: 0-387-82451-0 (New York), 3-211-82451-0 (Vienna) OR 0387824510 (New York), 3211824510 (Vienna)
ISSN: 0344-8029 OR 03448029
LCCN: QA297 .V27 1993
bibdate: Wed Oct 13 18:45:11 1999
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 1999.10.13 18:45:11 ???
note: Dedicated to Ulrich Kulisch on the occasion of his 60th birthday.
series: j-COMPUTING-SUPPLEMENTUM
keywords: convergence acceleration
acknowledgement: ack-nhfb
rawbooktitle: Validation numerics: theory and applications
raweditor: R. Albrecht and G. Alefeld and H. J. Stetter
rawnote: Dedicated to Ulrich Kulisch on the occasion of his 60th birthday.
rawtitle: Validation numerics: theory and applications
ISBN13:
978-0-387-82451-2 (New York), 978-3-211-82451-1 (Vienna) OR 9780387824512 (New York), 9783211824511 (Vienna)

entry:
@Proceedings{Albrecht:1993:VNT,
  editor =       "R. Albrecht and G. Alefeld and H. J. Stetter",
  booktitle =    "Validation numerics: theory and applications",
  title =        "Validation numerics: theory and applications",
  volume =       "9",
  publisher =    pub-SPRINGER-WIEN,
  address =      pub-SPRINGER-WIEN:adr,
  pages =        "291",
  year =         "1993",
  CODEN =        "COSPDM",
  ISBN =         "0-387-82451-0 (New York), 3-211-82451-0 (Vienna)",
  ISBN-13 =      "978-0-387-82451-2 (New York), 978-3-211-82451-1
                 (Vienna)",
  ISSN =         "0344-8029",
  LCCN =         "QA297 .V27 1993",
  bibdate =      "Wed Oct 13 18:45:11 1999",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Dedicated to Ulrich Kulisch on the occasion of his
                 60th birthday.",
  series =       j-COMPUTING-SUPPLEMENTUM,
  acknowledgement = ack-nhfb,
  keywords =     "convergence acceleration",
}


bibtype: proceedings
filename: elefunt.bib
label: Allasia:1993:PIJ
editor: G. Allasia and Luighi Gatteshi and Francesco Lerda
volume: 2(1/4)
publisher: Baltzer Science Publishers
address: Amsterdam, The Netherlands
pages: 474
year: 1993
ISSN: 1021-2655 OR 10212655
LCCN: QA297 A614 v. 2, no. 1/4
bibdate: Sat Oct 30 18:57:57 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 18:57:57 ???
series: Annals of numerical mathematics
acknowledgement: ack-nhfb
raweditor: G. Allasia and Luighi Gatteshi and Francesco Lerda
booktitle:
Proceedings of the International Joint Symposium on Special Functions and Artificial Intelligence, (1993: Turin, Italy)

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

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

entry:
@Proceedings{Allasia:1993:PIJ,
  editor =       "G. Allasia and Luighi Gatteshi and Francesco Lerda",
  booktitle =    "Proceedings of the International Joint Symposium on
                 Special Functions and Artificial Intelligence, (1993:
                 Turin, Italy)",
  title =        "Proceedings of the International Joint Symposium on
                 Special Functions and Artificial Intelligence, (1993:
                 Turin, Italy)",
  volume =       "2(1/4)",
  publisher =    "Baltzer Science Publishers",
  address =      "Amsterdam, The Netherlands",
  pages =        "474",
  year =         "1993",
  ISSN =         "1021-2655",
  LCCN =         "QA297 A614 v. 2, no. 1/4",
  bibdate =      "Sat Oct 30 18:57:57 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Annals of numerical mathematics",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Sincovec:1993:PSS
editor: Richard F. Sincovec and David E. Keyes and Michael R. Leuze
publisher: pub-SIAM
address: pub-SIAM:adr
pages: xix + 1041 + iv
year: 1993
ISBN: 0-89871-315-3 OR 0898713153
ISBN13: 978-0-89871-315-2 OR 9780898713152
LCCN: QA76.58 .S55 1993 v.1-2
bibdate: Tue Oct 11 12:21:40 1994
bibtimestamp: 1994.10.11 12:21:40 ???
note: Two volumes.
acknowledgement: ack-nhfb
raweditor: Richard F. Sincovec and David E. Keyes and Michael R. Leuze
rawnote: Two volumes.
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

bibsource:
https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

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

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

entry:
@Proceedings{Sincovec:1993:PSS,
  editor =       "Richard F. Sincovec and David E. Keyes and Michael R.
                 Leuze",
  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}",
  publisher =    pub-SIAM,
  address =      pub-SIAM:adr,
  pages =        "xix + 1041 + iv",
  year =         "1993",
  ISBN =         "0-89871-315-3",
  ISBN-13 =      "978-0-89871-315-2",
  LCCN =         "QA76.58 .S55 1993 v.1-2",
  bibdate =      "Tue Oct 11 12:21:40 1994",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/b/berger-marsha-j.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
}


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
year: 1993
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
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
bibtimestamp: 1994.09.01 22:58:49 ???
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)

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  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:
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  address =      pub-IEEE:adr,
  pages =        "various",
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  ISBN =         "0-8186-5050-8 (paper), 0-8186-5051-6 (microfiche)",
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  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

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@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",
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  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;
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                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
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  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)

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  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),
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                 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

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

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  booktitle =    "Conference record of the Twenty-Ninth Asilomar
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                 30--November 1, 1995 Pacific Grove, California",
  title =        "Conference record of the Twenty-Ninth Asilomar
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  note =         "Two volumes.",
  acknowledgement = ack-nhfb,
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bibtype: book
filename: elefunt.bib
label: Bartschat:1996:CAP
editor: Klaus Bartschat
booktitle: Computational Atomic Physics: Electron and Positron Collisions with Atoms and Ions
title: Computational Atomic Physics: Electron and Positron Collisions with Atoms and Ions
publisher: pub-SV
address: pub-SV:adr
pages: xviii + 249 + 13
year: 1996
DOI: https://doi.org/10.1007/978-3-642-61010-3
LCCN: QC794.6.C6 C655 1996
bibdate: Fri Apr 25 14:30:14 2025
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2025.04.25 14:30:14 ???
URL: https://link.springer.com/book/10.1007/978-3-642-61010-3
acknowledgement: ack-nhfb
rawbooktitle: Computational Atomic Physics: Electron and Positron Collisions with Atoms and Ions
raweditor: Klaus Bartschat
rawtitle: Computational Atomic Physics: Electron and Positron Collisions with Atoms and Ions
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TOC:
Front Matter / i--xvii Electron-Atom Scattering Theory: An Overview / Klaus Bartschat / 1--14 Core Potentials for Quasi One--Electron Systems / Klaus Bartschat / 15--26 Energies and Oscillator Strengths Using Configuration Interaction Wave Functions / Alan Hibbert / 27--64 The Distorted-Wave Method for Elastic Scattering and Atomic Excitation / Don H. Madison, Klaus Bartschat / 65--86 Distorted-Wave Methods for Ionization / Ian E. McCarthy, Xixiang Zhang / 87--100 The Close--Coupling Approximation / R. P. McEachran / 101--135 The R-Matrix Method / P. G. Burke, M. P. Scott / 137--159 Momentum-Space Convergent-Close-Coupling Method for a Model e--H Scattering Problem / Igor Bray, Andris Stelbovics / 161--180 The Calculation of Spherical Bessel and Coulomb Functions / A. R. Barnett / 181--202 Scattering Amplitudes for Electron--Atom Scattering / Klaus Bartschat / 203--217 Density Matrices: Connection Between Theory and Experiment / Klaus Bartschat / 219--246 Back Matter / 247--249

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Front Matter / i--xvii \\ Electron-Atom Scattering Theory: An Overview / Klaus Bartschat / 1--14 \\ Core Potentials for Quasi One--Electron Systems / Klaus Bartschat / 15--26 \\ Energies and Oscillator Strengths Using Configuration Interaction Wave Functions / Alan Hibbert / 27--64 \\ The Distorted-Wave Method for Elastic Scattering and Atomic Excitation / Don H. Madison, Klaus Bartschat / 65--86 \\ Distorted-Wave Methods for Ionization / Ian E. McCarthy, Xixiang Zhang / 87--100 \\ The Close--Coupling Approximation / R. P. McEachran / 101--135 \\ The R-Matrix Method / P. G. Burke, M. P. Scott / 137--159 \\ Momentum-Space Convergent-Close-Coupling Method for a Model e--H Scattering Problem / Igor Bray, Andris Stelbovics / 161--180 \\ The Calculation of Spherical Bessel and Coulomb Functions / A. R. Barnett / 181--202 \\ Scattering Amplitudes for Electron--Atom Scattering / Klaus Bartschat / 203--217 \\ Density Matrices: Connection Between Theory and Experiment / Klaus Bartschat / 219--246 \\ Back Matter / 247--249

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  editor =       "Klaus Bartschat",
  booktitle =    "Computational Atomic Physics: Electron and Positron
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  acknowledgement = ack-nhfb,
  tableofcontents = "Front Matter / i--xvii \\
                 Electron-Atom Scattering Theory: An Overview / Klaus
                 Bartschat / 1--14 \\
                 Core Potentials for Quasi One--Electron Systems / Klaus
                 Bartschat / 15--26 \\
                 Energies and Oscillator Strengths Using Configuration
                 Interaction Wave Functions / Alan Hibbert / 27--64 \\
                 The Distorted-Wave Method for Elastic Scattering and
                 Atomic Excitation / Don H. Madison, Klaus Bartschat /
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                 Distorted-Wave Methods for Ionization / Ian E.
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                 The Close--Coupling Approximation / R. P. McEachran /
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                 The R-Matrix Method / P. G. Burke, M. P. Scott /
                 137--159 \\
                 Momentum-Space Convergent-Close-Coupling Method for a
                 Model e--H Scattering Problem / Igor Bray, Andris
                 Stelbovics / 161--180 \\
                 The Calculation of Spherical Bessel and Coulomb
                 Functions / A. R. Barnett / 181--202 \\
                 Scattering Amplitudes for Electron--Atom Scattering /
                 Klaus Bartschat / 203--217 \\
                 Density Matrices: Connection Between Theory and
                 Experiment / Klaus Bartschat / 219--246 \\
                 Back Matter / 247--249",
}


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:
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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
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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

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  title =        "Quality of Numerical Software: Assessment and
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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.
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  title =        "13th {IEEE} Symposium on Computer Arithmetic:
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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:
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  subject =      "Array processors; Congresses; Signal processing;
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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{\'i}guez-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{\'i}nek \\ Radiation field integrals and their evaluation techniques / Shyam L. Kalla, H. G. Khajah \\ On the product of distributions / A. Kami{\'n}ski \\ 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{\'o}rnik \\ 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{\'o}rnik \\ 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{\`e}re \\ 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{\'i}guez-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{\'i}nek \\
                 Radiation field integrals and their evaluation
                 techniques / Shyam L. Kalla, H. G. Khajah \\
                 On the product of distributions / A. Kami{\'n}ski \\
                 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{\'o}rnik \\
                 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{\'o}rnik
                 \\
                 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{\`e}re \\
                 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",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  xxeditor =     "Frances M. Titsworth",
}


bibtype: proceedings
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
raweditor: Israel Koren and Peter Kornerup
rawnote: IEEE Computer Society Order Number PR00116. IEEE Order Plan Catalog Number 99CB36336.
rawtitle: 14th {IEEE} Symposium on Computer Arithmetic: proceedings: April 14--16, 1999, Adelaide, Australia
ISBN13:
978-0-7803-5609-2, 978-0-7695-0116-1, 978-0-7695-0118-5 OR 9780780356092, 9780769501161, 9780769501185

entry:
@Proceedings{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",
  ISBN-13 =      "978-0-7803-5609-2, 978-0-7695-0116-1,
                 978-0-7695-0118-5",
  ISSN =         "1063-6889",
  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",
  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.",
  source =       "Computer arithmetic",
  sponsor =      "IEEE.",
}


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
ISBN13: 978-0-8194-3293-3 OR 9780819432933
LCCN: TK5102.5 .A3325 1999; TK5102.5 .A3173 1999eb; TK5102.9 .A37 1999; TK5102.5; TS510 .S63
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:
Proceedings of {SPIE: Advanced signal processing algorithms, architectures, and implementations IX: 19--21 July, 1999, Denver, Colorado}

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

entry:
@Proceedings{Luk:1999:PSA,
  editor =       "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}",
  volume =       "3807",
  publisher =    pub-SPIE,
  address =      pub-SPIE:adr,
  pages =        "ix + 648",
  year =         "1999",
  ISBN =         "0-8194-3293-8",
  ISBN-13 =      "978-0-8194-3293-3",
  LCCN =         "TK5102.5 .A3325 1999; TK5102.5 .A3173 1999eb; TK5102.9
                 .A37 1999; TK5102.5; TS510 .S63",
  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",
  acknowledgement = ack-nhfb,
  subject =      "Signal processing; Digital techniques; Congresses;
                 Algorithms; Computer architecture",
}


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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  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",
}


bibtype: book
filename: elefunt.bib
label: Lide:2001:CEM
editor: David R. Lide
booktitle: A Century of Excellence in Measurements, Standards, and Technology
title: A Century of Excellence in Measurements, Standards, and Technology
volume: 958
publisher: pub-NIST
address: pub-NIST:adr
pages: ix + 386
year: 2001
bibdate: Fri Jul 09 06:29:11 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:29:11 ???
series: NIST special publication
acknowledgement: ack-nhfb
rawbooktitle: A Century of Excellence in Measurements, Standards, and Technology
raweditor: David R. Lide
rawtitle: A Century of Excellence in Measurements, Standards, and Technology
entry:
@Book{Lide:2001:CEM,
  editor =       "David R. Lide",
  booktitle =    "A Century of Excellence in Measurements, Standards,
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  title =        "A Century of Excellence in Measurements, Standards,
                 and Technology",
  volume =       "958",
  publisher =    pub-NIST,
  address =      pub-NIST:adr,
  pages =        "ix + 386",
  year =         "2001",
  bibdate =      "Fri Jul 09 06:29:11 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "NIST special publication",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Siafarikas:2001:PFI
editor: Panayiotis D. Siafarikas and Theodore Seio Chihara
volume: 133(1/2)
publisher: pub-ELSEVIER
address: pub-ELSEVIER:adr
pages: xxvii + 705
year: 2001
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
LCCN: QA76 J86 v. 133, no. 1/2
bibdate: Sat Oct 30 19:08:06 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:08:06 ???
series: Journal of computational and applied mathematics
acknowledgement: ack-nhfb
raweditor: Panayiotis D. Siafarikas and Theodore Seio Chihara
booktitle:
Proceedings of the Fifth International Symposium on Orthogonal Polynomials, Special Functions and their Applications: Patras, Greece, 20--24 September 1999

title:
Proceedings of the Fifth International Symposium on Orthogonal Polynomials, Special Functions and their Applications: Patras, Greece, 20--24 September 1999

rawbooktitle:
{Proceedings of the Fifth International Symposium on Orthogonal Polynomials, Special Functions and their Applications: Patras, Greece, 20--24 September 1999}

rawtitle:
{Proceedings of the Fifth International Symposium on Orthogonal Polynomials, Special Functions and their Applications: Patras, Greece, 20--24 September 1999}

entry:
@Proceedings{Siafarikas:2001:PFI,
  editor =       "Panayiotis D. Siafarikas and Theodore Seio Chihara",
  booktitle =    "{Proceedings of the Fifth International Symposium on
                 Orthogonal Polynomials, Special Functions and their
                 Applications: Patras, Greece, 20--24 September 1999}",
  title =        "{Proceedings of the Fifth International Symposium on
                 Orthogonal Polynomials, Special Functions and their
                 Applications: Patras, Greece, 20--24 September 1999}",
  volume =       "133(1/2)",
  publisher =    pub-ELSEVIER,
  address =      pub-ELSEVIER:adr,
  pages =        "xxvii + 705",
  year =         "2001",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  LCCN =         "QA76 J86 v. 133, no. 1/2",
  bibdate =      "Sat Oct 30 19:08:06 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Journal of computational and applied mathematics",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Borrione:2002:TIW
editor: Dominique Borrione
year: 2002
bibdate: Sat Jun 25 12:28:18 2005
bibtimestamp: 2005.06.25 12:28:18 ???
URL: http://www.cs.utexas.edu/users/moore/acl2/workshop-2002/
acknowledgement: ack-nhfb
raweditor: Dominique Borrione
booktitle:
Third International Workshop on the ACL2 Theorem Prover and its Applications (ACL2-2002), April 8--9, 2002, in Grenoble, France. Presentations, affiliated with ETAPS 2002

title:
Third International Workshop on the ACL2 Theorem Prover and its Applications (ACL2-2002), April 8--9, 2002, in Grenoble, France. Presentations, affiliated with ETAPS 2002

rawbooktitle:
{Third International Workshop on the ACL2 Theorem Prover and its Applications (ACL2-2002), April 8--9, 2002, in Grenoble, France. Presentations, affiliated with ETAPS 2002}

rawtitle:
{Third International Workshop on the ACL2 Theorem Prover and its Applications (ACL2-2002), April 8--9, 2002, in Grenoble, France. Presentations, affiliated with ETAPS 2002}

entry:
@Proceedings{Borrione:2002:TIW,
  editor =       "Dominique Borrione",
  booktitle =    "{Third International Workshop on the ACL2 Theorem
                 Prover and its Applications (ACL2-2002), April 8--9,
                 2002, in Grenoble, France. Presentations, affiliated
                 with ETAPS 2002}",
  title =        "{Third International Workshop on the ACL2 Theorem
                 Prover and its Applications (ACL2-2002), April 8--9,
                 2002, in Grenoble, France. Presentations, affiliated
                 with ETAPS 2002}",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "2002",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Sat Jun 25 12:28:18 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.cs.utexas.edu/users/moore/acl2/workshop-2002/",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Lide:2002:CEM
editor: David R. Lide
booktitle: A Century of Excellence in Measurements, Standards, and Technology
title: A Century of Excellence in Measurements, Standards, and Technology
publisher: pub-CRC
address: pub-CRC:adr
pages: ix + 386
year: 2002
ISBN: 0-8493-1247-7 OR 0849312477
ISBN13: 978-0-8493-1247-2 OR 9780849312472
LCCN: QC100.U6 .C46 2002
bibdate: Fri Jul 09 06:29:11 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:29:11 ???
note: Republication of cite Lide:2001:CEM.
URL: http://www.loc.gov/catdir/toc/fy031/2002283707.html
acknowledgement: ack-nhfb
rawbooktitle: A Century of Excellence in Measurements, Standards, and Technology
raweditor: David R. Lide
rawnote: Republication of \cite{Lide:2001:CEM}.
rawtitle: A Century of Excellence in Measurements, Standards, and Technology
TOC:
Introduction / 1 1901--1930 The Absolute Measurement of Inductance / 5 Determination of the Constants of Total Radiation From a Black Body / 7 The Testing of Thermal Insulators / 10 Precipitation Hardening of Metal Alloys / 14 Construction and Operation of a Simple Homemade Radio Receiving Outfit / 16 Methods for Standardizing and Testing Precision Gage Blocks / 19 Recommended Minimum Requirements for Small Dwelling Construction / 22 Visibility of Radiant Energy / 25 Test of the Severity of Building Fires / 28 Calculation of Compounds in Portland Cements / 33 Development of the Visual-Type Airway Radio-Beacon System / 38 1931--1950 A Hydrogen Isotope of Mass 2 / 43 Air Flow and Turbulence in Boundary Layers / 46 Thermodynamic Properties of Water and Steam for Power Generation / 49 Absolute Pressure Calibrations of Microphones / 53 Absolute Determination of the Ampere / 56 Radio Proximity Fuzes / 59 Stability of Double-Walled Manganin Resistors / 63 Manufacture of Paper for War Maps and Other Applications / 66 Transmission of Sound Waves in Gases at Low Pressures / 69 Atomic Energy Levels and Other Spectroscopic Data / 73 Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators / 77 1951--1960 Methods of Conjugate Gradients for Solving Linear Systems / 81 Computer Development at the National Bureau of Standards / 86 Thermal Converters as AC-DC Transfer Standards for Current and Voltage Measurements at Audio Frequencies / 90 Selected Values of Chemical Thermodynamic Properties / 93 Applied Inorganic Analysis / 97 The Diamond Anvil Pressure Cell / 100 Polymer Crystallization With Folded Chains / 104 Cryogenic Engineering / 107 Reversal of the Parity Conservation Law in Nuclear Physics / 111 1961--1970 Effects of Configuration Interaction on Intensities and Phase Shifts / 116 Electromagnetic Waves in Stratified Media / 120 ``Second Breakdown'' in Transistors / 123 Stress Relaxation With Finite Strain / 126 Realistic Evaluation of the Precision and Accuracy of Instrument Calibration Systems / 129 Experimental Statistics / 132 Handbook of Mathematical Functions / 135 Paths, Trees, and Flowers / 140 Concepts, Terminology, and Notation for Optical Modulation / 145 Theory of Light Scattering in Fluids / 149 Scaling Analysis of Thermodynamic Properties in the Critical Region of Fluids / 152 Resonance Tunneling of Field Emitted Electrons Through Adsorbates on Metal Surfaces / 155 Quantitative Electron Probe Microanalysis / 160 Limits for Qualitative Detection and Quantitative Determination / 164 Traceability: An Evolving Concept / 167 Code for Information Interchange --- ASCII / 172 Consumer Information Series / 174 Theory of Isoperibol Calorimetry for Laser Power and Energy Measurement / 178 Influence of Water on Crack Growth in Glass / 181 Phase Equilibria Diagrams / 184 Determination of Reduced Cells in Crystallography / 188 1971--1980 Speed of Light From Direct Frequency and Wavelength Measurements / 191 Connecting Visible Wavelength Standards With X Rays and $gamma $ Rays / 194 Laser Cooling of Atoms / 200 Spin-Polarized Electrons / 203 Needs for Radioactivity Standards and Measurements in Different Fields / 209 The Topografiner: An Instrument for Measuring Surface Microtopography / 214 Electron-Stimulated Desorption / 219 Photochemistry of Small Molecules / 224 Role of Standard Reference Materials in Measurement Systems / 227 Metrology and Standardization to Assist Industrializing Economies / 230 Publications Taking Us Toward a Metric America / 234 A New Approach to Manipulator Control: The Cerebellar Model Articulation Controller / 237 Three Dimensional Metrology / 241 Initial Graphics Exchange Specifications / 246 Data Encryption Standard / 250 OMNIDATA and the Computerization of Scientific Data / 254 FORTRAN Test Programs / 258 Design and Evaluation Criteria for Energy Conservation in New Buildings / 260 Computer Program for Heating and Cooling Loads in Buildings / 266 Methods for Testing and Rating the Performance of Heating and Air Conditioning Systems / 270 System for Fire Safety Evaluation of Health Care Facilities / 275 Estimation of Rate of Heat Release by Means of Oxygen Consumption Measurements / 280 Probability-Based Load Criteria for Structural Design / 283 Resistivity--Dopant Density Relationship for Phosphorus-Doped Silicon / 289 1981--1990 Critical Data for Critical Needs / 291 Materials at Low Temperatures / 294 Optical Fiber Characterization / 297 Quasicrystals / 300 Protein Crystallography by Joint X-Ray and Neutron Diffraction / 303 Strain Effects in Superconducting Compounds / 306 Dental Research at the National Bureau of Standards / 309 Handbook for Standard Reference Materials Users / 313 A Practical Josephson Voltage Standard at One Volt / 315 Plane-Wave Scattering-Matrix Theory of Antennas and Antenna--Antenna Interactions / 319 The Automated Manufacturing Research Facility / 322 Submicrometer Linewidth Metrology / 328 Observation of Atoms Laser-Cooled Below the Doppler Limit / 331 Laser-Excited Hot-Electron Induced Desorption / 334 Measurement of the Universal Gas Constant Using an Acoustic Resonator / 339 Thermal and Oxidative Degradation of Polymers / 344 HAZARD I: Software for Fire Hazard Assessment / 347 Analysis of the Catastrophic Rupture of a Pressure Vessel / 350 Curing Those Uncontrollable Fits of Interaction / 353 Baldrige Criteria for Performance Excellence / 357 1991--2000 The Advanced Technology Program / 359 NIST Manufacturing Extension Partnership / 363 Questions and Answers on Quality / 366 Uniformity in Weights and Measures Laws and Regulations / 368 Certification of 10 $mu $m Diameter Polystyrene Spheres (``Space Beads') / 371 Bose--Einstein Condensation in a Dilute Atomic Vapor / 375 Index / 379

rawTOC:
Introduction / 1 \\ 1901--1930 \\ The Absolute Measurement of Inductance / 5 \\ Determination of the Constants of Total Radiation From a Black Body / 7 \\ The Testing of Thermal Insulators / 10 \\ Precipitation Hardening of Metal Alloys / 14 \\ Construction and Operation of a Simple Homemade Radio Receiving Outfit / 16 \\ Methods for Standardizing and Testing Precision Gage Blocks / 19 \\ Recommended Minimum Requirements for Small Dwelling Construction / 22 \\ Visibility of Radiant Energy / 25 \\ Test of the Severity of Building Fires / 28 \\ Calculation of Compounds in Portland Cements / 33 \\ Development of the Visual-Type Airway Radio-Beacon System / 38 \\ 1931--1950 \\ A Hydrogen Isotope of Mass 2 / 43 \\ Air Flow and Turbulence in Boundary Layers / 46 \\ Thermodynamic Properties of Water and Steam for Power Generation / 49 \\ Absolute Pressure Calibrations of Microphones / 53 \\ Absolute Determination of the Ampere / 56 \\ Radio Proximity Fuzes / 59 \\ Stability of Double-Walled Manganin Resistors / 63 \\ Manufacture of Paper for War Maps and Other Applications / 66 \\ Transmission of Sound Waves in Gases at Low Pressures / 69 \\ Atomic Energy Levels and Other Spectroscopic Data / 73 \\ Iteration Method for the Solution of the Eigenvalue Problem of Linear Differential and Integral Operators / 77 \\ 1951--1960 \\ Methods of Conjugate Gradients for Solving Linear Systems / 81 \\ Computer Development at the National Bureau of Standards / 86 \\ Thermal Converters as AC-DC Transfer Standards for Current and Voltage Measurements at Audio Frequencies / 90 \\ Selected Values of Chemical Thermodynamic Properties / 93 \\ Applied Inorganic Analysis / 97 \\ The Diamond Anvil Pressure Cell / 100 \\ Polymer Crystallization With Folded Chains / 104 \\ Cryogenic Engineering / 107 \\ Reversal of the Parity Conservation Law in Nuclear Physics / 111 \\ 1961--1970 \\ Effects of Configuration Interaction on Intensities and Phase Shifts / 116 \\ Electromagnetic Waves in Stratified Media / 120 \\ ``Second Breakdown'' in Transistors / 123 \\ Stress Relaxation With Finite Strain / 126 \\ Realistic Evaluation of the Precision and Accuracy of Instrument Calibration Systems / 129 \\ Experimental Statistics / 132 \\ Handbook of Mathematical Functions / 135 \\ Paths, Trees, and Flowers / 140 \\ Concepts, Terminology, and Notation for Optical Modulation / 145 \\ Theory of Light Scattering in Fluids / 149 \\ Scaling Analysis of Thermodynamic Properties in the Critical Region of Fluids / 152 \\ Resonance Tunneling of Field Emitted Electrons Through Adsorbates on Metal Surfaces / 155 \\ Quantitative Electron Probe Microanalysis / 160 \\ Limits for Qualitative Detection and Quantitative Determination / 164 \\ Traceability: An Evolving Concept / 167 \\ Code for Information Interchange --- ASCII / 172 \\ Consumer Information Series / 174 \\ Theory of Isoperibol Calorimetry for Laser Power and Energy Measurement / 178 \\ Influence of Water on Crack Growth in Glass / 181 \\ Phase Equilibria Diagrams / 184 \\ Determination of Reduced Cells in Crystallography / 188 \\ 1971--1980 \\ Speed of Light From Direct Frequency and Wavelength Measurements / 191 \\ Connecting Visible Wavelength Standards With X Rays and $\gamma$ Rays / 194 \\ Laser Cooling of Atoms / 200 \\ Spin-Polarized Electrons / 203 \\ Needs for Radioactivity Standards and Measurements in Different Fields / 209 \\ The Topografiner: An Instrument for Measuring Surface Microtopography / 214 \\ Electron-Stimulated Desorption / 219 \\ Photochemistry of Small Molecules / 224 \\ Role of Standard Reference Materials in Measurement Systems / 227 \\ Metrology and Standardization to Assist Industrializing Economies / 230 \\ Publications Taking Us Toward a Metric America / 234 \\ A New Approach to Manipulator Control: The Cerebellar Model Articulation Controller / 237 \\ Three Dimensional Metrology / 241 \\ Initial Graphics Exchange Specifications / 246 \\ Data Encryption Standard / 250 \\ OMNIDATA and the Computerization of Scientific Data / 254 \\ FORTRAN Test Programs / 258 \\ Design and Evaluation Criteria for Energy Conservation in New Buildings / 260 \\ Computer Program for Heating and Cooling Loads in Buildings / 266 \\ Methods for Testing and Rating the Performance of Heating and Air Conditioning Systems / 270 \\ System for Fire Safety Evaluation of Health Care Facilities / 275 \\ Estimation of Rate of Heat Release by Means of Oxygen Consumption Measurements / 280 \\ Probability-Based Load Criteria for Structural Design / 283 \\ Resistivity--Dopant Density Relationship for Phosphorus-Doped Silicon / 289 \\ 1981--1990 \\ Critical Data for Critical Needs / 291 \\ Materials at Low Temperatures / 294 \\ Optical Fiber Characterization / 297 \\ Quasicrystals / 300 \\ Protein Crystallography by Joint X-Ray and Neutron Diffraction / 303 \\ Strain Effects in Superconducting Compounds / 306 \\ Dental Research at the National Bureau of Standards / 309 \\ Handbook for Standard Reference Materials Users / 313 \\ A Practical Josephson Voltage Standard at One Volt / 315 \\ Plane-Wave Scattering-Matrix Theory of Antennas and Antenna--Antenna Interactions / 319 \\ The Automated Manufacturing Research Facility / 322 \\ Submicrometer Linewidth Metrology / 328 \\ Observation of Atoms Laser-Cooled Below the Doppler Limit / 331 \\ Laser-Excited Hot-Electron Induced Desorption / 334 \\ Measurement of the Universal Gas Constant Using an Acoustic Resonator / 339 \\ Thermal and Oxidative Degradation of Polymers / 344 \\ HAZARD I: Software for Fire Hazard Assessment / 347 \\ Analysis of the Catastrophic Rupture of a Pressure Vessel / 350 \\ Curing Those Uncontrollable Fits of Interaction / 353 \\ Baldrige Criteria for Performance Excellence / 357 \\ 1991--2000 \\ The Advanced Technology Program / 359 \\ NIST Manufacturing Extension Partnership / 363 \\ Questions and Answers on Quality / 366 \\ Uniformity in Weights and Measures Laws and Regulations / 368 \\ Certification of 10 $\mu$m Diameter Polystyrene Spheres (``Space Beads') / 371 \\ Bose--Einstein Condensation in a Dilute Atomic Vapor / 375 \\ Index / 379

entry:
@Book{Lide:2002:CEM,
  editor =       "David R. Lide",
  booktitle =    "A Century of Excellence in Measurements, Standards,
                 and Technology",
  title =        "A Century of Excellence in Measurements, Standards,
                 and Technology",
  publisher =    pub-CRC,
  address =      pub-CRC:adr,
  pages =        "ix + 386",
  year =         "2002",
  ISBN =         "0-8493-1247-7",
  ISBN-13 =      "978-0-8493-1247-2",
  LCCN =         "QC100.U6 .C46 2002",
  bibdate =      "Fri Jul 09 06:29:11 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Republication of \cite{Lide:2001:CEM}.",
  URL =          "http://www.loc.gov/catdir/toc/fy031/2002283707.html",
  acknowledgement = ack-nhfb,
  tableofcontents = "Introduction / 1 \\
                 1901--1930 \\
                 The Absolute Measurement of Inductance / 5 \\
                 Determination of the Constants of Total Radiation From
                 a Black Body / 7 \\
                 The Testing of Thermal Insulators / 10 \\
                 Precipitation Hardening of Metal Alloys / 14 \\
                 Construction and Operation of a Simple Homemade Radio
                 Receiving Outfit / 16 \\
                 Methods for Standardizing and Testing Precision Gage
                 Blocks / 19 \\
                 Recommended Minimum Requirements for Small Dwelling
                 Construction / 22 \\
                 Visibility of Radiant Energy / 25 \\
                 Test of the Severity of Building Fires / 28 \\
                 Calculation of Compounds in Portland Cements / 33 \\
                 Development of the Visual-Type Airway Radio-Beacon
                 System / 38 \\
                 1931--1950 \\
                 A Hydrogen Isotope of Mass 2 / 43 \\
                 Air Flow and Turbulence in Boundary Layers / 46 \\
                 Thermodynamic Properties of Water and Steam for Power
                 Generation / 49 \\
                 Absolute Pressure Calibrations of Microphones / 53 \\
                 Absolute Determination of the Ampere / 56 \\
                 Radio Proximity Fuzes / 59 \\
                 Stability of Double-Walled Manganin Resistors / 63 \\
                 Manufacture of Paper for War Maps and Other
                 Applications / 66 \\
                 Transmission of Sound Waves in Gases at Low Pressures /
                 69 \\
                 Atomic Energy Levels and Other Spectroscopic Data / 73
                 \\
                 Iteration Method for the Solution of the Eigenvalue
                 Problem of Linear Differential and Integral Operators /
                 77 \\
                 1951--1960 \\
                 Methods of Conjugate Gradients for Solving Linear
                 Systems / 81 \\
                 Computer Development at the National Bureau of
                 Standards / 86 \\
                 Thermal Converters as AC-DC Transfer Standards for
                 Current and Voltage Measurements at Audio Frequencies /
                 90 \\
                 Selected Values of Chemical Thermodynamic Properties /
                 93 \\
                 Applied Inorganic Analysis / 97 \\
                 The Diamond Anvil Pressure Cell / 100 \\
                 Polymer Crystallization With Folded Chains / 104 \\
                 Cryogenic Engineering / 107 \\
                 Reversal of the Parity Conservation Law in Nuclear
                 Physics / 111 \\
                 1961--1970 \\
                 Effects of Configuration Interaction on Intensities and
                 Phase Shifts / 116 \\
                 Electromagnetic Waves in Stratified Media / 120 \\
                 ``Second Breakdown'' in Transistors / 123 \\
                 Stress Relaxation With Finite Strain / 126 \\
                 Realistic Evaluation of the Precision and Accuracy of
                 Instrument Calibration Systems / 129 \\
                 Experimental Statistics / 132 \\
                 Handbook of Mathematical Functions / 135 \\
                 Paths, Trees, and Flowers / 140 \\
                 Concepts, Terminology, and Notation for Optical
                 Modulation / 145 \\
                 Theory of Light Scattering in Fluids / 149 \\
                 Scaling Analysis of Thermodynamic Properties in the
                 Critical Region of Fluids / 152 \\
                 Resonance Tunneling of Field Emitted Electrons Through
                 Adsorbates on Metal Surfaces / 155 \\
                 Quantitative Electron Probe Microanalysis / 160 \\
                 Limits for Qualitative Detection and Quantitative
                 Determination / 164 \\
                 Traceability: An Evolving Concept / 167 \\
                 Code for Information Interchange --- ASCII / 172 \\
                 Consumer Information Series / 174 \\
                 Theory of Isoperibol Calorimetry for Laser Power and
                 Energy Measurement / 178 \\
                 Influence of Water on Crack Growth in Glass / 181 \\
                 Phase Equilibria Diagrams / 184 \\
                 Determination of Reduced Cells in Crystallography / 188
                 \\
                 1971--1980 \\
                 Speed of Light From Direct Frequency and Wavelength
                 Measurements / 191 \\
                 Connecting Visible Wavelength Standards With X Rays and
                 $\gamma$ Rays / 194 \\
                 Laser Cooling of Atoms / 200 \\
                 Spin-Polarized Electrons / 203 \\
                 Needs for Radioactivity Standards and Measurements in
                 Different Fields / 209 \\
                 The Topografiner: An Instrument for Measuring Surface
                 Microtopography / 214 \\
                 Electron-Stimulated Desorption / 219 \\
                 Photochemistry of Small Molecules / 224 \\
                 Role of Standard Reference Materials in Measurement
                 Systems / 227 \\
                 Metrology and Standardization to Assist Industrializing
                 Economies / 230 \\
                 Publications Taking Us Toward a Metric America / 234
                 \\
                 A New Approach to Manipulator Control: The Cerebellar
                 Model Articulation Controller / 237 \\
                 Three Dimensional Metrology / 241 \\
                 Initial Graphics Exchange Specifications / 246 \\
                 Data Encryption Standard / 250 \\
                 OMNIDATA and the Computerization of Scientific Data /
                 254 \\
                 FORTRAN Test Programs / 258 \\
                 Design and Evaluation Criteria for Energy Conservation
                 in New Buildings / 260 \\
                 Computer Program for Heating and Cooling Loads in
                 Buildings / 266 \\
                 Methods for Testing and Rating the Performance of
                 Heating and Air Conditioning Systems / 270 \\
                 System for Fire Safety Evaluation of Health Care
                 Facilities / 275 \\
                 Estimation of Rate of Heat Release by Means of Oxygen
                 Consumption Measurements / 280 \\
                 Probability-Based Load Criteria for Structural Design /
                 283 \\
                 Resistivity--Dopant Density Relationship for
                 Phosphorus-Doped Silicon / 289 \\
                 1981--1990 \\
                 Critical Data for Critical Needs / 291 \\
                 Materials at Low Temperatures / 294 \\
                 Optical Fiber Characterization / 297 \\
                 Quasicrystals / 300 \\
                 Protein Crystallography by Joint X-Ray and Neutron
                 Diffraction / 303 \\
                 Strain Effects in Superconducting Compounds / 306 \\
                 Dental Research at the National Bureau of Standards /
                 309 \\
                 Handbook for Standard Reference Materials Users / 313
                 \\
                 A Practical Josephson Voltage Standard at One Volt /
                 315 \\
                 Plane-Wave Scattering-Matrix Theory of Antennas and
                 Antenna--Antenna Interactions / 319 \\
                 The Automated Manufacturing Research Facility / 322 \\
                 Submicrometer Linewidth Metrology / 328 \\
                 Observation of Atoms Laser-Cooled Below the Doppler
                 Limit / 331 \\
                 Laser-Excited Hot-Electron Induced Desorption / 334 \\
                 Measurement of the Universal Gas Constant Using an
                 Acoustic Resonator / 339 \\
                 Thermal and Oxidative Degradation of Polymers / 344 \\
                 HAZARD I: Software for Fire Hazard Assessment / 347 \\
                 Analysis of the Catastrophic Rupture of a Pressure
                 Vessel / 350 \\
                 Curing Those Uncontrollable Fits of Interaction / 353
                 \\
                 Baldrige Criteria for Performance Excellence / 357 \\
                 1991--2000 \\
                 The Advanced Technology Program / 359 \\
                 NIST Manufacturing Extension Partnership / 363 \\
                 Questions and Answers on Quality / 366 \\
                 Uniformity in Weights and Measures Laws and Regulations
                 / 368 \\
                 Certification of 10 $\mu$m Diameter Polystyrene Spheres
                 (``Space Beads') / 371 \\
                 Bose--Einstein Condensation in a Dilute Atomic Vapor /
                 375 \\
                 Index / 379",
}


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filename: elefunt.bib
label: Anonymous:2003:CRN
editor: Anonymous
booktitle: 5th Conference on Real Numbers and Computers 2003 --- RNC5, Lyon, France, September 2003
title: 5th Conference on Real Numbers and Computers 2003 --- RNC5, Lyon, France, September 2003
year: 2003
bibdate: Sat Jun 25 14:57:33 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.06.25 14:57:33 ???
acknowledgement: ack-nhfb
rawbooktitle: 5th Conference on Real Numbers and Computers 2003 --- {RNC5}, Lyon, France, September 2003
raweditor: Anonymous
rawtitle: 5th Conference on Real Numbers and Computers 2003 --- {RNC5}, Lyon, France, September 2003
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bibtype: proceedings
filename: elefunt.bib
label: Koelink:2003:OPS
editor: Erik Koelink and Walter Van Assche
booktitle: Orthogonal polynomials and special functions: Leuven 2002
title: Orthogonal polynomials and special functions: Leuven 2002
volume: 1817
publisher: pub-SV
address: pub-SV:adr
pages: x + 249
year: 2003
ISBN: 3-540-40375-2 OR 3540403752
ISBN13: 978-3-540-40375-3 OR 9783540403753
ISSN: 0075-8434 (print), 1617-9692 (electronic) OR 00758434 (print), 16179692 (electronic)
LCCN: 33 33-06 33C 68W
bibdate: Sat Oct 30 17:00:03 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.bibsys.no:2100/BIBSYS
bibtimestamp: 2010.10.30 17:00:03 MDT
series: Lecture notes in mathematics
subject: functions, special; orthogonal polynomials
acknowledgement: ack-nhfb
rawbooktitle: Orthogonal polynomials and special functions: {Leuven 2002}
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rawtitle: Orthogonal polynomials and special functions: {Leuven 2002}
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bibtype: book
filename: elefunt.bib
label: Berggren:2004: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: Third
pages: xx + 797
year: 2004
DOI: https://doi.org/10.1007/978-1-4757-4217-6
ISBN: 0-387-20571-3 OR 0387205713
ISBN13: 978-0-387-20571-7 OR 9780387205717
MRclass: 11-00 (01A05 01A75 11-03)
MRnumber: 2065455
MRreviewer: F. Beukers
bibdate: Wed Aug 10 11:09:47 2016
bibtimestamp: 2016.08.10 11:09:47 ???
remark: CECM Preprint 2003:210.
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
TOC:
Preface to the Third Edition / v Preface to the Second Edition / vi Preface / vii Acknowledgments / x 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 --- (-250 B.C.) / 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 modem 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 (--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 (-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 / booktitle 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 / booktitle 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 $ / ?? 12. Huygens / booktitle De Circuli Magnitudine Inventa (1654) / Huygens's demonstration of how to triple the number of correct decimals over those in Archimedes' estimate of $ pi $ / 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 booktitle 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 booktitle 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 / booktitle 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 Shanks's report of his monumental hand calculation of $ pi $ / 147 21. Hermite / booktitle Sur La Fonction Exponentielle (1873) / The first proof of the transcendence of $ e $ / 162 22. Lindemann / booktitle Ueber die Zahl $ pi $ (1882) / The first proof of the transcendence of $ pi $ / 194 23. Weierstrass / booktitle Zu Lindemann's Abhandlung ``Uber die Ludolphsche Zahl'' (1885) / Weierstrass' proof of the transcendence of $ pi $ / 207 24. Hilbert / booktitle Ueber die Transzendenz 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.'' / ?? 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 B.C. 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 / 319 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 $ / 456 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 $ pi $ 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 $ zeta (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 $zeta (2) = pi ^2 / 6$ / 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 Borwein's 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 $ pi $ 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 Tale 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 (1997) / 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 Viele and Huygens / 690 Bibliography / 710 Credits / 717 A Pamphlet on Pi / 721 Contents / 723 1. Pi and Its Friends / 725 2. Normality of Numbers / 741 3. Historia Cyclometrica / 753 4. Demotica Cyclometrica / 771 References / 779 Index / 783

rawTOC:
Preface to the Third Edition / v \\ Preface to the Second Edition / vi \\ Preface / vii \\ Acknowledgments / x \\ 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 --- (-250 B.C.) / 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 modem 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 (--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 (-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 / \booktitle{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 / \booktitle{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$ / ?? \\ 12. Huygens / \booktitle{De Circuli Magnitudine Inventa} (1654) / Huygens's demonstration of how to triple the number of correct decimals over those in Archimedes' estimate of $ \pi $ / 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 \booktitle{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 \booktitle{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 / \booktitle{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 Shanks's report of his monumental hand calculation of $ \pi $ / 147 \\ 21. Hermite / \booktitle{Sur La Fonction Exponentielle} (1873) / The first proof of the transcendence of $ e $ / 162 \\ 22. Lindemann / \booktitle{Ueber die Zahl $ \pi $} (1882) / The first proof of the transcendence of $ \pi $ / 194 23. Weierstrass / \booktitle{Zu Lindemann's Abhandlung ``{\"U}ber die Ludolphsche Zahl''} (1885) / Weierstrass' proof of the transcendence of $ \pi $ / 207 24. Hilbert / \booktitle{Ueber die Transzendenz 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.'' / ?? \\ 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 B.C. 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 / 319 \\ 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 $ / 456 \\ 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 $ \pi $ 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 $ \zeta(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 $\zeta(2) = \pi^2 / 6$ / 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 Borwein's 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 $ \pi $ 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 Tale 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 (1997) / 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 Viele and Huygens / 690 \\ Bibliography / 710 \\ Credits / 717 \\ A Pamphlet on Pi / 721 \\ Contents / 723 \\ 1. Pi and Its Friends / 725 \\ 2. Normality of Numbers / 741 \\ 3. Historia Cyclometrica / 753 \\ 4. Demotica Cyclometrica / 771 \\ References / 779 \\ Index / 783

entry:
@Book{Berggren:2004: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 =      "Third",
  pages =        "xx + 797",
  year =         "2004",
  DOI =          "https://doi.org/10.1007/978-1-4757-4217-6",
  ISBN =         "0-387-20571-3",
  ISBN-13 =      "978-0-387-20571-7",
  MRclass =      "11-00 (01A05 01A75 11-03)",
  MRnumber =     "2065455",
  MRreviewer =   "F. Beukers",
  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",
  acknowledgement = ack-nhfb,
  author-dates = "Jonathan Michael Borwein (20 May 1951--2 August
                 2016)",
  ORCID-numbers = "Borwein, Jonathan/0000-0002-1263-0646",
  remark =       "CECM Preprint 2003:210.",
  tableofcontents = "Preface to the Third Edition / v \\
                 Preface to the Second Edition / vi \\
                 Preface / vii \\
                 Acknowledgments / x \\
                 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 --- (-250 B.C.)
                 / 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 modem 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 (--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
                 (-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 / \booktitle{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 / \booktitle{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$ / ?? \\
                 12. Huygens / \booktitle{De Circuli Magnitudine
                 Inventa} (1654) / Huygens's demonstration of how to
                 triple the number of correct decimals over those in
                 Archimedes' estimate of $ \pi $ / 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
                 \booktitle{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 \booktitle{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 / \booktitle{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 Shanks's report
                 of his monumental hand calculation of $ \pi $ / 147 \\
                 21. Hermite / \booktitle{Sur La Fonction Exponentielle}
                 (1873) / The first proof of the transcendence of $ e $
                 / 162 \\
                 22. Lindemann / \booktitle{Ueber die Zahl $ \pi $}
                 (1882) / The first proof of the transcendence of $ \pi
                 $ / 194 23. Weierstrass / \booktitle{Zu Lindemann's
                 Abhandlung ``{\"U}ber die Ludolphsche Zahl''} (1885) /
                 Weierstrass' proof of the transcendence of $ \pi $ /
                 207 24. Hilbert / \booktitle{Ueber die Transzendenz 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.'' / ?? \\
                 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
                 B.C. 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 / 319 \\
                 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 $ /
                 456 \\
                 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 $ \pi $ 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 $ \zeta(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 $\zeta(2) = \pi^2 / 6$ / 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 Borwein's 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 $
                 \pi $ 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 Tale 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 (1997)
                 / 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 Viele and Huygens / 690
                 \\
                 Bibliography / 710 \\
                 Credits / 717 \\
                 A Pamphlet on Pi / 721 \\
                 Contents / 723 \\
                 1. Pi and Its Friends / 725 \\
                 2. Normality of Numbers / 741 \\
                 3. Historia Cyclometrica / 753 \\
                 4. Demotica Cyclometrica / 771 \\
                 References / 779 \\
                 Index / 783",
}


bibtype: proceedings
filename: elefunt.bib
label: Frougny:2004:RCR
editor: Christiane Frougny and Vasco Brattka and Norbert Muller
booktitle: RNC'6, 6th Conference on Real Numbers and Computers: Nov 15--17, 2004, Dagstuhl, Germany
title: RNC'6, 6th Conference on Real Numbers and Computers: Nov 15--17, 2004, Dagstuhl, Germany
publisher: Universitaat Trier, Fachbereich IV, Mathematik, Informatik
address: Trier, Germany
pages: 216 + i
year: 2004
ISSN: 0944-0488 OR 09440488
ISSNL: 0944-0488 OR 09440488
bibdate: Thu Apr 28 05:55:01 2022
bibtimestamp: 2022.04.28 05:55:01 ???
note: Forschungsbericht Nr. 04-8.
keywords: base conversion; decimal floating-point arithmetic
acknowledgement: ack-nhfb
bookpages: 216 + i
rawbooktitle: {RNC'6, 6th Conference on Real Numbers and Computers: Nov 15--17, 2004, Dagstuhl, Germany}
raweditor: Christiane Frougny and Vasco Brattka and Norbert M{\"u}ller
rawnote: Forschungsbericht Nr. 04-8.
rawtitle: {RNC'6, 6th Conference on Real Numbers and Computers: Nov 15--17, 2004, Dagstuhl, Germany}
URL:
http://www.informatik.uni-trier.de/Reports/TR-08-2004; http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6-complete.pdf

TOC:
Introduction / Christiane Frougny / 1--4 Invited Lecture: New ideas and results for solving Differential equations symbolically [abstract only] / Benno Fuchssteiner / 5--5 Invited Lecture: A survey of Integer Relations algorithms and rational numbers [abstract only] / Simon Plouffe / 6--6 Invited Lecture: Real Numbers and Robustness in Computational Geometry / Stefan Schirra / 7--21 Bridging the gap between formal specification and bit-level floating-point arithmetic / Sylvie Boldo / 22--36 Automata, Borel functions and real numbers in Pisot base / B. Cagnard, P. Simonnet / 37--54 Generating formally certified bounds on values and round-off errors / Marc Daumas, Guillaume Melquiond / 55--70 A proven correctly rounded logarithm in double-precision / Florent de Dinechin, Catherine Loirat, Jean-Michel Muller / 71--85 A comparison of polynomial evaluation schemes / L. Fousse, S. Schmitt / 86--102 A comparison of real and complex pseudozero sets for polynomials with real coefficients / Stef Graillat, Philippe Langlois / 103--112 On Intermediate Precision Required for Correctly-Rounding Decimal-to-Binary Floating-Point Conversion / Michel Hack / 113--134 The Generic Multiple-Precision Floating-Point Addition With Exact Rounding (as in the MPFR Library) / Vincent Lefevre / 135--145 Software Division and Square Root Using Goldschmidt's Algorithms / Peter Markstein / 146--157 A Fast Algorithm for Julia Sets of Hyperbolic Rational Functions / R. Rettinger / 158--171 An extension of Chaitin's halting probability $Omega $ to measurement operator in infinite dimensional quantum system / Kohtaro Tadaki / 172--191 On the Hierarchy of $Delta _2^0$-Real Numbers / Xizhong Zheng / 192--215 Trierer Forschungsberichte Mathematik / Informatik [one page list of reports] / 1--1 (216--216)

rawTOC:
Introduction / Christiane Frougny / 1--4 \\ Invited Lecture: New ideas and results for solving Differential equations symbolically [abstract only] / Benno Fuchssteiner / 5--5 \\ Invited Lecture: A survey of Integer Relations algorithms and rational numbers [abstract only] / Simon Plouffe / 6--6 \\ Invited Lecture: Real Numbers and Robustness in Computational Geometry / Stefan Schirra / 7--21 \\ Bridging the gap between formal specification and bit-level floating-point arithmetic / Sylvie Boldo / 22--36 \\ Automata, Borel functions and real numbers in Pisot base / B. Cagnard, P. Simonnet / 37--54 \\ Generating formally certified bounds on values and round-off errors / Marc Daumas, Guillaume Melquiond / 55--70 \\ A proven correctly rounded logarithm in double-precision / Florent de Dinechin, Catherine Loirat, Jean-Michel Muller / 71--85 \\ A comparison of polynomial evaluation schemes / L. Fousse, S. Schmitt / 86--102 \\ A comparison of real and complex pseudozero sets for polynomials with real coefficients / Stef Graillat, Philippe Langlois / 103--112 \\ On Intermediate Precision Required for Correctly-Rounding Decimal-to-Binary Floating-Point Conversion / Michel Hack / 113--134 \\ The Generic Multiple-Precision Floating-Point Addition With Exact Rounding (as in the MPFR Library) / Vincent Lef{\`e}vre / 135--145 \\ Software Division and Square Root Using Goldschmidt's Algorithms / Peter Markstein / 146--157 \\ A Fast Algorithm for Julia Sets of Hyperbolic Rational Functions / R. Rettinger / 158--171 \\ An extension of Chaitin's halting probability $\Omega$ to measurement operator in infinite dimensional quantum system / Kohtaro Tadaki / 172--191 \\ On the Hierarchy of $\Delta_2^0$-Real Numbers / Xizhong Zheng / 192--215 \\ Trierer Forschungsberichte Mathematik / Informatik [one page list of reports] / 1--1 (216--216)

entry:
@Proceedings{Frougny:2004:RCR,
  editor =       "Christiane Frougny and Vasco Brattka and Norbert
                 M{\"u}ller",
  booktitle =    "{RNC'6, 6th Conference on Real Numbers and Computers:
                 Nov 15--17, 2004, Dagstuhl, Germany}",
  title =        "{RNC'6, 6th Conference on Real Numbers and Computers:
                 Nov 15--17, 2004, Dagstuhl, Germany}",
  publisher =    "Universita{\"a}t Trier, Fachbereich IV, Mathematik,
                 Informatik",
  address =      "Trier, Germany",
  bookpages =    "216 + i",
  pages =        "216 + i",
  year =         "2004",
  ISSN =         "0944-0488",
  ISSN-L =       "0944-0488",
  bibdate =      "Thu Apr 28 05:55:01 2022",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  note =         "Forschungsbericht Nr. 04-8.",
  URL =          "http://www.informatik.uni-trier.de/Reports/TR-08-2004;
                 http://www.informatik.uni-trier.de/Reports/TR-08-2004/rnc6-complete.pdf",
  acknowledgement = ack-nhfb,
  keywords =     "base conversion; decimal floating-point arithmetic",
  tableofcontents = "Introduction / Christiane Frougny / 1--4 \\
                 Invited Lecture: New ideas and results for solving
                 Differential equations symbolically [abstract only] /
                 Benno Fuchssteiner / 5--5 \\
                 Invited Lecture: A survey of Integer Relations
                 algorithms and rational numbers [abstract only] / Simon
                 Plouffe / 6--6 \\
                 Invited Lecture: Real Numbers and Robustness in
                 Computational Geometry / Stefan Schirra / 7--21 \\
                 Bridging the gap between formal specification and
                 bit-level floating-point arithmetic / Sylvie Boldo /
                 22--36 \\
                 Automata, Borel functions and real numbers in Pisot
                 base / B. Cagnard, P. Simonnet / 37--54 \\
                 Generating formally certified bounds on values and
                 round-off errors / Marc Daumas, Guillaume Melquiond /
                 55--70 \\
                 A proven correctly rounded logarithm in
                 double-precision / Florent de Dinechin, Catherine
                 Loirat, Jean-Michel Muller / 71--85 \\
                 A comparison of polynomial evaluation schemes / L.
                 Fousse, S. Schmitt / 86--102 \\
                 A comparison of real and complex pseudozero sets for
                 polynomials with real coefficients / Stef Graillat,
                 Philippe Langlois / 103--112 \\
                 On Intermediate Precision Required for
                 Correctly-Rounding Decimal-to-Binary Floating-Point
                 Conversion / Michel Hack / 113--134 \\
                 The Generic Multiple-Precision Floating-Point Addition
                 With Exact Rounding (as in the MPFR Library) / Vincent
                 Lef{\`e}vre / 135--145 \\
                 Software Division and Square Root Using Goldschmidt's
                 Algorithms / Peter Markstein / 146--157 \\
                 A Fast Algorithm for Julia Sets of Hyperbolic Rational
                 Functions / R. Rettinger / 158--171 \\
                 An extension of Chaitin's halting probability $\Omega$
                 to measurement operator in infinite dimensional quantum
                 system / Kohtaro Tadaki / 172--191 \\
                 On the Hierarchy of $\Delta_2^0$-Real Numbers / Xizhong
                 Zheng / 192--215 \\
                 Trierer Forschungsberichte Mathematik / Informatik [one
                 page list of reports] / 1--1 (216--216)",
}


bibtype: proceedings
filename: elefunt.bib
label: Wahdan:2004:IHE
editor: Abdel-Moniem Wahdan
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xlv + 954
year: 2004
ISBN: 0-7803-8575-6 OR 0780385756
ISBN13: 978-0-7803-8575-7 OR 9780780385757
LCCN: TK7801 .I5125 2004
bibdate: Tue Jul 19 08:01:02 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; melvyl.cdlib.org:210/CDL90
bibtimestamp: 2005.07.19 08:01:02 MDT
note: IEEE catalog number 04EX893.
subject: Electric engineering; Congresses; Electronics; Congresses; Computer engineering; Congresses
acknowledgement: ack-nhfb
raweditor: Abdel-Moniem Wahdan
rawnote: IEEE catalog number 04EX893.
booktitle:
ICEEC'04: 2004 International Conference on Electrical, Electronic and Computer Engineering: proceedings: 5--7 September, 2004, Cairo, Egypt

title:
ICEEC'04: 2004 International Conference on Electrical, Electronic and Computer Engineering: proceedings: 5--7 September, 2004, Cairo, Egypt

rawbooktitle:
{ICEEC'04: 2004 International Conference on Electrical, Electronic and Computer Engineering: proceedings: 5--7 September, 2004, Cairo, Egypt}

rawtitle:
{ICEEC'04: 2004 International Conference on Electrical, Electronic and Computer Engineering: proceedings: 5--7 September, 2004, Cairo, Egypt}

entry:
@Proceedings{Wahdan:2004:IHE,
  editor =       "Abdel-Moniem Wahdan",
  booktitle =    "{ICEEC'04: 2004 International Conference on
                 Electrical, Electronic and Computer Engineering:
                 proceedings: 5--7 September, 2004, Cairo, Egypt}",
  title =        "{ICEEC'04: 2004 International Conference on
                 Electrical, Electronic and Computer Engineering:
                 proceedings: 5--7 September, 2004, Cairo, Egypt}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xlv + 954",
  year =         "2004",
  ISBN =         "0-7803-8575-6",
  ISBN-13 =      "978-0-7803-8575-7",
  LCCN =         "TK7801 .I5125 2004",
  bibdate =      "Tue Jul 19 08:01:02 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 melvyl.cdlib.org:210/CDL90",
  note =         "IEEE catalog number 04EX893.",
  acknowledgement = ack-nhfb,
  subject =      "Electric engineering; Congresses; Electronics;
                 Congresses; Computer engineering; Congresses",
}


bibtype: proceedings
filename: elefunt.bib
label: IEEE:2005:PIS
editor: IEEE
publisher: pub-IEEE
address: pub-IEEE:adr
year: 2005
bibdate: Tue Jun 21 19:02:16 2005
bibsource: http://arith17.polito.it/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.06.21 19:02:16 ???
acknowledgement: ack-nhfb
raweditor: {IEEE}
booktitle:
Proceedings of the 17th IEEE Symposium on Computer Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod, Massachusetts, USA

title:
Proceedings of the 17th IEEE Symposium on Computer Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod, Massachusetts, USA

rawbooktitle:
{Proceedings of the 17th IEEE Symposium on Computer Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod, Massachusetts, USA}

rawtitle:
{Proceedings of the 17th IEEE Symposium on Computer Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod, Massachusetts, USA}

entry:
@Proceedings{IEEE:2005:PIS,
  editor =       "{IEEE}",
  booktitle =    "{Proceedings of the 17th IEEE Symposium on Computer
                 Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod,
                 Massachusetts, USA}",
  title =        "{Proceedings of the 17th IEEE Symposium on Computer
                 Arithmetic, ARITH-17, June 27--29, 2005, Cape Cod,
                 Massachusetts, USA}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "????",
  year =         "2005",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Jun 21 19:02:16 2005",
  bibsource =    "http://arith17.polito.it/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  xxnote =       "Not yet published: check editor??",
}


bibtype: book
filename: elefunt.bib
label: Ismail:2005:TAS
editor: Mourad E. H. Ismail and Erik Koelink
booktitle: Theory and Applications of Special Functions: a Volume Dedicated to Mizan Rahman
title: Theory and Applications of Special Functions: a Volume Dedicated to Mizan Rahman
volume: 13
publisher: pub-SV
address: pub-SV:adr
pages: x + 491
year: 2005
ISBN: 0-387-24231-7 (hardcover), 0-387-24233-3 (e-book) OR 0387242317 (hardcover), 0387242333 (ebook)
LCCN: QA351 .T44 2005
bibdate: Sat Oct 30 07:35:31 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 07:35:31 MDT
series: Developments in mathematics
acknowledgement: ack-nhfb
rawbooktitle: Theory and Applications of Special Functions: a Volume Dedicated to {Mizan Rahman}
raweditor: Mourad E. H. Ismail and Erik Koelink
rawtitle: Theory and Applications of Special Functions: a Volume Dedicated to {Mizan Rahman}
ISBN13:
978-0-387-24231-6 (hardcover), 978-0-387-24233-0(e-book) OR 9780387242316 (hardcover), 9780387242330(ebook)

URL:
http://www.loc.gov/catdir/enhancements/fy0663/2005275626-d.html; http://www.loc.gov/catdir/toc/fy0605/2005275626.html

abstract:
This book, dedicated to Mizan Rahman, is made up of a collection of articles on various aspects of q-series and special functions. It also includes an article by Askey, Ismail, and Koelink on Rahman's mathematical contributions and how they influenced the recent upsurge in the subject. Theory and Applications of Special Functions is intended for researchers and graduate students in special functions, algebraic combinatorics, quantum groups, and integrable systems.

subject:
Mathematics; Special Functions; Functions, special; Integral Transforms; Approximations and Expansions; Integral Transforms, Operational Calculus

TOC:
Mizan Rahman, his mathematics and literary writings / Richard Askey, Mourad E. H. Ismail and Erik Koelink On the completeness of sets of $q$-Bessel function $Jnu ^(3)(x; q)$ / L. D. Abreu and J. Bustoz $alpha $-Gaussian polynomials and finite Rogers-Ramanujan identities / George E. Andrews On a generalized gamma convolution related to the $q$-calculus / Christian Berg Ramanujan and cranks / Bruce C. Berndt, Heng Huat Chan, Song Heng Chan and Wen-Chin Liaw Saalschutz chain reactions and multiple $q$-series transformations / Chu Wenchang Painleve equations and associated polynomials / Peter A. Clarkson Zeta functions of Heisenberg graphs over finite rings / Michelle DeDeo, Maria Martinez, Archie Medrano, Marvin Minei, Harold Stark and Audrey Terras $q$-Analogues of some multivariable biorthogonal polynomials / George Gasper and Mizan Rahman ^?? : Some systems of multivariable orthogonal Askey-Wilson polynomials / George Gasper and Mizan Rahman Continuous Hahn functions as Clebsch--Gordan coefficients / Wolter Groenevelt, Erik Koelink and Hjalmar Rosengren New proofs of some $q$-series results / Mourad E. H. Ismail and Ruiming Zhang Little $q$-Jacobi functions of complex order / Kevin W. J. Kadell Second addition formula for continuous $q$-ultraspherical polynomials / Tom H. Koornwinder Bilateral series involving basic hypergeometric functions / Hjalmar Rosengren Hilbert space asymptotics of a class of orthonormal polynomials on a bounded interval / S. N. M. Ruijsenaars Abel--Rothe type generalizations of Jacobi's triple product identity / Michael Schlosser Summable sums of hypergeometric series / D. Stanton Askey--Wilson functions and quantum groups / Jasper V. Stokman Analog of the Cauchy--Hadamard formula for expansions in $q$-polynomials /Remarks on some basic hypergeometric series / Changgui Zhang

rawabstract:
This book, dedicated to Mizan Rahman, is made up of a collection of articles on various aspects of q-series and special functions. It also includes an article by Askey, Ismail, and Koelink on Rahman's mathematical contributions and how they influenced the recent upsurge in the subject. Theory and Applications of Special Functions is intended for researchers and graduate students in special functions, algebraic combinatorics, quantum groups, and integrable systems.

rawTOC:
Mizan Rahman, his mathematics and literary writings / Richard Askey, Mourad E. H. Ismail and Erik Koelink \\ On the completeness of sets of $q$-Bessel function $J\nu^{(3)}(x; q)$ / L. D. Abreu and J. Bustoz \\ $\alpha$-Gaussian polynomials and finite Rogers-Ramanujan identities / George E. Andrews \\ On a generalized gamma convolution related to the $q$-calculus / Christian Berg \\ Ramanujan and cranks / Bruce C. Berndt, Heng Huat Chan, Song Heng Chan and Wen-Chin Liaw \\ Saalschutz chain reactions and multiple $q$-series transformations / Chu Wenchang \\ Painleve equations and associated polynomials / Peter A. Clarkson \\ Zeta functions of Heisenberg graphs over finite rings / Michelle DeDeo, Maria Martinez, Archie Medrano, Marvin Minei, Harold Stark and Audrey Terras \\ $q$-Analogues of some multivariable biorthogonal polynomials / George Gasper and Mizan Rahman \\ ^?? : Some systems of multivariable orthogonal Askey-Wilson polynomials / George Gasper and Mizan Rahman \\ Continuous Hahn functions as Clebsch--Gordan coefficients / Wolter Groenevelt, Erik Koelink and Hjalmar Rosengren \\ New proofs of some $q$-series results / Mourad E. H. Ismail and Ruiming Zhang \\ Little $q$-Jacobi functions of complex order / Kevin W. J. Kadell \\ Second addition formula for continuous $q$-ultraspherical polynomials / Tom H. Koornwinder \\ Bilateral series involving basic hypergeometric functions / Hjalmar Rosengren \\ Hilbert space asymptotics of a class of orthonormal polynomials on a bounded interval / S. N. M. Ruijsenaars \\ Abel--Rothe type generalizations of Jacobi's triple product identity / Michael Schlosser \\ Summable sums of hypergeometric series / D. Stanton \\ Askey--Wilson functions and quantum groups / Jasper V. Stokman \\ Analog of the Cauchy--Hadamard formula for expansions in $q$-polynomials /Remarks on some basic hypergeometric series / Changgui Zhang

entry:
@Book{Ismail:2005:TAS,
  editor =       "Mourad E. H. Ismail and Erik Koelink",
  booktitle =    "Theory and Applications of Special Functions: a Volume
                 Dedicated to {Mizan Rahman}",
  title =        "Theory and Applications of Special Functions: a Volume
                 Dedicated to {Mizan Rahman}",
  volume =       "13",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "x + 491",
  year =         "2005",
  ISBN =         "0-387-24231-7 (hardcover), 0-387-24233-3 (e-book)",
  ISBN-13 =      "978-0-387-24231-6 (hardcover),
                 978-0-387-24233-0(e-book)",
  LCCN =         "QA351 .T44 2005",
  bibdate =      "Sat Oct 30 07:35:31 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Developments in mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0663/2005275626-d.html;
                 http://www.loc.gov/catdir/toc/fy0605/2005275626.html",
  abstract =     "This book, dedicated to Mizan Rahman, is made up of a
                 collection of articles on various aspects of q-series
                 and special functions. It also includes an article by
                 Askey, Ismail, and Koelink on Rahman's mathematical
                 contributions and how they influenced the recent
                 upsurge in the subject. Theory and Applications of
                 Special Functions is intended for researchers and
                 graduate students in special functions, algebraic
                 combinatorics, quantum groups, and integrable
                 systems.",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Special Functions; Functions, special;
                 Integral Transforms; Approximations and Expansions;
                 Integral Transforms, Operational Calculus",
  tableofcontents = "Mizan Rahman, his mathematics and literary writings
                 / Richard Askey, Mourad E. H. Ismail and Erik Koelink
                 \\
                 On the completeness of sets of $q$-Bessel function
                 $J\nu^{(3)}(x; q)$ / L. D. Abreu and J. Bustoz \\
                 $\alpha$-Gaussian polynomials and finite
                 Rogers-Ramanujan identities / George E. Andrews \\
                 On a generalized gamma convolution related to the
                 $q$-calculus / Christian Berg \\
                 Ramanujan and cranks / Bruce C. Berndt, Heng Huat Chan,
                 Song Heng Chan and Wen-Chin Liaw \\
                 Saalschutz chain reactions and multiple $q$-series
                 transformations / Chu Wenchang \\
                 Painleve equations and associated polynomials / Peter
                 A. Clarkson \\
                 Zeta functions of Heisenberg graphs over finite rings /
                 Michelle DeDeo, Maria Martinez, Archie Medrano, Marvin
                 Minei, Harold Stark and Audrey Terras \\
                 $q$-Analogues of some multivariable biorthogonal
                 polynomials / George Gasper and Mizan Rahman \\
                 ^?? : Some systems of multivariable orthogonal
                 Askey-Wilson polynomials / George Gasper and Mizan
                 Rahman \\
                 Continuous Hahn functions as Clebsch--Gordan
                 coefficients / Wolter Groenevelt, Erik Koelink and
                 Hjalmar Rosengren \\
                 New proofs of some $q$-series results / Mourad E. H.
                 Ismail and Ruiming Zhang \\
                 Little $q$-Jacobi functions of complex order / Kevin W.
                 J. Kadell \\
                 Second addition formula for continuous
                 $q$-ultraspherical polynomials / Tom H. Koornwinder \\
                 Bilateral series involving basic hypergeometric
                 functions / Hjalmar Rosengren \\
                 Hilbert space asymptotics of a class of orthonormal
                 polynomials on a bounded interval / S. N. M.
                 Ruijsenaars \\
                 Abel--Rothe type generalizations of Jacobi's triple
                 product identity / Michael Schlosser \\
                 Summable sums of hypergeometric series / D. Stanton \\
                 Askey--Wilson functions and quantum groups / Jasper V.
                 Stokman \\
                 Analog of the Cauchy--Hadamard formula for expansions
                 in $q$-polynomials /Remarks on some basic
                 hypergeometric series / Changgui Zhang",
}


bibtype: proceedings
filename: elefunt.bib
label: Vassiliadis:2005:IIC
editor: Stamatis Vassiliadis and Nikitas J. Dimopoulos and Sanjay Vishnu Rajopadhye
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xiii + 419
year: 2005
ISBN: 0-7695-2407-9 OR 0769524079
ISBN13: 978-0-7695-2407-8 OR 9780769524078
LCCN: TK7874.6 .I58 2005
bibdate: Sun Mar 4 21:53:56 MST 2007
bibtimestamp: 2007.03.04 21:53:56 MST
acknowledgement: ack-nhfb
raweditor: Stamatis Vassiliadis and Nikitas J. Dimopoulos and Sanjay Vishnu Rajopadhye
booktitle:
16th IEEE International Conference on Application-Specific Systems, Architectures, and Processors: ASAP 2005: 23--25 July 2005, Samos, Greece

title:
16th IEEE International Conference on Application-Specific Systems, Architectures, and Processors: ASAP 2005: 23--25 July 2005, Samos, Greece

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; melvyl.cdlib.org:210/CDL90

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

rawbooktitle:
{16th IEEE International Conference on Application-Specific Systems, Architectures, and Processors: ASAP 2005: 23--25 July 2005, Samos, Greece}

rawtitle:
{16th IEEE International Conference on Application-Specific Systems, Architectures, and Processors: ASAP 2005: 23--25 July 2005, Samos, Greece}

entry:
@Proceedings{Vassiliadis:2005:IIC,
  editor =       "Stamatis Vassiliadis and Nikitas J. Dimopoulos and
                 Sanjay Vishnu Rajopadhye",
  booktitle =    "{16th IEEE International Conference on
                 Application-Specific Systems, Architectures, and
                 Processors: ASAP 2005: 23--25 July 2005, Samos,
                 Greece}",
  title =        "{16th IEEE International Conference on
                 Application-Specific Systems, Architectures, and
                 Processors: ASAP 2005: 23--25 July 2005, Samos,
                 Greece}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiii + 419",
  year =         "2005",
  ISBN =         "0-7695-2407-9",
  ISBN-13 =      "978-0-7695-2407-8",
  LCCN =         "TK7874.6 .I58 2005",
  bibdate =      "Sun Mar 4 21:53:56 MST 2007",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 melvyl.cdlib.org:210/CDL90",
  acknowledgement = ack-nhfb,
  meetingname =  "International Conference on Application-Specific
                 Systems, Architectures, and Processors (16th: 2005:
                 Samos, Greece)",
  subject =      "Array processors; Congresses; Signal processing;
                 Digital techniques; Application specific integrated
                 circuits",
}


bibtype: proceedings
filename: elefunt.bib
label: zuCastell:2005:ILO
editor: Wolfgang zu Castell and Frank Filbir and Brigitte Forster
booktitle: Inzell lectures on orthogonal polynomials
title: Inzell lectures on orthogonal polynomials
publisher: Nova Science
address: Hauppauge, NY, USA
pages: x + 199
year: 2005
ISBN: 1-59454-108-6 OR 1594541086
ISBN13: 978-1-59454-108-7 OR 9781594541087
LCCN: QA404.5 .I595 2005
bibdate: Sat Oct 30 17:16:08 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager
bibtimestamp: 2010.10.30 17:16:08 MDT
series: Advances in the theory of special functions and orthogonal polynomials
subject: Orthogonal polynomials
acknowledgement: ack-nhfb
rawbooktitle: {Inzell lectures on orthogonal polynomials}
raweditor: Wolfgang zu Castell and Frank Filbir and Brigitte Forster
rawtitle: {Inzell lectures on orthogonal polynomials}
note:
Lectures from the Inzell Summer School on Orthogonal Polynomials, Harmonic Analysis, Approximation, and Applications, held in Inzell, Germany, September 17--21, 2001.

remark:
Canonical moments, orthogonal polynomials with applications to statistics / Holger Dette Discrete commutative hypergroups / Rupert Lasser Orthogonal polynomials and Banach algebras / Ryszard Szwarc Lecture notes on orthogonal polynomials of several variables / Yuan Xu

rawnote:
Lectures from the Inzell Summer School on Orthogonal Polynomials, Harmonic Analysis, Approximation, and Applications, held in Inzell, Germany, September 17--21, 2001.

entry:
@Proceedings{zuCastell:2005:ILO,
  editor =       "Wolfgang zu Castell and Frank Filbir and Brigitte
                 Forster",
  booktitle =    "{Inzell lectures on orthogonal polynomials}",
  title =        "{Inzell lectures on orthogonal polynomials}",
  publisher =    "Nova Science",
  address =      "Hauppauge, NY, USA",
  pages =        "x + 199",
  year =         "2005",
  ISBN =         "1-59454-108-6",
  ISBN-13 =      "978-1-59454-108-7",
  LCCN =         "QA404.5 .I595 2005",
  bibdate =      "Sat Oct 30 17:16:08 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  note =         "Lectures from the Inzell Summer School on Orthogonal
                 Polynomials, Harmonic Analysis, Approximation, and
                 Applications, held in Inzell, Germany, September
                 17--21, 2001.",
  series =       "Advances in the theory of special functions and
                 orthogonal polynomials",
  acknowledgement = ack-nhfb,
  remark =       "Canonical moments, orthogonal polynomials with
                 applications to statistics / Holger Dette \\
                 Discrete commutative hypergroups / Rupert Lasser \\
                 Orthogonal polynomials and Banach algebras / Ryszard
                 Szwarc \\
                 Lecture notes on orthogonal polynomials of several
                 variables / Yuan Xu",
  subject =      "Orthogonal polynomials",
}


bibtype: proceedings
filename: elefunt.bib
label: Anonymous:2006:PCR
editor: Anonymous
year: 2006
bibdate: Tue Jun 27 10:26:43 2006
bibsource: http://rnc7.loria.fr/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2006.06.27 10:26:43 ???
acknowledgement: ack-nhfb
raweditor: Anonymous
booktitle:
Proceedings of the 7th Conference on Real Numbers and Computers (RNC 7) LORIA, Nancy, France, July 10--12, 2006

title:
Proceedings of the 7th Conference on Real Numbers and Computers (RNC 7) LORIA, Nancy, France, July 10--12, 2006

rawbooktitle:
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rawtitle:
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entry:
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  editor =       "Anonymous",
  booktitle =    "{Proceedings of the 7th Conference on Real Numbers and
                 Computers (RNC 7) LORIA, Nancy, France, July 10--12,
                 2006}",
  title =        "{Proceedings of the 7th Conference on Real Numbers and
                 Computers (RNC 7) LORIA, Nancy, France, July 10--12,
                 2006}",
  publisher =    "????",
  address =      "????",
  pages =        "????",
  year =         "2006",
  ISBN =         "????",
  ISBN-13 =      "????",
  LCCN =         "????",
  bibdate =      "Tue Jun 27 10:26:43 2006",
  bibsource =    "http://rnc7.loria.fr/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Menezes:2006:PAS
editor: Ronaldo Menezes
publisher: pub-ACM
address: pub-ACM:adr
pages: 823
year: 2006
ISBN: 1-59593-315-8 (print) OR 1595933158 (print)
ISBN13: 978-1-59593-315-7 (print) OR 9781595933157 (print)
LCCN: QA75.5 A184 2006 E
bibdate: Sat Oct 9 15:04:24 MDT 2010
bibtimestamp: 2010.10.09 15:04:24 MDT
subject: Computer-assisted instruction; Congresses; Database management; Electronic data processing
acknowledgement: ack-nhfb
raweditor: Ronaldo Menezes
booktitle:
Proceedings of the 44th annual Southeast Regional Conference 2006: Melbourne, Florida, March 10--12, 2006

title:
Proceedings of the 44th annual Southeast Regional Conference 2006: Melbourne, Florida, March 10--12, 2006

bibsource:
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rawbooktitle:
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rawtitle:
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entry:
@Proceedings{Menezes:2006:PAS,
  editor =       "Ronaldo Menezes",
  booktitle =    "{Proceedings of the 44th annual Southeast Regional
                 Conference 2006: Melbourne, Florida, March 10--12,
                 2006}",
  title =        "{Proceedings of the 44th annual Southeast Regional
                 Conference 2006: Melbourne, Florida, March 10--12,
                 2006}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "823",
  year =         "2006",
  ISBN =         "1-59593-315-8 (print)",
  ISBN-13 =      "978-1-59593-315-7 (print)",
  LCCN =         "QA75.5 A184 2006 E",
  bibdate =      "Sat Oct 9 15:04:24 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
  subject =      "Computer-assisted instruction; Congresses; Database
                 management; Electronic data processing",
}


bibtype: proceedings
filename: elefunt.bib
label: Brown:2007:PIS
editor: C. W. Brown
publisher: pub-ACM
address: pub-ACM:adr
year: 2007
ISBN: 1-59593-743-9 (print), 1-59593-742-0 (CD-ROM) OR 1595937439 (print), 1595937420 (CDROM)
LCCN: QA76.5 S98 2007
bibdate: Fri Jun 20 08:53:37 2008
bibtimestamp: 2008.06.20 08:53:37 ???
note: ACM order number 505070.
acknowledgement: ack-nhfb
raweditor: C. W. Brown
rawnote: ACM order number 505070.
booktitle:
Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, July 29--August 1, 2007, University of Waterloo, Waterloo, Ontario, Canada

title:
Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, July 29--August 1, 2007, University of Waterloo, Waterloo, Ontario, Canada

ISBN13:
978-1-59593-743-8 (print), 978-1-59593-742-1 (CD-ROM) OR 9781595937438 (print), 9781595937421 (CDROM)

bibsource:
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rawbooktitle:
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rawtitle:
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entry:
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  editor =       "C. W. Brown",
  booktitle =    "{Proceedings of the 2007 International Symposium on
                 Symbolic and Algebraic Computation, July 29--August 1,
                 2007, University of Waterloo, Waterloo, Ontario,
                 Canada}",
  title =        "{Proceedings of the 2007 International Symposium on
                 Symbolic and Algebraic Computation, July 29--August 1,
                 2007, University of Waterloo, Waterloo, Ontario,
                 Canada}",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "????",
  year =         "2007",
  ISBN =         "1-59593-743-9 (print), 1-59593-742-0 (CD-ROM)",
  ISBN-13 =      "978-1-59593-743-8 (print), 978-1-59593-742-1
                 (CD-ROM)",
  LCCN =         "QA76.5 S98 2007",
  bibdate =      "Fri Jun 20 08:53:37 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/axiom.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/maple-extract.bib",
  note =         "ACM order number 505070.",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: Holzapfel:2007:AGA
editor: Rolf-Peter Holzapfel and A. Muhammed Uludag and Masaaki Yoshida
volume: 235
publisher: pub-BIRKHAUSER
address: pub-BIRKHAUSER:adr
pages: viii + 437
year: 2007
ISBN: 3-7643-8283-X OR 376438283X
ISBN13: 978-3-7643-8283-4 OR 9783764382834
LCCN: QA245 .S86 2005
bibdate: Sat Oct 30 21:12:24 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.10.30 21:12:24 MDT
series: Progress in mathematics
subject: Algebra; Congresses.; Geometry, Algebraic; Congresses; Number theory
acknowledgement: ack-nhfb
raweditor: Rolf-Peter Holzapfel and A. Muhammed Uludag and Masaaki Yoshida
booktitle:
Arithmetic and geometry around hypergeometric functions: lecture notes of a CIMPA Summer School held at Galatasaray University, Istanbul, Turkey, June 13--25, 2005

title:
Arithmetic and geometry around hypergeometric functions: lecture notes of a CIMPA Summer School held at Galatasaray University, Istanbul, Turkey, June 13--25, 2005

URL:
http://www.loc.gov/catdir/enhancements/fy0913/2006939568-d.html; http://www.loc.gov/catdir/enhancements/fy0913/2006939568-t.html

rawbooktitle:
{Arithmetic and geometry around hypergeometric functions: lecture notes of a CIMPA Summer School held at Galatasaray University, Istanbul, Turkey, June 13--25, 2005}

rawtitle:
{Arithmetic and geometry around hypergeometric functions: lecture notes of a CIMPA Summer School held at Galatasaray University, Istanbul, Turkey, June 13--25, 2005}

entry:
@Proceedings{Holzapfel:2007:AGA,
  editor =       "Rolf-Peter Holzapfel and A. Muhammed Uludag and
                 Masaaki Yoshida",
  booktitle =    "{Arithmetic and geometry around hypergeometric
                 functions: lecture notes of a CIMPA Summer School held
                 at Galatasaray University, Istanbul, Turkey, June
                 13--25, 2005}",
  title =        "{Arithmetic and geometry around hypergeometric
                 functions: lecture notes of a CIMPA Summer School held
                 at Galatasaray University, Istanbul, Turkey, June
                 13--25, 2005}",
  volume =       "235",
  publisher =    pub-BIRKHAUSER,
  address =      pub-BIRKHAUSER:adr,
  pages =        "viii + 437",
  year =         "2007",
  ISBN =         "3-7643-8283-X",
  ISBN-13 =      "978-3-7643-8283-4",
  LCCN =         "QA245 .S86 2005",
  bibdate =      "Sat Oct 30 21:12:24 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Progress in mathematics",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0913/2006939568-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0913/2006939568-t.html",
  acknowledgement = ack-nhfb,
  subject =      "Algebra; Congresses.; Geometry, Algebraic; Congresses;
                 Number theory",
}


bibtype: proceedings
filename: elefunt.bib
label: Iske:2007:AAP
editor: Armin Iske and Jeremy Levesley
booktitle: Algorithms for Approximation: Proceedings of the 5th International Conference, Chester, July 2005
title: Algorithms for Approximation: Proceedings of the 5th International Conference, Chester, July 2005
publisher: pub-SV
address: pub-SV:adr
pages: 300
year: 2007
DOI: https://doi.org/10.1007/978-3-540-46551-5
ISBN: 3-540-46551-0, 3-540-33283-9 OR 3540465510, 3540332839
ISBN13: 978-3-540-46551-5, 978-3-540-33283-1 OR 9783540465515, 9783540332831
LCCN: QA221 .A44 2007
bibdate: Thu Dec 1 09:41:19 MST 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.bibsys.no:2100/BIBSYS
bibtimestamp: 2011.12.01 09:41:19 MST
acknowledgement: ack-nhfb
rawbooktitle: {Algorithms for Approximation: Proceedings of the 5th International Conference, Chester, July 2005}
raweditor: Armin Iske and Jeremy Levesley
rawtitle: {Algorithms for Approximation: Proceedings of the 5th International Conference, Chester, July 2005}
subject:
Mathematics; Special Functions; Functions, special; Engineering mathematics; Mathematics of Computing; Approximations and Expansions; Computer science; Computational Mathematics and Numerical Analysis; Appl. Mathematics / Computational Methods of Engineering

entry:
@Proceedings{Iske:2007:AAP,
  editor =       "Armin Iske and Jeremy Levesley",
  booktitle =    "{Algorithms for Approximation: Proceedings of the 5th
                 International Conference, Chester, July 2005}",
  title =        "{Algorithms for Approximation: Proceedings of the 5th
                 International Conference, Chester, July 2005}",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "300",
  year =         "2007",
  DOI =          "https://doi.org/10.1007/978-3-540-46551-5",
  ISBN =         "3-540-46551-0, 3-540-33283-9",
  ISBN-13 =      "978-3-540-46551-5, 978-3-540-33283-1",
  LCCN =         "QA221 .A44 2007",
  bibdate =      "Thu Dec 1 09:41:19 MST 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  acknowledgement = ack-nhfb,
  subject =      "Mathematics; Special Functions; Functions, special;
                 Engineering mathematics; Mathematics of Computing;
                 Approximations and Expansions; Computer science;
                 Computational Mathematics and Numerical Analysis; Appl.
                 Mathematics / Computational Methods of Engineering",
}


bibtype: proceedings
filename: elefunt.bib
label: Kornerup:2007:PIS
editor: Peter Kornerup and Jean-Michel Muller
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xii + 269
year: 2007
ISBN: 0-7695-2854-6 OR 0769528546
ISBN13: 978-0-7695-2854-0 OR 9780769528540
ISSN: 1063-6889 OR 10636889
LCCN: QA76.9.C62
bibdate: Tue Jun 27 10:26:43 2006
bibtimestamp: 2006.06.27 10:26:43 ???
URL: http://www.lirmm.fr/arith18/
keywords: ARITH-18
acknowledgement: ack-nhfb
raweditor: Peter Kornerup and Jean-Michel Muller
booktitle:
Proceedings of the 18th IEEE Symposium on Computer Arithmetic, June 25--27, 2007, Montpellier, France

title:
Proceedings of the 18th IEEE Symposium on Computer Arithmetic, June 25--27, 2007, Montpellier, France

bibsource:
http://www.lirmm.fr/arith18/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; odin2.bib.sdu.dk:210/Horizon

rawbooktitle:
{Proceedings of the 18th IEEE Symposium on Computer Arithmetic, June 25--27, 2007, Montpellier, France}

rawtitle:
{Proceedings of the 18th IEEE Symposium on Computer Arithmetic, June 25--27, 2007, Montpellier, France}

entry:
@Proceedings{Kornerup:2007:PIS,
  editor =       "Peter Kornerup and Jean-Michel Muller",
  booktitle =    "{Proceedings of the 18th IEEE Symposium on Computer
                 Arithmetic, June 25--27, 2007, Montpellier, France}",
  title =        "{Proceedings of the 18th IEEE Symposium on Computer
                 Arithmetic, June 25--27, 2007, Montpellier, France}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xii + 269",
  year =         "2007",
  ISBN =         "0-7695-2854-6",
  ISBN-13 =      "978-0-7695-2854-0",
  ISSN =         "1063-6889",
  LCCN =         "QA76.9.C62",
  bibdate =      "Tue Jun 27 10:26:43 2006",
  bibsource =    "http://www.lirmm.fr/arith18/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 odin2.bib.sdu.dk:210/Horizon",
  URL =          "http://www.lirmm.fr/arith18/",
  acknowledgement = ack-nhfb,
  keywords =     "ARITH-18",
}


bibtype: book
filename: elefunt.bib
label: Cerone:2008:AIS
editor: Pietro Cerone and Sever Silvestru Dragomir
booktitle: Advances in Inequalities for Special Functions
title: Advances in Inequalities for Special Functions
publisher: Nova Science Publishers
address: New York, NY, USA
pages: 170
year: 2008
ISBN: 1-60021-919-5 (hardcover), 1-60692-621-7 (e-book) OR 1600219195 (hardcover), 1606926217 (ebook)
LCCN: QA351 .A375 2008
bibdate: Fri Oct 18 16:18:25 MDT 2024
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.10.18 16:18:25 MDT
series: Advances in mathematical inequalities
URL: http://catalog.hathitrust.org/api/volumes/oclc/159822357.html
acknowledgement: ack-nhfb
rawbooktitle: Advances in Inequalities for Special Functions
raweditor: Pietro Cerone and Sever Silvestru Dragomir
rawtitle: Advances in Inequalities for Special Functions
ISBN13:
978-1-60021-919-1 (hardcover), 978-1-60692-621-5 (e-book) OR 9781600219191 (hardcover), 9781606926215 (ebook)

subject:
Functions, Special; Inequalities (Mathematics); Fonctions speciales; Inegalites (Mathematiques); MATHEMATICS; Calculus; Mathematical Analysis; Functions, Special; Inequalities (Mathematics)

TOC:
Special functions approximations and bounds via integral representation / P. Cerone / 1 Inequalities for positive Dirichlet series / P. Cerone and S. S. Dragomir / 37 Monotonicity of the mean value function of normalized Bessel functions of first kind / Stamatis Koumandos / 67 Sturm theory for some classes of Sturm--Liouville equations and inequalities and monotonicity properties for the zeros of Bessel functions / Andrea Laforgia and Pierpaolo Natalini / 73 Inequalities for the Gamma function via convexity / Milan Merkle / 81 Some inequalities for hyperharmonic series / Istvan Mezo / 101 The Hermite--Hadamard inequalities for double Dirichlet averages and their applications to special functions / Edward Neuman / 107 On new inequalities involving convex functions / B. G. Pachpatte / 119 On growth rates of Weierstrass $wp '(z)$ and $wp (z)$ / Tibor K. Pogany / 125 On certain special functions of number theory and mathematical analysis / Jozsef Sandor / 133 On the operator $oplus ^k_B$ related to the Bessel-wave equation and Laplacian--Bessel / Mehmet Zeki Sarikaya and Huseyin Yildirim / 149 Inequalities for Walsh polynomials with semi-monotone coefficients of higher order / Zivorad Tomovski / 161 Index / 169

rawTOC:
Special functions approximations and bounds via integral representation / P. Cerone / 1 \\ Inequalities for positive Dirichlet series / P. Cerone and S. S. Dragomir / 37 \\ Monotonicity of the mean value function of normalized Bessel functions of first kind / Stamatis Koumandos / 67 \\ Sturm theory for some classes of Sturm--Liouville equations and inequalities and monotonicity properties for the zeros of Bessel functions / Andrea Laforgia and Pierpaolo Natalini / 73 \\ Inequalities for the Gamma function via convexity / Milan Merkle / 81 \\ Some inequalities for hyperharmonic series / Istv{\'a}n Mez{\H{o}} / 101 \\ The Hermite--Hadamard inequalities for double Dirichlet averages and their applications to special functions / Edward Neuman / 107 \\ On new inequalities involving convex functions / B. G. Pachpatte / 119 \\ On growth rates of Weierstrass $\wp'(z)$ and $\wp(z)$ / Tibor K. Pog{\'a}ny / 125 \\ On certain special functions of number theory and mathematical analysis / J{\'o}zsef S{\'a}ndor / 133 \\ On the operator $\oplus^k_B$ related to the Bessel-wave equation and Laplacian--Bessel / Mehmet Zeki Sarikaya and H{\"u}seyin Yildirim / 149 \\ Inequalities for Walsh polynomials with semi-monotone coefficients of higher order / {\v{Z}}ivorad Tomovski / 161 \\ Index / 169

entry:
@Book{Cerone:2008:AIS,
  editor =       "Pietro Cerone and Sever Silvestru Dragomir",
  booktitle =    "Advances in Inequalities for Special Functions",
  title =        "Advances in Inequalities for Special Functions",
  publisher =    "Nova Science Publishers",
  address =      "New York, NY, USA",
  pages =        "170",
  year =         "2008",
  ISBN =         "1-60021-919-5 (hardcover), 1-60692-621-7 (e-book)",
  ISBN-13 =      "978-1-60021-919-1 (hardcover), 978-1-60692-621-5
                 (e-book)",
  LCCN =         "QA351 .A375 2008",
  bibdate =      "Fri Oct 18 16:18:25 MDT 2024",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Advances in mathematical inequalities",
  URL =          "http://catalog.hathitrust.org/api/volumes/oclc/159822357.html",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Special; Inequalities (Mathematics);
                 Fonctions sp{\'e}ciales; In{\'e}galit{\'e}s
                 (Math{\'e}matiques); MATHEMATICS; Calculus;
                 Mathematical Analysis; Functions, Special;
                 Inequalities (Mathematics)",
  tableofcontents = "Special functions approximations and bounds via
                 integral representation / P. Cerone / 1 \\
                 Inequalities for positive Dirichlet series / P. Cerone
                 and S. S. Dragomir / 37 \\
                 Monotonicity of the mean value function of normalized
                 Bessel functions of first kind / Stamatis Koumandos /
                 67 \\
                 Sturm theory for some classes of Sturm--Liouville
                 equations and inequalities and monotonicity properties
                 for the zeros of Bessel functions / Andrea Laforgia and
                 Pierpaolo Natalini / 73 \\
                 Inequalities for the Gamma function via convexity /
                 Milan Merkle / 81 \\
                 Some inequalities for hyperharmonic series / Istv{\'a}n
                 Mez{\H{o}} / 101 \\
                 The Hermite--Hadamard inequalities for double Dirichlet
                 averages and their applications to special functions /
                 Edward Neuman / 107 \\
                 On new inequalities involving convex functions / B. G.
                 Pachpatte / 119 \\
                 On growth rates of Weierstrass $\wp'(z)$ and $\wp(z)$ /
                 Tibor K. Pog{\'a}ny / 125 \\
                 On certain special functions of number theory and
                 mathematical analysis / J{\'o}zsef S{\'a}ndor / 133 \\
                 On the operator $\oplus^k_B$ related to the Bessel-wave
                 equation and Laplacian--Bessel / Mehmet Zeki Sarikaya
                 and H{\"u}seyin Yildirim / 149 \\
                 Inequalities for Walsh polynomials with semi-monotone
                 coefficients of higher order / {\v{Z}}ivorad Tomovski /
                 161 \\
                 Index / 169",
}


bibtype: proceedings
filename: elefunt.bib
label: Dominici:2008:SFO
editor: Diego Dominici and Robert S. Maier
volume: 471
publisher: pub-AMS
address: pub-AMS:adr
pages: v + 218
year: 2008
ISBN: 0-8218-4650-7 OR 0821846507
ISBN13: 978-0-8218-4650-6 OR 9780821846506
bibdate: Sat Oct 30 17:30:10 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.bibsys.no:2100/BIBSYS
bibtimestamp: 2010.10.30 17:30:10 MDT
series: Contemporary mathematics
acknowledgement: ack-nhfb
raweditor: Diego Dominici and Robert S. Maier
booktitle:
Special functions and orthogonal polynomials: AMS Special Session on Special Functions and Orthogonal Polynomials, April 21--22, 2007, Tucson, Arizona

title:
Special functions and orthogonal polynomials: AMS Special Session on Special Functions and Orthogonal Polynomials, April 21--22, 2007, Tucson, Arizona

rawbooktitle:
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rawtitle:
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entry:
@Proceedings{Dominici:2008:SFO,
  editor =       "Diego Dominici and Robert S. Maier",
  booktitle =    "{Special functions and orthogonal polynomials: AMS
                 Special Session on Special Functions and Orthogonal
                 Polynomials, April 21--22, 2007, Tucson, Arizona}",
  title =        "{Special functions and orthogonal polynomials: AMS
                 Special Session on Special Functions and Orthogonal
                 Polynomials, April 21--22, 2007, Tucson, Arizona}",
  volume =       "471",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "v + 218",
  year =         "2008",
  ISBN =         "0-8218-4650-7",
  ISBN-13 =      "978-0-8218-4650-6",
  LCCN =         "????",
  bibdate =      "Sat Oct 30 17:30:10 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.bibsys.no:2100/BIBSYS",
  series =       "Contemporary mathematics",
  acknowledgement = ack-nhfb,
}


bibtype: proceedings
filename: elefunt.bib
label: IEEE:2008:ICA
editor: IEEE
publisher: pub-IEEE
address: pub-IEEE:adr
pages: xiv + 309 + 12
year: 2008
ISBN: 1-4244-1897-6 (paperback), 1-4244-1898-4 OR 1424418976 (paperback), 1424418984
ISBN13: 978-1-4244-1897-8 (paperback), 978-1-4244-1898-5 OR 9781424418978 (paperback), 9781424418985
bibdate: Mon Feb 10 07:31:38 MST 2020
bibtimestamp: 2020.02.10 07:31:38 MST
note: IEEE catalog number CFP08063-PRT.
remark: Kongress auch zitiert als: ASAP 08. Parallel als Online-Ausg. erschienen. ASAP 08.
acknowledgement: ack-nhfb
raweditor: {IEEE}
rawnote: IEEE catalog number CFP08063-PRT.
booktitle:
2008 International Conference on Application-Specific Systems, Architectures and Processors: Leuven, Belgium, 2--4 July 2008

title:
2008 International Conference on Application-Specific Systems, Architectures and Processors: Leuven, Belgium, 2--4 July 2008

bibsource:
fsz3950.oclc.org:210/WorldCat; 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/prng.bib

URL:
http://ieeexplore.ieee.org/servlet/opac?punumber=4569858; http://www.gbv.de/dms/tib-ub-hannover/631855815.pdf

TOC:
ASAP08 Conference proceedings / c1--c1 / doi: 10.1109/ASAP.2008.4580199 ASAP08 Conference proceedings / c2--c2 / doi: 10.1109/ASAP.2008.4580200 Frontmatter and table of contents / c1--xiii / doi: 10.1109/ASAP.2008.4580202 ASAP Organizing and Steering Committees / ix ASAP Technical Technical Program Committee / x Keynote 1: Security and Opportunities for Application-Specific Processors / Ruby B. Lee / xii Keynote 2: Art of of Application-Specific Processor Design: Great Artists use Good Tools / Gert Goossens / xiv Session 1: Application-Specific Processor Instruction Sets / 1 Copyright notice / i--i / doi: 10.1109/ASAP.2008.4580197 Copyright notice / ii--ii / doi: 10.1109/ASAP.2008.4580198 K. Atasu, O. Mencer, W. Luk, C. Ozturan and G. Dundar / Fast custom instruction identification by convex subgraph enumeration / 1--6 / doi: 10.1109/ASAP.2008.4580145 Y. Hilewitz, C. Lauradoux and R. B. Lee / Bit matrix multiplication in commodity processors / 7--12 / doi: 10.1109/ASAP.2008.4580146 M. Alle et al. / Synthesis of application accelerators on Runtime Reconfigurable Hardware / 13--18 / doi: 10.1109/ASAP.2008.4580147 A. Amaricai, M. Vladutiu, M. Udrescu, L. Prodan and O. Boncalo / Floating point multiplication rounding schemes for interval arithmetic / 19--24 / doi: 10.1109/ASAP.2008.4580148 S. Balasubramanian, H. W. Carter, A. Bogdanov, A. Rupp and Jintai Ding / Fast multivariate signature generation in hardware: The case of rainbow / 25--30 / doi: 10.1109/ASAP.2008.4580149 M. Hosseinabady and J. Nunez-Yanez / Fault-tolerant dynamically reconfigurable NoC-based SoC / 31--36 / doi: 10.1109/ASAP.2008.4580150 T. Lorunser et al. / Security Processor with Quantum Key Distribution / 37--42 / doi: 10.1109/ASAP.2008.4580151 P. K. Meher and J. C. Patra / Fully-pipelined efficient architectures for FPGA realization of discrete Hadamard transform / 43--48 / doi: 10.1109/ASAP.2008.4580152 R. Rajore, G. Garga, H. S. Jamadagni and S. K. Nandy / Reconfigurable Viterbi decoder on mesh connected multiprocessor architecture / 49--54 / doi: 10.1109/ASAP.2008.4580153 T. Ramdas, G. K. Egan, D. Abramson and K. K. Baldridge / Run-time thread sorting to expose data-level parallelism / 55--60 / doi: 10.1109/ASAP.2008.4580154 S. Jovanovic, C. Tanougast and S. Weber / A New High-Performance Scalable Dynamic Interconnection for FPGA-based Reconfigurable Systems / 61--66 / doi: 10.1109/ASAP.2008.4580155 D. Dickin and L. Shannon / Extending the SIMPPL SoC architectural framework to support application-specific architectures on multi-FPGA platforms / 67--72 / doi: 10.1109/ASAP.2008.4580156 A. E. Kiasari, S. Hessabi and H. Sarbazi-Azad / PERMAP: A performance-aware mapping for application-specific SoCs / 73--78 / doi: 10.1109/ASAP.2008.4580157 A. C. Atici, L. Batina, Junfeng Fan, I. Verbauwhede and S. Berna Ors Yalcin / Low-cost implementations of NTRU for pervasive security / 79--84 / doi: 10.1109/ASAP.2008.4580158 M. Knezzevic, K. Sakiyama, Y. K. Lee and I. Verbauwhede / On the high-throughput implementation of RIPEMD-160 hash algorithm / 85--90 / doi: 10.1109/ASAP.2008.4580159 Wang Haixin, Bai Guoqiang and Chen Hongyi / Zodiac: System architecture implementation for a high-performance Network Security Processor / 91--96 / doi: 10.1109/ASAP.2008.4580160 P. K. Meher / Efficient systolization of cyclic convolution for systolic implementation of sinusoidal transforms / 97--101 / doi: 10.1109/ASAP.2008.4580161 D. B. Thomas and W. Luk / Resource efficient generators for the floating-point uniform and exponential distributions / 102--107 / doi: 10.1109/ASAP.2008.4580162 I. L. Dalal, D. Stefan and J. Harwayne-Gidansky / Low discrepancy sequences for Monte Carlo simulations on reconfigurable platforms / 108--113 / doi: 10.1109/ASAP.2008.4580163 Y. Vanderperren and W. Dehaene / A subsampling pulsed UWB demodulator based on a flexible complex SVD / 114--119 / doi: 10.1109/ASAP.2008.4580164 J. Divyasree, H. Rajashekar and K. Varghese / Dynamically reconfigurable regular expression matching architecture / 120--125 / doi: 10.1109/ASAP.2008.4580165 J. Khan, S. Niar, A. Menhaj, Y. Elhillali and J. L. Dekeyser / An MPSoC architecture for the Multiple Target Tracking application in driver assistant system / 126--131 / doi: 10.1109/ASAP.2008.4580166 Wangyuan Zhang and Tao Li / Managing multi-core soft-error reliability through utility-driven cross domain optimization / 132--137 / doi: 10.1109/ASAP.2008.4580167 S. Braganza and M. Leeser / An efficient implementation of a phase unwrapping kernel on reconfigurable hardware / 138--143 / doi: 10.1109/ASAP.2008.4580168 H. Flatt, S. Blume, S. Hesselbarth, T. Schunemann and P. Pirsch / A parallel hardware architecture for connected component labeling based on fast label merging / 144--149 / doi: 10.1109/ASAP.2008.4580169 Yuki Kobayashi, M. Jayapala, P. Raghavan, F. Catthoor and Masaharu Imai / Operation shuffling over cycle boundaries for low energy L0 clustering / 150--155 / doi: 10.1109/ASAP.2008.4580170 V. Kundeti, Yunsi Fei and S. Rajasekaran / An efficient digital circuit for implementing Sequence Alignment algorithm in an extended processor / 156--161 / doi: 10.1109/ASAP.2008.4580171 B. K. Mohanty and P. K. Meher / Concurrent systolic architecture for high-throughput implementation of 3-dimensional discrete wavelet transform / 162--166 / doi: 10.1109/ASAP.2008.4580172 S. Mirzaei, A. Irturk, R. Kastner, B. T. Weals and R. E. Cagley / Design space exploration of a cooperative MIMO receiver for reconfigurable architectures / 167--172 / doi: 10.1109/ASAP.2008.4580173 Mao Nakajima and Minoru Watanabe / Dynamic holographic reconfiguration on a four-context ODRGA / 173--178 / doi: 10.1109/ASAP.2008.4580174 F. Pardo, P. Lopez and D. Cabello / FPGA-based hardware accelerator of the heat equation with applications on infrared thermography / 179--184 / doi: 10.1109/ASAP.2008.4580175 M. Rahmati, M. S. Sadri and M. A. Naeini / FPGA based singular value decomposition for image processing applications / 185--190 / doi: 10.1109/ASAP.2008.4580176 A. Jacob, J. Buhler and R. D. Chamberlain / Accelerating Nussinov RNA secondary structure prediction with systolic arrays on FPGAs / 191--196 / doi: 10.1109/ASAP.2008.4580177 J. Lee, L. Shannon, M. J. Yedlin and G. F. Margrave / A multi-FPGA application-specific architecture for accelerating a floating point Fourier Integral Operator / 197--202 / doi: 10.1109/ASAP.2008.4580178 K. F. C. Yiu, Chun Hok Ho, N. Grbric, Yao Lu, Xiaoxiang Shi and W. Luk / Reconfigurable acceleration of microphone array algorithms for speech enhancement / 203--208 / doi: 10.1109/ASAP.2008.4580179 Yang Sun, Yuming Zhu, M. Goel and J. R. Cavallaro / Configurable and scalable high throughput turbo decoder architecture for multiple 4G wireless standards / 209--214 / doi: 10.1109/ASAP.2008.4580180 M. B. S. Tavares, S. Kunze, E. Matus and G. P. Fettweis / Architecture and VLSI realization of a high-speed programmable decoder for LDPC convolutional codes / 215--220 / doi: 10.1109/ASAP.2008.4580181 D. Llorente, K. Karras, T. Wild and A. Herkersdorf / Buffer allocation for advanced packet segmentation in Network Processors / 221--226 / doi: 10.1109/ASAP.2008.4580182 A. Vazquez and E. Antelo / New insights on Ling adders / 227--232 / doi: 10.1109/ASAP.2008.4580183 N. Brisebarre, F. de Dinechin and J. Muller / Integer and floating-point constant multipliers for FPGAs / 239--244 / doi: 10.1109/ASAP.2008.4580184 N. Brisebarre, S. Chevillard, M. D. Ercegovac, J. Muller and S. Torres / An efficient method for evaluating polynomial and rational function approximations / 233--238 / doi: 10.1109/ASAP.2008.4580185 A. Garcia, M. Berekovic and T. Vander Aa / Mapping of the AES cryptographic algorithm on a Coarse-Grain reconfigurable array processor / 245--250 / doi: 10.1109/ASAP.2008.4580186 J. Nimmy et al. / RECONNECT: A NoC for polymorphic ASICs using a low overhead single cycle router / 251--256 / doi: 10.1109/ASAP.2008.4580187 M. Mbaye, N. Belanger, Y. Savaria and S. Pierre / Loop-oriented metrics for exploring an application-specific architecture design-space / 257--262 / doi: 10.1109/ASAP.2008.4580188 S. K. Dash and T. Srikanthan / Rapid estimation of instruction cache hit rates using loop profiling / 263--268 / doi: 10.1109/ASAP.2008.4580189 Xuan Guan and Yunsi Fei / Reducing power consumption of embedded processors through register file partitioning and compiler support / 269--274 / doi: 10.1109/ASAP.2008.4580190 A. Tumeo, M. Monchiero, G. Palermo, F. Ferrandi and D. Sciuto / Lightweight DMA management mechanisms for multiprocessors on FPGA / 275--280 / doi: 10.1109/ASAP.2008.4580191 P. de Langen and B. Juurlink / Memory copies in multi-level memory systems / 281--286 / doi: 10.1109/ASAP.2008.4580192 R. Adrsha, Mythri, S. K. Nandy and R. Narayan / Architecture of a polymorphic ASIC for interoperability across multi-mode H.264 decoders / 287--292 / doi: 10.1109/ASAP.2008.4580193 R. R. Osorio and J. D. Bruguera / An FPGA architecture for CABAC decoding in manycore systems / 293--298 / doi: 10.1109/ASAP.2008.4580194 A. Guntoro and M. Glesner / Novel approach on lifting-based DWT and IDWT processor with multi-context configuration to support different wavelet filters / 299--304 / doi: 10.1109/ASAP.2008.4580195 B. K. Mohanty and P. K. Meher / Throughput-scalable hybrid-pipeline architecture for multilevel lifting 2-D DWT of JPEG 2000 coder / 305--309 / doi: 10.1109/ASAP.2008.4580196 Author index / 310--321 / doi: 10.1109/ASAP.2008.4580201

rawbooktitle:
{2008 International Conference on Application-Specific Systems, Architectures and Processors: Leuven, Belgium, 2--4 July 2008}

rawtitle:
{2008 International Conference on Application-Specific Systems, Architectures and Processors: Leuven, Belgium, 2--4 July 2008}

rawTOC:
ASAP08 Conference proceedings / c1--c1 / doi: 10.1109/ASAP.2008.4580199 \\ ASAP08 Conference proceedings / c2--c2 / doi: 10.1109/ASAP.2008.4580200 \\ Frontmatter and table of contents / c1--xiii / doi: 10.1109/ASAP.2008.4580202 \\ ASAP Organizing and Steering Committees / ix \\ ASAP Technical Technical Program Committee / x \\ Keynote 1: Security and Opportunities for Application-Specific Processors / Ruby B. Lee / xii \\ Keynote 2: Art of of Application-Specific Processor Design: Great Artists use Good Tools / Gert Goossens / xiv \\ Session 1: Application-Specific Processor Instruction Sets / 1 \\ Copyright notice / i--i / doi: 10.1109/ASAP.2008.4580197 \\ Copyright notice / ii--ii / doi: 10.1109/ASAP.2008.4580198 \\ K. Atasu, O. Mencer, W. Luk, C. Ozturan and G. Dundar / Fast custom instruction identification by convex subgraph enumeration / 1--6 / doi: 10.1109/ASAP.2008.4580145 \\ Y. Hilewitz, C. Lauradoux and R. B. Lee / Bit matrix multiplication in commodity processors / 7--12 / doi: 10.1109/ASAP.2008.4580146 \\ M. Alle et al. / Synthesis of application accelerators on Runtime Reconfigurable Hardware / 13--18 / doi: 10.1109/ASAP.2008.4580147 \\ A. Amaricai, M. Vladutiu, M. Udrescu, L. Prodan and O. Boncalo / Floating point multiplication rounding schemes for interval arithmetic / 19--24 / doi: 10.1109/ASAP.2008.4580148 \\ S. Balasubramanian, H. W. Carter, A. Bogdanov, A. Rupp and Jintai Ding / Fast multivariate signature generation in hardware: The case of rainbow / 25--30 / doi: 10.1109/ASAP.2008.4580149 \\ M. Hosseinabady and J. Nunez-Yanez / Fault-tolerant dynamically reconfigurable NoC-based SoC / 31--36 / doi: 10.1109/ASAP.2008.4580150 \\ T. Lorunser et al. / Security Processor with Quantum Key Distribution / 37--42 / doi: 10.1109/ASAP.2008.4580151 \\ P. K. Meher and J. C. Patra / Fully-pipelined efficient architectures for FPGA realization of discrete Hadamard transform / 43--48 / doi: 10.1109/ASAP.2008.4580152 \\ R. Rajore, G. Garga, H. S. Jamadagni and S. K. Nandy / Reconfigurable Viterbi decoder on mesh connected multiprocessor architecture / 49--54 / doi: 10.1109/ASAP.2008.4580153 \\ T. Ramdas, G. K. Egan, D. Abramson and K. K. Baldridge / Run-time thread sorting to expose data-level parallelism / 55--60 / doi: 10.1109/ASAP.2008.4580154 \\ S. Jovanovic, C. Tanougast and S. Weber / A New High-Performance Scalable Dynamic Interconnection for FPGA-based Reconfigurable Systems / 61--66 / doi: 10.1109/ASAP.2008.4580155 \\ D. Dickin and L. Shannon / Extending the SIMPPL SoC architectural framework to support application-specific architectures on multi-FPGA platforms / 67--72 / doi: 10.1109/ASAP.2008.4580156 \\ A. E. Kiasari, S. Hessabi and H. Sarbazi-Azad / PERMAP: A performance-aware mapping for application-specific SoCs / 73--78 / doi: 10.1109/ASAP.2008.4580157 \\ A. C. Atici, L. Batina, Junfeng Fan, I. Verbauwhede and S. Berna Ors Yalcin / Low-cost implementations of NTRU for pervasive security / 79--84 / doi: 10.1109/ASAP.2008.4580158 \\ M. Knezzevic, K. Sakiyama, Y. K. Lee and I. Verbauwhede / On the high-throughput implementation of RIPEMD-160 hash algorithm / 85--90 / doi: 10.1109/ASAP.2008.4580159 \\ Wang Haixin, Bai Guoqiang and Chen Hongyi / Zodiac: System architecture implementation for a high-performance Network Security Processor / 91--96 / doi: 10.1109/ASAP.2008.4580160 \\ P. K. Meher / Efficient systolization of cyclic convolution for systolic implementation of sinusoidal transforms / 97--101 / doi: 10.1109/ASAP.2008.4580161 \\ D. B. Thomas and W. Luk / Resource efficient generators for the floating-point uniform and exponential distributions / 102--107 / doi: 10.1109/ASAP.2008.4580162 \\ I. L. Dalal, D. Stefan and J. Harwayne-Gidansky / Low discrepancy sequences for Monte Carlo simulations on reconfigurable platforms / 108--113 / doi: 10.1109/ASAP.2008.4580163 \\ Y. Vanderperren and W. Dehaene / A subsampling pulsed UWB demodulator based on a flexible complex SVD / 114--119 / doi: 10.1109/ASAP.2008.4580164 \\ J. Divyasree, H. Rajashekar and K. Varghese / Dynamically reconfigurable regular expression matching architecture / 120--125 / doi: 10.1109/ASAP.2008.4580165 \\ J. Khan, S. Niar, A. Menhaj, Y. Elhillali and J. L. Dekeyser / An MPSoC architecture for the Multiple Target Tracking application in driver assistant system / 126--131 / doi: 10.1109/ASAP.2008.4580166 \\ Wangyuan Zhang and Tao Li / Managing multi-core soft-error reliability through utility-driven cross domain optimization / 132--137 / doi: 10.1109/ASAP.2008.4580167 \\ S. Braganza and M. Leeser / An efficient implementation of a phase unwrapping kernel on reconfigurable hardware / 138--143 / doi: 10.1109/ASAP.2008.4580168 \\ H. Flatt, S. Blume, S. Hesselbarth, T. Schunemann and P. Pirsch / A parallel hardware architecture for connected component labeling based on fast label merging / 144--149 / doi: 10.1109/ASAP.2008.4580169 \\ Yuki Kobayashi, M. Jayapala, P. Raghavan, F. Catthoor and Masaharu Imai / Operation shuffling over cycle boundaries for low energy L0 clustering / 150--155 / doi: 10.1109/ASAP.2008.4580170 \\ V. Kundeti, Yunsi Fei and S. Rajasekaran / An efficient digital circuit for implementing Sequence Alignment algorithm in an extended processor / 156--161 / doi: 10.1109/ASAP.2008.4580171 \\ B. K. Mohanty and P. K. Meher / Concurrent systolic architecture for high-throughput implementation of 3-dimensional discrete wavelet transform / 162--166 / doi: 10.1109/ASAP.2008.4580172 \\ S. Mirzaei, A. Irturk, R. Kastner, B. T. Weals and R. E. Cagley / Design space exploration of a cooperative MIMO receiver for reconfigurable architectures / 167--172 / doi: 10.1109/ASAP.2008.4580173 \\ Mao Nakajima and Minoru Watanabe / Dynamic holographic reconfiguration on a four-context ODRGA / 173--178 / doi: 10.1109/ASAP.2008.4580174 \\ F. Pardo, P. Lopez and D. Cabello / FPGA-based hardware accelerator of the heat equation with applications on infrared thermography / 179--184 / doi: 10.1109/ASAP.2008.4580175 \\ M. Rahmati, M. S. Sadri and M. A. Naeini / FPGA based singular value decomposition for image processing applications / 185--190 / doi: 10.1109/ASAP.2008.4580176 \\ A. Jacob, J. Buhler and R. D. Chamberlain / Accelerating Nussinov RNA secondary structure prediction with systolic arrays on FPGAs / 191--196 / doi: 10.1109/ASAP.2008.4580177 \\ J. Lee, L. Shannon, M. J. Yedlin and G. F. Margrave / A multi-FPGA application-specific architecture for accelerating a floating point Fourier Integral Operator / 197--202 / doi: 10.1109/ASAP.2008.4580178 \\ K. F. C. Yiu, Chun Hok Ho, N. Grbric, Yao Lu, Xiaoxiang Shi and W. Luk / Reconfigurable acceleration of microphone array algorithms for speech enhancement / 203--208 / doi: 10.1109/ASAP.2008.4580179 \\ Yang Sun, Yuming Zhu, M. Goel and J. R. Cavallaro / Configurable and scalable high throughput turbo decoder architecture for multiple 4G wireless standards / 209--214 / doi: 10.1109/ASAP.2008.4580180 \\ M. B. S. Tavares, S. Kunze, E. Matus and G. P. Fettweis / Architecture and VLSI realization of a high-speed programmable decoder for LDPC convolutional codes / 215--220 / doi: 10.1109/ASAP.2008.4580181 \\ D. Llorente, K. Karras, T. Wild and A. Herkersdorf / Buffer allocation for advanced packet segmentation in Network Processors / 221--226 / doi: 10.1109/ASAP.2008.4580182 \\ A. Vazquez and E. Antelo / New insights on Ling adders / 227--232 / doi: 10.1109/ASAP.2008.4580183 \\ N. Brisebarre, F. de Dinechin and J. Muller / Integer and floating-point constant multipliers for FPGAs / 239--244 / doi: 10.1109/ASAP.2008.4580184 \\ N. Brisebarre, S. Chevillard, M. D. Ercegovac, J. Muller and S. Torres / An efficient method for evaluating polynomial and rational function approximations / 233--238 / doi: 10.1109/ASAP.2008.4580185 \\ A. Garcia, M. Berekovic and T. Vander Aa / Mapping of the AES cryptographic algorithm on a Coarse-Grain reconfigurable array processor / 245--250 / doi: 10.1109/ASAP.2008.4580186 \\ J. Nimmy et al. / RECONNECT: A NoC for polymorphic ASICs using a low overhead single cycle router / 251--256 / doi: 10.1109/ASAP.2008.4580187 \\ M. Mbaye, N. Belanger, Y. Savaria and S. Pierre / Loop-oriented metrics for exploring an application-specific architecture design-space / 257--262 / doi: 10.1109/ASAP.2008.4580188 \\ S. K. Dash and T. Srikanthan / Rapid estimation of instruction cache hit rates using loop profiling / 263--268 / doi: 10.1109/ASAP.2008.4580189 \\ Xuan Guan and Yunsi Fei / Reducing power consumption of embedded processors through register file partitioning and compiler support / 269--274 / doi: 10.1109/ASAP.2008.4580190 \\ A. Tumeo, M. Monchiero, G. Palermo, F. Ferrandi and D. Sciuto / Lightweight DMA management mechanisms for multiprocessors on FPGA / 275--280 / doi: 10.1109/ASAP.2008.4580191 \\ P. de Langen and B. Juurlink / Memory copies in multi-level memory systems / 281--286 / doi: 10.1109/ASAP.2008.4580192 \\ R. Adrsha, Mythri, S. K. Nandy and R. Narayan / Architecture of a polymorphic ASIC for interoperability across multi-mode H.264 decoders / 287--292 / doi: 10.1109/ASAP.2008.4580193 \\ R. R. Osorio and J. D. Bruguera / An FPGA architecture for CABAC decoding in manycore systems / 293--298 / doi: 10.1109/ASAP.2008.4580194 \\ A. Guntoro and M. Glesner / Novel approach on lifting-based DWT and IDWT processor with multi-context configuration to support different wavelet filters / 299--304 / doi: 10.1109/ASAP.2008.4580195 \\ B. K. Mohanty and P. K. Meher / Throughput-scalable hybrid-pipeline architecture for multilevel lifting 2-D DWT of JPEG 2000 coder / 305--309 / doi: 10.1109/ASAP.2008.4580196 \\ Author index / 310--321 / doi: 10.1109/ASAP.2008.4580201

entry:
@Proceedings{IEEE:2008:ICA,
  editor =       "{IEEE}",
  booktitle =    "{2008 International Conference on Application-Specific
                 Systems, Architectures and Processors: Leuven, Belgium,
                 2--4 July 2008}",
  title =        "{2008 International Conference on Application-Specific
                 Systems, Architectures and Processors: Leuven, Belgium,
                 2--4 July 2008}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "xiv + 309 + 12",
  year =         "2008",
  ISBN =         "1-4244-1897-6 (paperback), 1-4244-1898-4",
  ISBN-13 =      "978-1-4244-1897-8 (paperback), 978-1-4244-1898-5",
  LCCN =         "????",
  bibdate =      "Mon Feb 10 07:31:38 MST 2020",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 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/prng.bib",
  note =         "IEEE catalog number CFP08063-PRT.",
  URL =          "http://ieeexplore.ieee.org/servlet/opac?punumber=4569858;
                 http://www.gbv.de/dms/tib-ub-hannover/631855815.pdf",
  acknowledgement = ack-nhfb,
  remark =       "Kongress auch zitiert als: ASAP 08. Parallel als
                 Online-Ausg. erschienen. ASAP 08.",
  tableofcontents = "ASAP08 Conference proceedings / c1--c1 / doi:
                 10.1109/ASAP.2008.4580199 \\
                 ASAP08 Conference proceedings / c2--c2 / doi:
                 10.1109/ASAP.2008.4580200 \\
                 Frontmatter and table of contents / c1--xiii / doi:
                 10.1109/ASAP.2008.4580202 \\
                 ASAP Organizing and Steering Committees / ix \\
                 ASAP Technical Technical Program Committee / x \\
                 Keynote 1: Security and Opportunities for
                 Application-Specific Processors / Ruby B. Lee / xii \\
                 Keynote 2: Art of of Application-Specific Processor
                 Design: Great Artists use Good Tools / Gert Goossens /
                 xiv \\
                 Session 1: Application-Specific Processor Instruction
                 Sets / 1 \\
                 Copyright notice / i--i / doi:
                 10.1109/ASAP.2008.4580197 \\
                 Copyright notice / ii--ii / doi:
                 10.1109/ASAP.2008.4580198 \\
                 K. Atasu, O. Mencer, W. Luk, C. Ozturan and G. Dundar /
                 Fast custom instruction identification by convex
                 subgraph enumeration / 1--6 / doi:
                 10.1109/ASAP.2008.4580145 \\
                 Y. Hilewitz, C. Lauradoux and R. B. Lee / Bit matrix
                 multiplication in commodity processors / 7--12 / doi:
                 10.1109/ASAP.2008.4580146 \\
                 M. Alle et al. / Synthesis of application accelerators
                 on Runtime Reconfigurable Hardware / 13--18 / doi:
                 10.1109/ASAP.2008.4580147 \\
                 A. Amaricai, M. Vladutiu, M. Udrescu, L. Prodan and O.
                 Boncalo / Floating point multiplication rounding
                 schemes for interval arithmetic / 19--24 / doi:
                 10.1109/ASAP.2008.4580148 \\
                 S. Balasubramanian, H. W. Carter, A. Bogdanov, A. Rupp
                 and Jintai Ding / Fast multivariate signature
                 generation in hardware: The case of rainbow / 25--30 /
                 doi: 10.1109/ASAP.2008.4580149 \\
                 M. Hosseinabady and J. Nunez-Yanez / Fault-tolerant
                 dynamically reconfigurable NoC-based SoC / 31--36 /
                 doi: 10.1109/ASAP.2008.4580150 \\
                 T. Lorunser et al. / Security Processor with Quantum
                 Key Distribution / 37--42 / doi:
                 10.1109/ASAP.2008.4580151 \\
                 P. K. Meher and J. C. Patra / Fully-pipelined efficient
                 architectures for FPGA realization of discrete Hadamard
                 transform / 43--48 / doi: 10.1109/ASAP.2008.4580152 \\
                 R. Rajore, G. Garga, H. S. Jamadagni and S. K. Nandy /
                 Reconfigurable Viterbi decoder on mesh connected
                 multiprocessor architecture / 49--54 / doi:
                 10.1109/ASAP.2008.4580153 \\
                 T. Ramdas, G. K. Egan, D. Abramson and K. K. Baldridge
                 / Run-time thread sorting to expose data-level
                 parallelism / 55--60 / doi: 10.1109/ASAP.2008.4580154
                 \\
                 S. Jovanovic, C. Tanougast and S. Weber / A New
                 High-Performance Scalable Dynamic Interconnection for
                 FPGA-based Reconfigurable Systems / 61--66 / doi:
                 10.1109/ASAP.2008.4580155 \\
                 D. Dickin and L. Shannon / Extending the SIMPPL SoC
                 architectural framework to support application-specific
                 architectures on multi-FPGA platforms / 67--72 / doi:
                 10.1109/ASAP.2008.4580156 \\
                 A. E. Kiasari, S. Hessabi and H. Sarbazi-Azad / PERMAP:
                 A performance-aware mapping for application-specific
                 SoCs / 73--78 / doi: 10.1109/ASAP.2008.4580157 \\
                 A. C. Atici, L. Batina, Junfeng Fan, I. Verbauwhede and
                 S. Berna Ors Yalcin / Low-cost implementations of NTRU
                 for pervasive security / 79--84 / doi:
                 10.1109/ASAP.2008.4580158 \\
                 M. Knezzevic, K. Sakiyama, Y. K. Lee and I. Verbauwhede
                 / On the high-throughput implementation of RIPEMD-160
                 hash algorithm / 85--90 / doi:
                 10.1109/ASAP.2008.4580159 \\
                 Wang Haixin, Bai Guoqiang and Chen Hongyi / Zodiac:
                 System architecture implementation for a
                 high-performance Network Security Processor / 91--96 /
                 doi: 10.1109/ASAP.2008.4580160 \\
                 P. K. Meher / Efficient systolization of cyclic
                 convolution for systolic implementation of sinusoidal
                 transforms / 97--101 / doi: 10.1109/ASAP.2008.4580161
                 \\
                 D. B. Thomas and W. Luk / Resource efficient generators
                 for the floating-point uniform and exponential
                 distributions / 102--107 / doi:
                 10.1109/ASAP.2008.4580162 \\
                 I. L. Dalal, D. Stefan and J. Harwayne-Gidansky / Low
                 discrepancy sequences for Monte Carlo simulations on
                 reconfigurable platforms / 108--113 / doi:
                 10.1109/ASAP.2008.4580163 \\
                 Y. Vanderperren and W. Dehaene / A subsampling pulsed
                 UWB demodulator based on a flexible complex SVD /
                 114--119 / doi: 10.1109/ASAP.2008.4580164 \\
                 J. Divyasree, H. Rajashekar and K. Varghese /
                 Dynamically reconfigurable regular expression matching
                 architecture / 120--125 / doi:
                 10.1109/ASAP.2008.4580165 \\
                 J. Khan, S. Niar, A. Menhaj, Y. Elhillali and J. L.
                 Dekeyser / An MPSoC architecture for the Multiple
                 Target Tracking application in driver assistant system
                 / 126--131 / doi: 10.1109/ASAP.2008.4580166 \\
                 Wangyuan Zhang and Tao Li / Managing multi-core
                 soft-error reliability through utility-driven cross
                 domain optimization / 132--137 / doi:
                 10.1109/ASAP.2008.4580167 \\
                 S. Braganza and M. Leeser / An efficient implementation
                 of a phase unwrapping kernel on reconfigurable hardware
                 / 138--143 / doi: 10.1109/ASAP.2008.4580168 \\
                 H. Flatt, S. Blume, S. Hesselbarth, T. Schunemann and
                 P. Pirsch / A parallel hardware architecture for
                 connected component labeling based on fast label
                 merging / 144--149 / doi: 10.1109/ASAP.2008.4580169 \\
                 Yuki Kobayashi, M. Jayapala, P. Raghavan, F. Catthoor
                 and Masaharu Imai / Operation shuffling over cycle
                 boundaries for low energy L0 clustering / 150--155 /
                 doi: 10.1109/ASAP.2008.4580170 \\
                 V. Kundeti, Yunsi Fei and S. Rajasekaran / An efficient
                 digital circuit for implementing Sequence Alignment
                 algorithm in an extended processor / 156--161 / doi:
                 10.1109/ASAP.2008.4580171 \\
                 B. K. Mohanty and P. K. Meher / Concurrent systolic
                 architecture for high-throughput implementation of
                 3-dimensional discrete wavelet transform / 162--166 /
                 doi: 10.1109/ASAP.2008.4580172 \\
                 S. Mirzaei, A. Irturk, R. Kastner, B. T. Weals and R.
                 E. Cagley / Design space exploration of a cooperative
                 MIMO receiver for reconfigurable architectures /
                 167--172 / doi: 10.1109/ASAP.2008.4580173 \\
                 Mao Nakajima and Minoru Watanabe / Dynamic holographic
                 reconfiguration on a four-context ODRGA / 173--178 /
                 doi: 10.1109/ASAP.2008.4580174 \\
                 F. Pardo, P. Lopez and D. Cabello / FPGA-based hardware
                 accelerator of the heat equation with applications on
                 infrared thermography / 179--184 / doi:
                 10.1109/ASAP.2008.4580175 \\
                 M. Rahmati, M. S. Sadri and M. A. Naeini / FPGA based
                 singular value decomposition for image processing
                 applications / 185--190 / doi:
                 10.1109/ASAP.2008.4580176 \\
                 A. Jacob, J. Buhler and R. D. Chamberlain /
                 Accelerating Nussinov RNA secondary structure
                 prediction with systolic arrays on FPGAs / 191--196 /
                 doi: 10.1109/ASAP.2008.4580177 \\
                 J. Lee, L. Shannon, M. J. Yedlin and G. F. Margrave / A
                 multi-FPGA application-specific architecture for
                 accelerating a floating point Fourier Integral Operator
                 / 197--202 / doi: 10.1109/ASAP.2008.4580178 \\
                 K. F. C. Yiu, Chun Hok Ho, N. Grbric, Yao Lu, Xiaoxiang
                 Shi and W. Luk / Reconfigurable acceleration of
                 microphone array algorithms for speech enhancement /
                 203--208 / doi: 10.1109/ASAP.2008.4580179 \\
                 Yang Sun, Yuming Zhu, M. Goel and J. R. Cavallaro /
                 Configurable and scalable high throughput turbo decoder
                 architecture for multiple 4G wireless standards /
                 209--214 / doi: 10.1109/ASAP.2008.4580180 \\
                 M. B. S. Tavares, S. Kunze, E. Matus and G. P. Fettweis
                 / Architecture and VLSI realization of a high-speed
                 programmable decoder for LDPC convolutional codes /
                 215--220 / doi: 10.1109/ASAP.2008.4580181 \\
                 D. Llorente, K. Karras, T. Wild and A. Herkersdorf /
                 Buffer allocation for advanced packet segmentation in
                 Network Processors / 221--226 / doi:
                 10.1109/ASAP.2008.4580182 \\
                 A. Vazquez and E. Antelo / New insights on Ling adders
                 / 227--232 / doi: 10.1109/ASAP.2008.4580183 \\
                 N. Brisebarre, F. de Dinechin and J. Muller / Integer
                 and floating-point constant multipliers for FPGAs /
                 239--244 / doi: 10.1109/ASAP.2008.4580184 \\
                 N. Brisebarre, S. Chevillard, M. D. Ercegovac, J.
                 Muller and S. Torres / An efficient method for
                 evaluating polynomial and rational function
                 approximations / 233--238 / doi:
                 10.1109/ASAP.2008.4580185 \\
                 A. Garcia, M. Berekovic and T. Vander Aa / Mapping of
                 the AES cryptographic algorithm on a Coarse-Grain
                 reconfigurable array processor / 245--250 / doi:
                 10.1109/ASAP.2008.4580186 \\
                 J. Nimmy et al. / RECONNECT: A NoC for polymorphic
                 ASICs using a low overhead single cycle router /
                 251--256 / doi: 10.1109/ASAP.2008.4580187 \\
                 M. Mbaye, N. Belanger, Y. Savaria and S. Pierre /
                 Loop-oriented metrics for exploring an
                 application-specific architecture design-space /
                 257--262 / doi: 10.1109/ASAP.2008.4580188 \\
                 S. K. Dash and T. Srikanthan / Rapid estimation of
                 instruction cache hit rates using loop profiling /
                 263--268 / doi: 10.1109/ASAP.2008.4580189 \\
                 Xuan Guan and Yunsi Fei / Reducing power consumption of
                 embedded processors through register file partitioning
                 and compiler support / 269--274 / doi:
                 10.1109/ASAP.2008.4580190 \\
                 A. Tumeo, M. Monchiero, G. Palermo, F. Ferrandi and D.
                 Sciuto / Lightweight DMA management mechanisms for
                 multiprocessors on FPGA / 275--280 / doi:
                 10.1109/ASAP.2008.4580191 \\
                 P. de Langen and B. Juurlink / Memory copies in
                 multi-level memory systems / 281--286 / doi:
                 10.1109/ASAP.2008.4580192 \\
                 R. Adrsha, Mythri, S. K. Nandy and R. Narayan /
                 Architecture of a polymorphic ASIC for interoperability
                 across multi-mode H.264 decoders / 287--292 / doi:
                 10.1109/ASAP.2008.4580193 \\
                 R. R. Osorio and J. D. Bruguera / An FPGA architecture
                 for CABAC decoding in manycore systems / 293--298 /
                 doi: 10.1109/ASAP.2008.4580194 \\
                 A. Guntoro and M. Glesner / Novel approach on
                 lifting-based DWT and IDWT processor with multi-context
                 configuration to support different wavelet filters /
                 299--304 / doi: 10.1109/ASAP.2008.4580195 \\
                 B. K. Mohanty and P. K. Meher / Throughput-scalable
                 hybrid-pipeline architecture for multilevel lifting 2-D
                 DWT of JPEG 2000 coder / 305--309 / doi:
                 10.1109/ASAP.2008.4580196 \\
                 Author index / 310--321 / doi:
                 10.1109/ASAP.2008.4580201",
}


