# bibtab

bibtype: inproceedings
filename: elefunt.bib
label: Takahashi:2000:IMP
author: D. Takahashi
booktitle: Proceedings of the 2000 International Workshops on Parallel Processing
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 229--235
year: 2000
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: D. Takahashi
rawbooktitle: Proceedings of the 2000 International Workshops on Parallel Processing
title:
Implementation of multiple-precision parallel division and square root on distributed-memory parallel computers

rawtitle:
Implementation of multiple-precision parallel division and square root on distributed-memory parallel computers

entry:
@InProceedings{Takahashi:2000:IMP,
  author =       "D. Takahashi",
  booktitle =    "Proceedings of the 2000 International Workshops on
                 Parallel Processing",
  title =        "Implementation of multiple-precision parallel division
                 and square root on distributed-memory parallel
                 computers",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "229--235",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present efficient parallel algorithms for
                 multiple-precision division and square root operation
                 of more than several million decimal digits on
                 distributed-memory parallel computers. It is well known
                 that multiple-precision division and square \ldots{}",
}


bibtype: inproceedings
filename: elefunt.bib
label: Tchoumatchenko:2000:FBS
author: V. Tchoumatchenko and T. Vassileva and P. Gurov
title: A FPGA based square-root coprocessor
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 520--525
year: 2000
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: V. Tchoumatchenko and T. Vassileva and P. Gurov
rawtitle: A {FPGA} based square-root coprocessor
booktitle:
Proceedings of the 22nd EUROMICRO Conference EUROMICRO 96. 'Beyond 2000: Hardware and Software Design Strategies'

rawbooktitle:
{Proceedings of the 22nd EUROMICRO Conference EUROMICRO 96. 'Beyond 2000: Hardware and Software Design Strategies'}

entry:
@InProceedings{Tchoumatchenko:2000:FBS,
  author =       "V. Tchoumatchenko and T. Vassileva and P. Gurov",
  booktitle =    "{Proceedings of the 22nd EUROMICRO Conference
                 EUROMICRO 96. 'Beyond 2000: Hardware and Software
                 Design Strategies'}",
  title =        "A {FPGA} based square-root coprocessor",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "520--525",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We present an FPGA implementation of a non-restoring
                 integer square-root algorithm, that uses estimates for
                 result-digit selection and radix-$2$ redundant addition
                 in recurrence. On-the-fly conversion of the
                 result-digit and signed-digit adder/ \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Temme:2000:NAA
author: Nico M. Temme
title: Numerical and asymptotic aspects of parabolic cylinder functions
journal: j-J-COMPUT-APPL-MATH
volume: 121
number: 1--2
pages: 221--246
day: 1
month: sep
monthnumber: 9
year: 2000
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:43:36 MST 2017
bibtimestamp: 2017.02.25 12:43:36 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700003472
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Nico M. Temme
rawtitle: Numerical and asymptotic aspects of parabolic cylinder functions
entry:
@Article{Temme:2000:NAA,
  author =       "Nico M. Temme",
  title =        "Numerical and asymptotic aspects of parabolic cylinder
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "121",
  number =       "1--2",
  pages =        "221--246",
  day =          "1",
  month =        sep,
  year =         "2000",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:43:36 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700003472",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Tommiska:2000:AEI
author: M. T. Tommiska
title: Area-efficient implementation of a fast square root algorithm
publisher: pub-IEEE
address: pub-IEEE:adr
pages: S18/1--S18/4
year: 2000
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: M. T. Tommiska
rawtitle: Area-efficient implementation of a fast square root algorithm
booktitle:
Proceedings of the 2000 Third IEEE International Caracas Conference on Devices, Circuits and Systems, 15--17 March 2000

rawbooktitle:
Proceedings of the 2000 Third {IEEE} International Caracas Conference on Devices, Circuits and Systems, 15--17 March 2000

entry:
@InProceedings{Tommiska:2000:AEI,
  author =       "M. T. Tommiska",
  booktitle =    "Proceedings of the 2000 Third {IEEE} International
                 Caracas Conference on Devices, Circuits and Systems,
                 15--17 March 2000",
  title =        "Area-efficient implementation of a fast square root
                 algorithm",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "S18/1--S18/4",
  year =         "2000",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "An area-efficient implementation of a fast-converging
                 square-root algorithm is presented. The design of
                 special arithmetic operations differs in many ways from
                 the traditional tasks that digital designers are used
                 to, and the role of \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Wachspress:2000:EEF
author: E. L. Wachspress
title: Evaluating elliptic functions and their inverses
journal: j-COMPUT-MATH-APPL
volume: 39
number: 3--4
pages: 131--136
month: feb
monthnumber: 2
year: 2000
CODEN: CMAPDK
DOI: https://doi.org/10.1016/S0898-1221(99)00339-9
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:49:06 MST 2017
bibtimestamp: 2017.03.01 21:49:06 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122199003399
fjournal: Computers and Mathematics with Applications
keywords: arithmetic-geometric mean (AGM)
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: E. L. Wachspress
rawtitle: Evaluating elliptic functions and their inverses
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Wachspress:2000:EEF,
  author =       "E. L. Wachspress",
  title =        "Evaluating elliptic functions and their inverses",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "39",
  number =       "3--4",
  pages =        "131--136",
  month =        feb,
  year =         "2000",
  CODEN =        "CMAPDK",
  DOI =          "https://doi.org/10.1016/S0898-1221(99)00339-9",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:06 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122199003399",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
  keywords =     "arithmetic-geometric mean (AGM)",
}


bibtype: book
filename: elefunt.bib
label: Wall:2000:ATC
author: H. S. Wall
title: Analytic Theory of Continued Fractions
publisher: pub-AMS
address: pub-AMS:adr
pages: xiii + 433
year: 2000
ISBN: 0-8218-2106-7 OR 0821821067
ISBN13: 978-0-8218-2106-0 OR 9780821821060
LCCN: QA295 .W28 2000
bibdate: Thu Apr 3 20:24:06 MDT 2008
bibtimestamp: 2008.04.03 20:24:06 MDT
note: This is a reprint of the definitive, and widely cited, treatise first published in 1948.
URL: https://archive.org/details/dli.ernet.16804/
remark: Originally published: New York: D. Van Nostrand Co., 1948.
subject: Continued fractions
acknowledgement: ack-nhfb
rawauthor: H. S. Wall
rawnote: This is a reprint of the definitive, and widely cited, treatise first published in 1948.
rawtitle: Analytic Theory of Continued Fractions
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

TOC:
Preface / vi Introduction / 1 Part I: Convergence Theory I: The Continued fraction as a Product of Linear Fractional Transformations 1. Definitions and Formulas / 13 2. Continued Fractions and Series / 17 3. Equivalence Transformations / 19 4. Even and Odd Parts of a Continued Fraction / 20 II: Convergence Theorems 5. Some General Remarks on the Convergence Problem / 25 6. Necessary Conditions for Convergence / 27 7. A Sufficient Condition for Convergence / 33 8. Convergence of Periodic Continued Fractions / 35 III: Convergence of Continued Fractions Whose Partial Denominators Are Equal to Unity 9. The First Interpretation of the Fundamental Inequalities / 40 10. Worpitzky's Theorem / 42 11. Convergence of Continued Fractions Whose Partial Quotients Are of the Form $(1 - g_p - 1) g_p x_p / 1$ / 45 12. A Convergence Theorem of von Koch / 50 13. Second Interpretation of the Fundamental Inequalities / 52 14. The Parabola Theorem / 56 15. ``Convergence Neighborhoods'' of a Point (1) / 62 IV: Introduction to the Theory of Positive Definite Continued Fractions 16. Definition of a Positive Definite Continued Fraction / 64 17. The Nest of Circles / 170 18. Positive Definite Continued Fractions and the Parabola Theorem / 175 19. Chain Sequences / 19 20. Quadratic Forms and Chain Sequences / 86 V: Some General Convergence Theorems 21. Schwarz's Inequality / 95 22. The Theorem of Invariability / 96 23. The Indeterminate Case / 99 24. Convergence Continuation Theorem / 104 25. The Determinate Case / 109 26. Bounded J-fractions / 110 27. Real J-fractions / 114 VI: Stieltjes Type Continued Fractions 28. Convergence and Divergence of the Continued Fraction of Stieltjes / 118 29. The Condition (H) / 122 30. Three Convergence Theorems / 131 VII: Extensions of the Parabola Theorem 31. A Family of Parabolic Domains / 135 32. ``Convergence Neighborhoods'' of a Point (2) / 137 33. A Theorem of Van Vleck / 138 34. The Cardioid Theorem / 140 35. An Extension of a Theorem of Szasz / 143 VIII: The Value Region Problem 36. A Sufficient Condition / 147 37. The Two-Circle Theorem / 148 38. Circular Element Regions with Centers at the Origin / 150 39. A Family of Parabolic Element Regions / 152 Part II: Function Theory IX: J-Fraction Expansions for Rational Functions 40. The Expansion Algorithm / 161 41. Conditions Involving Determinants / 164 42. Relationship Between the J-fraction and the Power Series for $f_1 / f_0$ / 166 43. Rational Fractions with Simple Poles and Positive Residues / 167 44, Expansion of Rational Functions into Stieltjes Type Continued Fractions / 170 X: Theory of Equations 45. The Test-Fraction / 174 46. Polygonal Bounds for the Roots of a Polynomial / 176 47. Polynomials Whose Roots Are in a Given Half-Plane / 178 48. Determination of the Number of Roots of P(z) in Each of the Half Planes R(z) 20 / 182 49. Computation of the Roots of Polynomials / 185 XI: J-Fraction Expansions for Power Series 50. Polynomials Orthogonal Relative to a Sequence / 192 51. Algorithm for Expanding a Power Series into a J-fraction / 196 52. Stieltjes Type Continued Fraction Expansions for Power Series / 200 53. Stieltjes' Expansion Theorem / 202 54. Convergence Questions 208 XII: Matrix Theory of Continued Fractions 55. Linear Forms / 214 56. Bilinear Forms / 216 57. Bounded Matrices / 218 58. Bounded Reciprocals of Bounded Matrices / 223 59. The Bounded Reciprocal of a Bounded J-matrix / 226 60. Reciprocals of an Arbitrary J-matrix / 228 61. Reciprocals of the J-matrix Associated with a Positive Definite J-fraction / 230 62. Estimates for the Equivalent Functions / 235 XIII: Continued Fractions and Definite Integrals 63. The Stieltjes Integral / 239 64. Sequences of Stieltjes Integrals / 245 65. The Stieltjes Inversion Formula / 247 66. Representation of an Equivalent Function of a Positive Definite J-fraction as a Stieltjes Transform / 250 67. Proper Equivalent Functions / 254 XIV: The Moment Problem for a Finite Interval 68. Formulation of the Problem / 258 69. Solution of the Moment Problem by Means of S-fractions / 260 70. Some Geometry / 263 71. Totally Monotone Sequences / 267 72. Composition of Moment Sequences / 269 XV: Bounded Analytic Functions 73. Integral Formulas for Bounded Analytic Functions / 275 74. Continued Fraction Expansions for Real Analytic Functions / 278 75. Continued Fraction Expansions for $1/G(z)$ and for $G[-z / (1 + z)]$ in Terms of the Expansions for $G(z)$ / 280 76. Condition for $G(z)/sqrt 1 + z$ to Be Bounded in the Unit Circle / 283 77. Analytic Functions Bounded in the Unit Circle / 285 78. Continued Fraction Expansions for Arbitrary Functions Which Are Analytic and Have Positive Real Parts in $Ext (-1, -infty )$ / 288 XVI: Hausdorff Summability 79. Hausdorff Matrices / 302 80. A Theorem on $(A, d_n)$-Transformations / 304 81. Hausdorff Means / 306 82. Examples of Hausdorff Means / 309 83. The Hausdorff Inclusion Problem / 310 XVII: The Moment Problem for an Infinite Interval 84. Asymptotic Expressions for J-fractions / 316 85. A Theorem of Hamburger / 321 86. The Moment Problem for the Interval $(-infty , +infty )$ / 325 87. The Stieltjes Moment Problem / 327 88. A Theorem of Carleman / 330 XVIII: The Continued Fraction of Gauss 89. General Properties / 335 90. Elementary Functions / 342 91. Certain Meromorphic Functions / 347 92. A Class of Divergent Series / 349 XIX: Stieltjes Summability 93. Definition and Illustrative Examples / 362 94. List of Expansion Formulas / 369 XX: The Pade Table 95. Definitions / 37 96. The Normal Pade Table / 379 97. The Pade Table for the Series of Stieltjes / 389 98. General Theorems on the Pade Table / 393 99. C-fractions / 399 100. Regular C-fractions and Power Series / 405 101. $alpha $-regular C-fractions / 409 102. Concluding Remarks on the Pade Table / 410 Bibliography / 417 Index / 427

shortTOC:
Preface Introduction Part I: Convergence Theory I: The Continued fraction as a Product of Linear Fractional Transformations II: Convergence Theorems III: Convergence of Continued Fractions Whose Partial Denominators Are Equal to Unity IV: Introduction to the Theory of Positive Definite Continued Fractions V: Some General Convergence Theorems VI: Stieltjes Type Continued Fractions VII: Extensions of the Parabola Theorem VIII: The Value Region Problem Part II: Function Theory IX: J-Fraction Expansions for Rational Functions X: Theory of Equations XI: J-Fraction Expansions for Power Series XII: Matrix Theory of Continued Fractions XIII: Continued Fractions and Definite Integrals XIV: The Moment Problem for a Finite Interval XV: Bounded Analytic Functions XVI: Hausdorff Summability XVII: The Moment Problem for an Infinite Interval XVIII: The Continued Fraction of Gauss XIX: Stieltjes Summability XX: The Pade Table Bibliography Index

rawshortTOC:
Preface \\ Introduction \\ Part I: Convergence Theory \\ I: The Continued fraction as a Product of Linear Fractional Transformations \\ II: Convergence Theorems \\ III: Convergence of Continued Fractions Whose Partial Denominators Are Equal to Unity \\ IV: Introduction to the Theory of Positive Definite Continued Fractions \\ V: Some General Convergence Theorems \\ VI: Stieltjes Type Continued Fractions \\ VII: Extensions of the Parabola Theorem \\ VIII: The Value Region Problem \\ Part II: Function Theory \\ IX: J-Fraction Expansions for Rational Functions \\ X: Theory of Equations \\ XI: J-Fraction Expansions for Power Series \\ XII: Matrix Theory of Continued Fractions \\ XIII: Continued Fractions and Definite Integrals \\ XIV: The Moment Problem for a Finite Interval \\ XV: Bounded Analytic Functions \\ XVI: Hausdorff Summability \\ XVII: The Moment Problem for an Infinite Interval \\ XVIII: The Continued Fraction of Gauss \\ XIX: Stieltjes Summability \\ XX: The Pad{\'e} Table \\ Bibliography \\ Index

rawTOC:
Preface / vi \\ Introduction / 1 \\ Part I: Convergence Theory \\ \\ I: The Continued fraction as a Product of Linear Fractional Transformations \\ 1. Definitions and Formulas / 13 \\ 2. Continued Fractions and Series / 17 \\ 3. Equivalence Transformations / 19 \\ 4. Even and Odd Parts of a Continued Fraction / 20 \\ \\ II: Convergence Theorems \\ 5. Some General Remarks on the Convergence Problem / 25 \\ 6. Necessary Conditions for Convergence / 27 \\ 7. A Sufficient Condition for Convergence / 33 \\ 8. Convergence of Periodic Continued Fractions / 35 \\ \\ III: Convergence of Continued Fractions Whose Partial Denominators Are Equal to Unity \\ 9. The First Interpretation of the Fundamental Inequalities / 40 \\ 10. Worpitzky's Theorem / 42 \\ 11. Convergence of Continued Fractions Whose Partial Quotients Are of the Form $(1 - g_{p - 1}) g_p x_p / 1$ / 45 \\ 12. A Convergence Theorem of von Koch / 50 \\ 13. Second Interpretation of the Fundamental Inequalities / 52 \\ 14. The Parabola Theorem / 56 \\ 15. ``Convergence Neighborhoods'' of a Point (1) / 62 \\ \\ IV: Introduction to the Theory of Positive Definite Continued Fractions \\ 16. Definition of a Positive Definite Continued Fraction / 64 \\ 17. The Nest of Circles / 170 \\ 18. Positive Definite Continued Fractions and the Parabola Theorem / 175 \\ 19. Chain Sequences / 19 \\ 20. Quadratic Forms and Chain Sequences / 86 \\ \\ V: Some General Convergence Theorems \\ 21. Schwarz's Inequality / 95 \\ 22. The Theorem of Invariability / 96 \\ 23. The Indeterminate Case / 99 \\ 24. Convergence Continuation Theorem / 104 \\ 25. The Determinate Case / 109 \\ 26. Bounded J-fractions / 110 \\ 27. Real J-fractions / 114 \\ \\ VI: Stieltjes Type Continued Fractions \\ 28. Convergence and Divergence of the Continued Fraction of Stieltjes / 118 \\ 29. The Condition (H) / 122 \\ 30. Three Convergence Theorems / 131 \\ \\ VII: Extensions of the Parabola Theorem \\ 31. A Family of Parabolic Domains / 135 \\ 32. ``Convergence Neighborhoods'' of a Point (2) / 137 \\ 33. A Theorem of Van Vleck / 138 \\ 34. The Cardioid Theorem / 140 \\ 35. An Extension of a Theorem of Sz{\'a}sz / 143 \\ \\ VIII: The Value Region Problem \\ 36. A Sufficient Condition / 147 \\ 37. The Two-Circle Theorem / 148 \\ 38. Circular Element Regions with Centers at the Origin / 150 \\ 39. A Family of Parabolic Element Regions / 152 \\ \\ Part II: Function Theory \\ \\ IX: J-Fraction Expansions for Rational Functions \\ 40. The Expansion Algorithm / 161 \\ 41. Conditions Involving Determinants / 164 \\ 42. Relationship Between the J-fraction and the Power Series for $f_1 / f_0$ / 166 \\ 43. Rational Fractions with Simple Poles and Positive Residues / 167 \\ 44, Expansion of Rational Functions into Stieltjes Type Continued Fractions / 170 \\ \\ X: Theory of Equations \\ 45. The Test-Fraction / 174 \\ 46. Polygonal Bounds for the Roots of a Polynomial / 176 \\ 47. Polynomials Whose Roots Are in a Given Half-Plane / 178 \\ 48. Determination of the Number of Roots of P(z) in Each of the Half Planes R(z) 20 / 182 \\ 49. Computation of the Roots of Polynomials / 185 \\ \\ XI: J-Fraction Expansions for Power Series \\ 50. Polynomials Orthogonal Relative to a Sequence / 192 \\ 51. Algorithm for Expanding a Power Series into a J-fraction / 196 \\ 52. Stieltjes Type Continued Fraction Expansions for Power Series / 200 \\ 53. Stieltjes' Expansion Theorem / 202 \\ 54. Convergence Questions 208 \\ \\ XII: Matrix Theory of Continued Fractions \\ 55. Linear Forms / 214 \\ 56. Bilinear Forms / 216 \\ 57. Bounded Matrices / 218 \\ 58. Bounded Reciprocals of Bounded Matrices / 223 \\ 59. The Bounded Reciprocal of a Bounded J-matrix / 226 \\ 60. Reciprocals of an Arbitrary J-matrix / 228 \\ 61. Reciprocals of the J-matrix Associated with a Positive Definite J-fraction / 230 \\ 62. Estimates for the Equivalent Functions / 235 \\ XIII: Continued Fractions and Definite Integrals \\ 63. The Stieltjes Integral / 239 \\ 64. Sequences of Stieltjes Integrals / 245 \\ 65. The Stieltjes Inversion Formula / 247 \\ 66. Representation of an Equivalent Function of a Positive Definite J-fraction as a Stieltjes Transform / 250 \\ 67. Proper Equivalent Functions / 254 \\ \\ XIV: The Moment Problem for a Finite Interval \\ 68. Formulation of the Problem / 258 \\ 69. Solution of the Moment Problem by Means of S-fractions / 260 \\ 70. Some Geometry / 263 \\ 71. Totally Monotone Sequences / 267 \\ 72. Composition of Moment Sequences / 269 \\ \\ XV: Bounded Analytic Functions \\ 73. Integral Formulas for Bounded Analytic Functions / 275 \\ 74. Continued Fraction Expansions for Real Analytic Functions / 278 \\ 75. Continued Fraction Expansions for $1/G(z)$ and for $G[-z / (1 + z)]$ in Terms of the Expansions for $G(z)$ / 280 \\ 76. Condition for $G(z)/\sqrt{1 + z}$ to Be Bounded in the Unit Circle / 283 \\ 77. Analytic Functions Bounded in the Unit Circle / 285 \\ 78. Continued Fraction Expansions for Arbitrary Functions Which Are Analytic and Have Positive Real Parts in $\Ext(-1, -\infty)$ / 288 \\ \\ XVI: Hausdorff Summability \\ 79. Hausdorff Matrices / 302 \\ 80. A Theorem on $(A, d_n)$-Transformations / 304 \\ 81. Hausdorff Means / 306 \\ 82. Examples of Hausdorff Means / 309 \\ 83. The Hausdorff Inclusion Problem / 310 \\ \\ XVII: The Moment Problem for an Infinite Interval \\ 84. Asymptotic Expressions for J-fractions / 316 \\ 85. A Theorem of Hamburger / 321 \\ 86. The Moment Problem for the Interval $(-\infty, +\infty)$ / 325 \\ 87. The Stieltjes Moment Problem / 327 \\ 88. A Theorem of Carleman / 330 \\ \\ XVIII: The Continued Fraction of Gauss \\ 89. General Properties / 335 \\ 90. Elementary Functions / 342 \\ 91. Certain Meromorphic Functions / 347 \\ 92. A Class of Divergent Series / 349 \\ \\ XIX: Stieltjes Summability \\ 93. Definition and Illustrative Examples / 362 \\ 94. List of Expansion Formulas / 369 \\ \\ XX: The Pad{\'e} Table \\ 95. Definitions / 37 \\ 96. The Normal Pad{\'e} Table / 379 \\ 97. The Pad{\'e} Table for the Series of Stieltjes / 389 \\ 98. General Theorems on the Pad{\'e} Table / 393 \\ 99. C-fractions / 399 \\ 100. Regular C-fractions and Power Series / 405 \\ 101. $\alpha$-regular C-fractions / 409 \\ 102. Concluding Remarks on the Pad{\'e} Table / 410 \\ \\ Bibliography / 417 \\ Index / 427

entry:
@Book{Wall:2000:ATC,
  author =       "H. S. Wall",
  title =        "Analytic Theory of Continued Fractions",
  publisher =    pub-AMS,
  address =      pub-AMS:adr,
  pages =        "xiii + 433",
  year =         "2000",
  ISBN =         "0-8218-2106-7",
  ISBN-13 =      "978-0-8218-2106-0",
  LCCN =         "QA295 .W28 2000",
  bibdate =      "Thu Apr 3 20:24:06 MDT 2008",
  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",
  note =         "This is a reprint of the definitive, and widely cited,
                 treatise first published in 1948.",
  URL =          "https://archive.org/details/dli.ernet.16804/",
  acknowledgement = ack-nhfb,
  remark =       "Originally published: New York: D. Van Nostrand Co.,
                 1948.",
  shorttableofcontents = "Preface \\
                 Introduction \\
                 Part I: Convergence Theory \\
                 I: The Continued fraction as a Product of Linear
                 Fractional Transformations \\
                 II: Convergence Theorems \\
                 III: Convergence of Continued Fractions Whose Partial
                 Denominators Are Equal to Unity \\
                 IV: Introduction to the Theory of Positive Definite
                 Continued Fractions \\
                 V: Some General Convergence Theorems \\
                 VI: Stieltjes Type Continued Fractions \\
                 VII: Extensions of the Parabola Theorem \\
                 VIII: The Value Region Problem \\
                 Part II: Function Theory \\
                 IX: J-Fraction Expansions for Rational Functions \\
                 X: Theory of Equations \\
                 XI: J-Fraction Expansions for Power Series \\
                 XII: Matrix Theory of Continued Fractions \\
                 XIII: Continued Fractions and Definite Integrals \\
                 XIV: The Moment Problem for a Finite Interval \\
                 XV: Bounded Analytic Functions \\
                 XVI: Hausdorff Summability \\
                 XVII: The Moment Problem for an Infinite Interval \\
                 XVIII: The Continued Fraction of Gauss \\
                 XIX: Stieltjes Summability \\
                 XX: The Pad{\'e} Table \\
                 Bibliography \\
                 Index",
  subject =      "Continued fractions",
  tableofcontents = "Preface / vi \\
                 Introduction / 1 \\
                 Part I: Convergence Theory \\
                 \\
                 I: The Continued fraction as a Product of Linear
                 Fractional Transformations \\
                 1. Definitions and Formulas / 13 \\
                 2. Continued Fractions and Series / 17 \\
                 3. Equivalence Transformations / 19 \\
                 4. Even and Odd Parts of a Continued Fraction / 20 \\
                 \\
                 II: Convergence Theorems \\
                 5. Some General Remarks on the Convergence Problem / 25
                 \\
                 6. Necessary Conditions for Convergence / 27 \\
                 7. A Sufficient Condition for Convergence / 33 \\
                 8. Convergence of Periodic Continued Fractions / 35 \\
                 \\
                 III: Convergence of Continued Fractions Whose Partial
                 Denominators Are Equal to Unity \\
                 9. The First Interpretation of the Fundamental
                 Inequalities / 40 \\
                 10. Worpitzky's Theorem / 42 \\
                 11. Convergence of Continued Fractions Whose Partial
                 Quotients Are of the Form $(1 - g_{p - 1}) g_p x_p / 1$
                 / 45 \\
                 12. A Convergence Theorem of von Koch / 50 \\
                 13. Second Interpretation of the Fundamental
                 Inequalities / 52 \\
                 14. The Parabola Theorem / 56 \\
                 15. ``Convergence Neighborhoods'' of a Point (1) / 62
                 \\
                 \\
                 IV: Introduction to the Theory of Positive Definite
                 Continued Fractions \\
                 16. Definition of a Positive Definite Continued
                 Fraction / 64 \\
                 17. The Nest of Circles / 170 \\
                 18. Positive Definite Continued Fractions and the
                 Parabola Theorem / 175 \\
                 19. Chain Sequences / 19 \\
                 20. Quadratic Forms and Chain Sequences / 86 \\
                 \\
                 V: Some General Convergence Theorems \\
                 21. Schwarz's Inequality / 95 \\
                 22. The Theorem of Invariability / 96 \\
                 23. The Indeterminate Case / 99 \\
                 24. Convergence Continuation Theorem / 104 \\
                 25. The Determinate Case / 109 \\
                 26. Bounded J-fractions / 110 \\
                 27. Real J-fractions / 114 \\
                 \\
                 VI: Stieltjes Type Continued Fractions \\
                 28. Convergence and Divergence of the Continued
                 Fraction of Stieltjes / 118 \\
                 29. The Condition (H) / 122 \\
                 30. Three Convergence Theorems / 131 \\
                 \\
                 VII: Extensions of the Parabola Theorem \\
                 31. A Family of Parabolic Domains / 135 \\
                 32. ``Convergence Neighborhoods'' of a Point (2) / 137
                 \\
                 33. A Theorem of Van Vleck / 138 \\
                 34. The Cardioid Theorem / 140 \\
                 35. An Extension of a Theorem of Sz{\'a}sz / 143 \\
                 \\
                 VIII: The Value Region Problem \\
                 36. A Sufficient Condition / 147 \\
                 37. The Two-Circle Theorem / 148 \\
                 38. Circular Element Regions with Centers at the Origin
                 / 150 \\
                 39. A Family of Parabolic Element Regions / 152 \\
                 \\
                 Part II: Function Theory \\
                 \\
                 IX: J-Fraction Expansions for Rational Functions \\
                 40. The Expansion Algorithm / 161 \\
                 41. Conditions Involving Determinants / 164 \\
                 42. Relationship Between the J-fraction and the Power
                 Series for $f_1 / f_0$ / 166 \\
                 43. Rational Fractions with Simple Poles and Positive
                 Residues / 167 \\
                 44, Expansion of Rational Functions into Stieltjes Type
                 Continued Fractions / 170 \\
                 \\
                 X: Theory of Equations \\
                 45. The Test-Fraction / 174 \\
                 46. Polygonal Bounds for the Roots of a Polynomial /
                 176 \\
                 47. Polynomials Whose Roots Are in a Given Half-Plane /
                 178 \\
                 48. Determination of the Number of Roots of P(z) in
                 Each of the Half Planes R(z) 20 / 182 \\
                 49. Computation of the Roots of Polynomials / 185 \\
                 \\
                 XI: J-Fraction Expansions for Power Series \\
                 50. Polynomials Orthogonal Relative to a Sequence / 192
                 \\
                 51. Algorithm for Expanding a Power Series into a
                 J-fraction / 196 \\
                 52. Stieltjes Type Continued Fraction Expansions for
                 Power Series / 200 \\
                 53. Stieltjes' Expansion Theorem / 202 \\
                 54. Convergence Questions 208 \\
                 \\
                 XII: Matrix Theory of Continued Fractions \\
                 55. Linear Forms / 214 \\
                 56. Bilinear Forms / 216 \\
                 57. Bounded Matrices / 218 \\
                 58. Bounded Reciprocals of Bounded Matrices / 223 \\
                 59. The Bounded Reciprocal of a Bounded J-matrix / 226
                 \\
                 60. Reciprocals of an Arbitrary J-matrix / 228 \\
                 61. Reciprocals of the J-matrix Associated with a
                 Positive Definite J-fraction / 230 \\
                 62. Estimates for the Equivalent Functions / 235 \\
                 XIII: Continued Fractions and Definite Integrals \\
                 63. The Stieltjes Integral / 239 \\
                 64. Sequences of Stieltjes Integrals / 245 \\
                 65. The Stieltjes Inversion Formula / 247 \\
                 66. Representation of an Equivalent Function of a
                 Positive Definite J-fraction as a Stieltjes Transform /
                 250 \\
                 67. Proper Equivalent Functions / 254 \\
                 \\
                 XIV: The Moment Problem for a Finite Interval \\
                 68. Formulation of the Problem / 258 \\
                 69. Solution of the Moment Problem by Means of
                 S-fractions / 260 \\
                 70. Some Geometry / 263 \\
                 71. Totally Monotone Sequences / 267 \\
                 72. Composition of Moment Sequences / 269 \\
                 \\
                 XV: Bounded Analytic Functions \\
                 73. Integral Formulas for Bounded Analytic Functions /
                 275 \\
                 74. Continued Fraction Expansions for Real Analytic
                 Functions / 278 \\
                 75. Continued Fraction Expansions for $1/G(z)$ and for
                 $G[-z / (1 + z)]$ in Terms of the Expansions for $G(z)$
                 / 280 \\
                 76. Condition for $G(z)/\sqrt{1 + z}$ to Be Bounded in
                 the Unit Circle / 283 \\
                 77. Analytic Functions Bounded in the Unit Circle / 285
                 \\
                 78. Continued Fraction Expansions for Arbitrary
                 Functions Which Are Analytic and Have Positive Real
                 Parts in $\Ext(-1, -\infty)$ / 288 \\
                 \\
                 XVI: Hausdorff Summability \\
                 79. Hausdorff Matrices / 302 \\
                 80. A Theorem on $(A, d_n)$-Transformations / 304 \\
                 81. Hausdorff Means / 306 \\
                 82. Examples of Hausdorff Means / 309 \\
                 83. The Hausdorff Inclusion Problem / 310 \\
                 \\
                 XVII: The Moment Problem for an Infinite Interval \\
                 84. Asymptotic Expressions for J-fractions / 316 \\
                 85. A Theorem of Hamburger / 321 \\
                 86. The Moment Problem for the Interval $(-\infty,
                 +\infty)$ / 325 \\
                 87. The Stieltjes Moment Problem / 327 \\
                 88. A Theorem of Carleman / 330 \\
                 \\
                 XVIII: The Continued Fraction of Gauss \\
                 89. General Properties / 335 \\
                 90. Elementary Functions / 342 \\
                 91. Certain Meromorphic Functions / 347 \\
                 92. A Class of Divergent Series / 349 \\
                 \\
                 XIX: Stieltjes Summability \\
                 93. Definition and Illustrative Examples / 362 \\
                 94. List of Expansion Formulas / 369 \\
                 \\
                 XX: The Pad{\'e} Table \\
                 95. Definitions / 37 \\
                 96. The Normal Pad{\'e} Table / 379 \\
                 97. The Pad{\'e} Table for the Series of Stieltjes /
                 389 \\
                 98. General Theorems on the Pad{\'e} Table / 393 \\
                 99. C-fractions / 399 \\
                 100. Regular C-fractions and Power Series / 405 \\
                 101. $\alpha$-regular C-fractions / 409 \\
                 102. Concluding Remarks on the Pad{\'e} Table / 410 \\
                 \\
                 Bibliography / 417 \\
                 Index / 427",
  xxauthor =     "H. S. (Hubert Stanley) Wall",
}


bibtype: techreport
filename: elefunt.bib
label: Zimmermann:2000:PGF
author: Paul Zimmermann
title: A proof of GMP fast division and square root implementations
type: Technical report
institution: inst-LORIA-INRIA-LORRAINE
address: inst-LORIA-INRIA-LORRAINE:adr
pages: 14
month: sep
monthnumber: 9
year: 2000
bibdate: Sun Sep 10 08:48:46 2006
bibtimestamp: 2006.09.10 08:48:46 ???
URL: http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz
acknowledgement: ack-nhfb
rawauthor: Paul Zimmermann
rawtitle: A proof of {GMP} fast division and square root implementations
abstract:
This short note gives a detailed correctness proof of fast (i.e., subquadratic) versions of the GNU MP tt mpn_bz_divrem_n and tt mpn_sqrtrem functions, together with complete GMP code. The tt mpn_bz_divrem_n function divides (with remainder) a number of $ 2 n $ limbs by a divisor of $n$ limbs in $ 2 K(n) $, where $ K(n) $ is the time spent in a $ (n times n) $ multiplication, using the Moenck--Borodin--Jebelean--Burnikel--Ziegler algorithm. The tt mpn_sqrtrem computes the square root and the remainder of a number of $ 2 n $ limbs (square root and remainder have about $n$ limbs each) in time $ 3 K(n) / 2 $; it uses Karatsuba Square Root.

rawabstract:
This short note gives a detailed correctness proof of fast (i.e., subquadratic) versions of the GNU MP {\tt mpn\_bz\_divrem\_n} and {\tt mpn\_sqrtrem} functions, together with complete GMP code. The {\tt mpn\_bz\_divrem\_n} function divides (with remainder) a number of $ 2 n $ limbs by a divisor of $n$ limbs in $ 2 K(n) $, where $ K(n) $ is the time spent in a $ (n \times n) $ multiplication, using the Moenck--Borodin--Jebelean--Burnikel--Ziegler algorithm. The {\tt mpn\_sqrtrem} computes the square root and the remainder of a number of $ 2 n $ limbs (square root and remainder have about $n$ limbs each) in time $ 3 K(n) / 2 $; it uses Karatsuba Square Root.

entry:
@TechReport{Zimmermann:2000:PGF,
  author =       "Paul Zimmermann",
  title =        "A proof of {GMP} fast division and square root
                 implementations",
  type =         "Technical report",
  institution =  inst-LORIA-INRIA-LORRAINE,
  address =      inst-LORIA-INRIA-LORRAINE:adr,
  pages =        "14",
  month =        sep,
  year =         "2000",
  bibdate =      "Sun Sep 10 08:48:46 2006",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.loria.fr/~zimmerma/papers/proof-div-sqrt.ps.gz",
  abstract =     "This short note gives a detailed correctness proof of
                 fast (i.e., subquadratic) versions of the GNU MP {\tt
                 mpn\_bz\_divrem\_n} and {\tt mpn\_sqrtrem} functions,
                 together with complete GMP code. The {\tt
                 mpn\_bz\_divrem\_n} function divides (with remainder) a
                 number of $ 2 n $ limbs by a divisor of $n$ limbs in $
                 2 K(n) $, where $ K(n) $ is the time spent in a $ (n
                 \times n) $ multiplication, using the
                 Moenck--Borodin--Jebelean--Burnikel--Ziegler algorithm.
                 The {\tt mpn\_sqrtrem} computes the square root and the
                 remainder of a number of $ 2 n $ limbs (square root and
                 remainder have about $n$ limbs each) in time $ 3 K(n) /
                 2 $; it uses Karatsuba Square Root.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Arfken:2001:MMP
author: George B. (George Brown) Arfken and Hans-Jurgen Weber
title: Mathematical methods for physicists
publisher: Harcourt/Academic Press
address: San Diego, CA, USA
edition: Fifth
pages: xiv + 1112
year: 2001
ISBN: 0-12-059825-6, 0-12-059826-4 OR 0120598256, 0120598264
ISBN13: 978-0-12-059825-0, 978-0-12-059826-7 OR 9780120598250, 9780120598267
LCCN: QA37.3 .A74 2001
MRclass: 00A06, 15-01, 26-01, 30-01, 34-01, 35-01, 65-01
bibdate: Wed Mar 15 06:50:49 MDT 2017
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.15 06:50:49 MDT
URL: http://catalog.hathitrust.org/api/volumes/oclc/45705658.html
acknowledgement: ack-nhfb
authordates: 1922--
rawauthor: George B. (George Brown) Arfken and Hans-Jurgen Weber
rawtitle: Mathematical methods for physicists
subject:
Mathematics; Mathematical physics; Matematicas; Fisica matematica; Mathematical physics; Mathematics; Wiskundige methoden; Natuurkunde; Matematica; Fisica; Mathematiques; Physique mathematique

TOC:
1: Vector Analysis / 1 1.2: Rotation of the Coordinate Axes / 8 1.3: Scalar or Dot Product / 13 1.4: Vector or Cross Product / 19 1.5: Triple Scalar Product, Triple Vector Product / 27 1.6: Gradient, [down triangle, open] / 35 1.7: Divergence, [down triangle, open] / 40 1.8: Curl, [down triangle, open] x / 44 1.9: Successive Applications of [down triangle, open] / 51 1.10: Vector Integration / 55 1.11: Gauss's Theorem / 61 1.12: Stokes's Theorem / 65 1.13: Potential Theory / 69 1.14: Gauss's Law, Poisson's Equation / 80 1.15: Dirac Delta Function / 84 1.16: Helmholtz's Theorem / 96 2: Curved Coordinates, Tensors / 103 2.1: Orthogonal Coordinates / 103 2.2: Differential Vector Operators / 108 2.3: Special Coordinate Systems: Introduction / 113 2.4: Circular Cylindrical Coordinates / 114 2.5: Spherical Polar Coordinates / 121 2.6: Tensor Analysis / 131 2.7: Contraction, Direct Product / 137 2.8: Quotient Rule / 139 2.9: Pseudotensors, Dual Tensors / 141 2.10: Non-Cartesian Tensors / 150 2.11: Tensor Derivative Operators / 160 3: Determinants and Matrices / 165 3.1: Determinants / 165 3.2: Matrices / 174 3.3: Orthogonal Matrices / 192 3.4: Hermitian Matrices, Unitary Matrices / 206 3.5: Diagonalization of Matrices / 213 3.6: Normal Matrices / 227 4: Group Theory / 237 4.1: Introduction to Group Theory / 237 4.2: Generators of Continuous Groups / 242 4.3: Orbital Angular Momentum / 258 4.4: Angular Momentum Coupling / 263 4.5: Homogeneous Lorentz Group / 275 4.6: Lorentz Covariance of Maxwell's Equations / 278 4.7: Discrete Groups / 286 5: Infinite Series / 303 5.2: Convergence Tests / 306 5.3: Alternating Series / 322 5.4: Algebra of Series / 325 5.5: Series of Functions / 329 5.6: Taylor's Expansion / 334 5.7: Power Series / 346 5.8: Elliptic Integrals / 354 5.9: Bernoulli Numbers, Euler--Maclaurin Formula / 360 5.10: Asymptotic Series / 373 5.11: Infinite Products / 381 6: Functions of a Complex Variable I / 389 6.1: Complex Algebra / 390 6.2: Cauchy--Riemann Conditions / 399 6.3: Cauchy's Integral Theorem / 404 6.4: Cauchy's Integral Formula / 411 6.5: Laurent Expansion / 416 6.6: Mapping / 425 6.7: Conformal Mapping / 434 7: Functions of a Complex Variable II / 439 7.1: Singularities / 439 7.2: Calculus of Residues / 444 7.3: Dispersion Relations / 469 7.4: Method of Steepest Descents / 477 8: Differential Equations / 487 8.1: Partial Differential Equations / 487 8.2: First-Order Differential Equations / 496 8.3: Separation of Variables / 506 8.4: Singular Points / 516 8.5: Series Solutions--Frobenius's Method / 518 8.6: A Second Solution / 533 8.7: Nonhomogeneous Equation--Green's Function / 548 8.8: Numerical Solutions / 567 9: Sturm--Liouville Theory / 575 9.1: Self-Adjoint ODEs / 575 9.2: Hermitian Operators / 588 9.3: Gram--Schmidt Orthogonalization / 596 9.4: Completeness of Eigenfunctions / 604 9.5: Green's Function--Eigenfunction Expansion / 616 10: Gamma-Factorial Function / 631 10.1: Definitions, Simple Properties / 631 10.2: Digamma and Polygamma Functions / 643 10.3: Stirling's Series / 649 10.4: Beta Function / 654 10.5: Incomplete Gamma Function / 660 11: Bessel Functions / 669 11.1: Bessel Functions of the First Kind J[subscript v](x) / 669 11.2: Orthogonality / 688 11.3: Neumann Functions, Bessel Functions of the Second Kind / 694 11.4: Hankel Functions / 702 11.5: Modified Bessel Functions I[subscript v](x) and K[subscript v](x) / 709 11.6: Asymptotic Expansions / 716 11.7: Spherical Bessel Functions / 722 12: Legendre Functions / 739 12.1: Generating Function / 739 12.2: Recurrence Relations / 748 12.3: Orthogonality / 755 12.4: Alternate Definitions / 767 12.5: Associated Legendre Functions / 771 12.6G: Spherical Harmonics / 786 12.7: Orbital Angular Momentum Operators / 792 12.8: Addition Theorem for Spherical Harmonics / 796 12.9: Integrals of Three Ys / 802 12.10: Legendre Functions of the Second Kind / 806 12.11: Vector Spherical Harmonics / 813 13: Special Functions / 817 13.1: Hermite Functions / 817 13.2: Laguerre Functions / 828 13.3: Chebyshev Polynomials / 839 13.4: Hypergeometric Functions / 850 13.5: Confluent Hypergeometric Functions / 855 14: Fourier Series / 863 14.1: General Properties / 863 14.2: Advantages, Uses of Fouries Series / 870 14.3: Applications of Fourier Series / 874 14.4: Properties of Fourier Series / 886 14.5: Gibbs Phenomenon / 893 14.6: Discrete Fourier Transform / 898 15: Integral Transforms / 905 15.1: Integral Transforms / 905 15.2: Development of the Fourier Integral / 909 15.3: Fourier Transforms--Inversion Theorem / 911 15.4: Fourier Transform of Derivatives / 920 15.5: Convolution Theorem / 924 15.6: Momentum Representation / 928 15.7: Transfer Functions / 935 15.8: Laplace Transforms / 938 15.9: Laplace Transform of Derivatives / 946 15.10: Other Properties / 953 15.11: Convolution or Faltungs Theorem / 965 15.12: Inverse Laplace Transform / 969 16: Integral Equations / 983 16.2: Integral Transforms, Generating Functions / 991 16.3: Neumann Series, Separable Kernels / 997 16.4: Hilbert--Schmidt Theory / 1009 17: Calculus of Variations / 1017 17.1: A Dependent and an Independent Variable / 1018 17.2: Applications of the Euler Equation / 1023 17.3: Several Dependent Variables / 1031 17.4: Several Independent Variables / 1036 17.5: Several Dependent and Independent Variables / 1038 17.6: Lagrangian Multipliers / 1039 17.7: Variation With Constraints / 1045 17.8: Rayleigh--Ritz Variational Technique / 1052 18: Nonlinear Methods and Chaos / 1059 18.2: Logistic Map / 1060 18.3: Sensitivity to Initial Conditions / 1064 18.4: Nonlinear Differential Equations / 1068 Appendix 1: Real Zeros of a Function / 1085 Appendix 2: Gaussian Quadrature / 1089

rawTOC:
1: Vector Analysis / 1 \\ 1.2: Rotation of the Coordinate Axes / 8 \\ 1.3: Scalar or Dot Product / 13 \\ 1.4: Vector or Cross Product / 19 \\ 1.5: Triple Scalar Product, Triple Vector Product / 27 \\ 1.6: Gradient, [down triangle, open] / 35 \\ 1.7: Divergence, [down triangle, open] / 40 \\ 1.8: Curl, [down triangle, open] x / 44 \\ 1.9: Successive Applications of [down triangle, open] / 51 \\ 1.10: Vector Integration / 55 \\ 1.11: Gauss's Theorem / 61 \\ 1.12: Stokes's Theorem / 65 \\ 1.13: Potential Theory / 69 \\ 1.14: Gauss's Law, Poisson's Equation / 80 \\ 1.15: Dirac Delta Function / 84 \\ 1.16: Helmholtz's Theorem / 96 \\ 2: Curved Coordinates, Tensors / 103 \\ 2.1: Orthogonal Coordinates / 103 \\ 2.2: Differential Vector Operators / 108 \\ 2.3: Special Coordinate Systems: Introduction / 113 \\ 2.4: Circular Cylindrical Coordinates / 114 \\ 2.5: Spherical Polar Coordinates / 121 \\ 2.6: Tensor Analysis / 131 \\ 2.7: Contraction, Direct Product / 137 \\ 2.8: Quotient Rule / 139 \\ 2.9: Pseudotensors, Dual Tensors / 141 \\ 2.10: Non-Cartesian Tensors / 150 \\ 2.11: Tensor Derivative Operators / 160 \\ 3: Determinants and Matrices / 165 \\ 3.1: Determinants / 165 \\ 3.2: Matrices / 174 \\ 3.3: Orthogonal Matrices / 192 \\ 3.4: Hermitian Matrices, Unitary Matrices / 206 \\ 3.5: Diagonalization of Matrices / 213 \\ 3.6: Normal Matrices / 227 \\ 4: Group Theory / 237 \\ 4.1: Introduction to Group Theory / 237 \\ 4.2: Generators of Continuous Groups / 242 \\ 4.3: Orbital Angular Momentum / 258 \\ 4.4: Angular Momentum Coupling / 263 \\ 4.5: Homogeneous Lorentz Group / 275 \\ 4.6: Lorentz Covariance of Maxwell's Equations / 278 \\ 4.7: Discrete Groups / 286 \\ 5: Infinite Series / 303 \\ 5.2: Convergence Tests / 306 \\ 5.3: Alternating Series / 322 \\ 5.4: Algebra of Series / 325 \\ 5.5: Series of Functions / 329 \\ 5.6: Taylor's Expansion / 334 \\ 5.7: Power Series / 346 \\ 5.8: Elliptic Integrals / 354 \\ 5.9: Bernoulli Numbers, Euler--Maclaurin Formula / 360 \\ 5.10: Asymptotic Series / 373 \\ 5.11: Infinite Products / 381 \\ 6: Functions of a Complex Variable I / 389 \\ 6.1: Complex Algebra / 390 \\ 6.2: Cauchy--Riemann Conditions / 399 \\ 6.3: Cauchy's Integral Theorem / 404 \\ 6.4: Cauchy's Integral Formula / 411 \\ 6.5: Laurent Expansion / 416 \\ 6.6: Mapping / 425 \\ 6.7: Conformal Mapping / 434 \\ 7: Functions of a Complex Variable II / 439 \\ 7.1: Singularities / 439 \\ 7.2: Calculus of Residues / 444 \\ 7.3: Dispersion Relations / 469 \\ 7.4: Method of Steepest Descents / 477 \\ 8: Differential Equations / 487 \\ 8.1: Partial Differential Equations / 487 \\ 8.2: First-Order Differential Equations / 496 \\ 8.3: Separation of Variables / 506 \\ 8.4: Singular Points / 516 \\ 8.5: Series Solutions--Frobenius's Method / 518 \\ 8.6: A Second Solution / 533 \\ 8.7: Nonhomogeneous Equation--Green's Function / 548 \\ 8.8: Numerical Solutions / 567 \\ 9: Sturm--Liouville Theory / 575 \\ 9.1: Self-Adjoint ODEs / 575 \\ 9.2: Hermitian Operators / 588 \\ 9.3: Gram--Schmidt Orthogonalization / 596 \\ 9.4: Completeness of Eigenfunctions / 604 \\ 9.5: Green's Function--Eigenfunction Expansion / 616 \\ 10: Gamma-Factorial Function / 631 \\ 10.1: Definitions, Simple Properties / 631 \\ 10.2: Digamma and Polygamma Functions / 643 \\ 10.3: Stirling's Series / 649 \\ 10.4: Beta Function / 654 \\ 10.5: Incomplete Gamma Function / 660 \\ 11: Bessel Functions / 669 \\ 11.1: Bessel Functions of the First Kind J[subscript v](x) / 669 \\ 11.2: Orthogonality / 688 \\ 11.3: Neumann Functions, Bessel Functions of the Second Kind / 694 \\ 11.4: Hankel Functions / 702 \\ 11.5: Modified Bessel Functions I[subscript v](x) and K[subscript v](x) / 709 \\ 11.6: Asymptotic Expansions / 716 \\ 11.7: Spherical Bessel Functions / 722 \\ 12: Legendre Functions / 739 \\ 12.1: Generating Function / 739 \\ 12.2: Recurrence Relations / 748 \\ 12.3: Orthogonality / 755 \\ 12.4: Alternate Definitions / 767 \\ 12.5: Associated Legendre Functions / 771 \\ 12.6G: Spherical Harmonics / 786 \\ 12.7: Orbital Angular Momentum Operators / 792 \\ 12.8: Addition Theorem for Spherical Harmonics / 796 \\ 12.9: Integrals of Three Ys / 802 \\ 12.10: Legendre Functions of the Second Kind / 806 \\ 12.11: Vector Spherical Harmonics / 813 \\ 13: Special Functions / 817 \\ 13.1: Hermite Functions / 817 \\ 13.2: Laguerre Functions / 828 \\ 13.3: Chebyshev Polynomials / 839 \\ 13.4: Hypergeometric Functions / 850 \\ 13.5: Confluent Hypergeometric Functions / 855 \\ 14: Fourier Series / 863 \\ 14.1: General Properties / 863 \\ 14.2: Advantages, Uses of Fouries Series / 870 \\ 14.3: Applications of Fourier Series / 874 \\ 14.4: Properties of Fourier Series / 886 \\ 14.5: Gibbs Phenomenon / 893 \\ 14.6: Discrete Fourier Transform / 898 \\ 15: Integral Transforms / 905 \\ 15.1: Integral Transforms / 905 \\ 15.2: Development of the Fourier Integral / 909 \\ 15.3: Fourier Transforms--Inversion Theorem / 911 \\ 15.4: Fourier Transform of Derivatives / 920 \\ 15.5: Convolution Theorem / 924 \\ 15.6: Momentum Representation / 928 \\ 15.7: Transfer Functions / 935 \\ 15.8: Laplace Transforms / 938 \\ 15.9: Laplace Transform of Derivatives / 946 \\ 15.10: Other Properties / 953 \\ 15.11: Convolution or Faltungs Theorem / 965 \\ 15.12: Inverse Laplace Transform / 969 \\ 16: Integral Equations / 983 \\ 16.2: Integral Transforms, Generating Functions / 991 \\ 16.3: Neumann Series, Separable Kernels / 997 \\ 16.4: Hilbert--Schmidt Theory / 1009 \\ 17: Calculus of Variations / 1017 \\ 17.1: A Dependent and an Independent Variable / 1018 \\ 17.2: Applications of the Euler Equation / 1023 \\ 17.3: Several Dependent Variables / 1031 \\ 17.4: Several Independent Variables / 1036 \\ 17.5: Several Dependent and Independent Variables / 1038 \\ 17.6: Lagrangian Multipliers / 1039 \\ 17.7: Variation With Constraints / 1045 \\ 17.8: Rayleigh--Ritz Variational Technique / 1052 \\ 18: Nonlinear Methods and Chaos / 1059 \\ 18.2: Logistic Map / 1060 \\ 18.3: Sensitivity to Initial Conditions / 1064 \\ 18.4: Nonlinear Differential Equations / 1068 \\ Appendix 1: Real Zeros of a Function / 1085 \\ Appendix 2: Gaussian Quadrature / 1089

entry:
@Book{Arfken:2001:MMP,
  author =       "George B. (George Brown) Arfken and Hans-Jurgen
                 Weber",
  title =        "Mathematical methods for physicists",
  publisher =    "Harcourt/Academic Press",
  address =      "San Diego, CA, USA",
  edition =      "Fifth",
  pages =        "xiv + 1112",
  year =         "2001",
  ISBN =         "0-12-059825-6, 0-12-059826-4",
  ISBN-13 =      "978-0-12-059825-0, 978-0-12-059826-7",
  LCCN =         "QA37.3 .A74 2001",
  MRclass =      "00A06, 15-01, 26-01, 30-01, 34-01, 35-01, 65-01",
  bibdate =      "Wed Mar 15 06:50:49 MDT 2017",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://catalog.hathitrust.org/api/volumes/oclc/45705658.html",
  acknowledgement = ack-nhfb,
  author-dates = "1922--",
  subject =      "Mathematics; Mathematical physics; Matem{\'a}ticas;
                 F{\'i}sica matem{\'a}tica; Mathematical physics;
                 Mathematics; Wiskundige methoden; Natuurkunde;
                 Matem{\'a}tica; F{\'i}sica; Math{\'e}matiques; Physique
                 math{\'e}matique",
  tableofcontents = "1: Vector Analysis / 1 \\
                 1.2: Rotation of the Coordinate Axes / 8 \\
                 1.3: Scalar or Dot Product / 13 \\
                 1.4: Vector or Cross Product / 19 \\
                 1.5: Triple Scalar Product, Triple Vector Product / 27
                 \\
                 1.6: Gradient, [down triangle, open] / 35 \\
                 1.7: Divergence, [down triangle, open] / 40 \\
                 1.8: Curl, [down triangle, open] x / 44 \\
                 1.9: Successive Applications of [down triangle, open] /
                 51 \\
                 1.10: Vector Integration / 55 \\
                 1.11: Gauss's Theorem / 61 \\
                 1.12: Stokes's Theorem / 65 \\
                 1.13: Potential Theory / 69 \\
                 1.14: Gauss's Law, Poisson's Equation / 80 \\
                 1.15: Dirac Delta Function / 84 \\
                 1.16: Helmholtz's Theorem / 96 \\
                 2: Curved Coordinates, Tensors / 103 \\
                 2.1: Orthogonal Coordinates / 103 \\
                 2.2: Differential Vector Operators / 108 \\
                 2.3: Special Coordinate Systems: Introduction / 113 \\
                 2.4: Circular Cylindrical Coordinates / 114 \\
                 2.5: Spherical Polar Coordinates / 121 \\
                 2.6: Tensor Analysis / 131 \\
                 2.7: Contraction, Direct Product / 137 \\
                 2.8: Quotient Rule / 139 \\
                 2.9: Pseudotensors, Dual Tensors / 141 \\
                 2.10: Non-Cartesian Tensors / 150 \\
                 2.11: Tensor Derivative Operators / 160 \\
                 3: Determinants and Matrices / 165 \\
                 3.1: Determinants / 165 \\
                 3.2: Matrices / 174 \\
                 3.3: Orthogonal Matrices / 192 \\
                 3.4: Hermitian Matrices, Unitary Matrices / 206 \\
                 3.5: Diagonalization of Matrices / 213 \\
                 3.6: Normal Matrices / 227 \\
                 4: Group Theory / 237 \\
                 4.1: Introduction to Group Theory / 237 \\
                 4.2: Generators of Continuous Groups / 242 \\
                 4.3: Orbital Angular Momentum / 258 \\
                 4.4: Angular Momentum Coupling / 263 \\
                 4.5: Homogeneous Lorentz Group / 275 \\
                 4.6: Lorentz Covariance of Maxwell's Equations / 278
                 \\
                 4.7: Discrete Groups / 286 \\
                 5: Infinite Series / 303 \\
                 5.2: Convergence Tests / 306 \\
                 5.3: Alternating Series / 322 \\
                 5.4: Algebra of Series / 325 \\
                 5.5: Series of Functions / 329 \\
                 5.6: Taylor's Expansion / 334 \\
                 5.7: Power Series / 346 \\
                 5.8: Elliptic Integrals / 354 \\
                 5.9: Bernoulli Numbers, Euler--Maclaurin Formula / 360
                 \\
                 5.10: Asymptotic Series / 373 \\
                 5.11: Infinite Products / 381 \\
                 6: Functions of a Complex Variable I / 389 \\
                 6.1: Complex Algebra / 390 \\
                 6.2: Cauchy--Riemann Conditions / 399 \\
                 6.3: Cauchy's Integral Theorem / 404 \\
                 6.4: Cauchy's Integral Formula / 411 \\
                 6.5: Laurent Expansion / 416 \\
                 6.6: Mapping / 425 \\
                 6.7: Conformal Mapping / 434 \\
                 7: Functions of a Complex Variable II / 439 \\
                 7.1: Singularities / 439 \\
                 7.2: Calculus of Residues / 444 \\
                 7.3: Dispersion Relations / 469 \\
                 7.4: Method of Steepest Descents / 477 \\
                 8: Differential Equations / 487 \\
                 8.1: Partial Differential Equations / 487 \\
                 8.2: First-Order Differential Equations / 496 \\
                 8.3: Separation of Variables / 506 \\
                 8.4: Singular Points / 516 \\
                 8.5: Series Solutions--Frobenius's Method / 518 \\
                 8.6: A Second Solution / 533 \\
                 8.7: Nonhomogeneous Equation--Green's Function / 548
                 \\
                 8.8: Numerical Solutions / 567 \\
                 9: Sturm--Liouville Theory / 575 \\
                 9.1: Self-Adjoint ODEs / 575 \\
                 9.2: Hermitian Operators / 588 \\
                 9.3: Gram--Schmidt Orthogonalization / 596 \\
                 9.4: Completeness of Eigenfunctions / 604 \\
                 9.5: Green's Function--Eigenfunction Expansion / 616
                 \\
                 10: Gamma-Factorial Function / 631 \\
                 10.1: Definitions, Simple Properties / 631 \\
                 10.2: Digamma and Polygamma Functions / 643 \\
                 10.3: Stirling's Series / 649 \\
                 10.4: Beta Function / 654 \\
                 10.5: Incomplete Gamma Function / 660 \\
                 11: Bessel Functions / 669 \\
                 11.1: Bessel Functions of the First Kind J[subscript
                 v](x) / 669 \\
                 11.2: Orthogonality / 688 \\
                 11.3: Neumann Functions, Bessel Functions of the Second
                 Kind / 694 \\
                 11.4: Hankel Functions / 702 \\
                 11.5: Modified Bessel Functions I[subscript v](x) and
                 K[subscript v](x) / 709 \\
                 11.6: Asymptotic Expansions / 716 \\
                 11.7: Spherical Bessel Functions / 722 \\
                 12: Legendre Functions / 739 \\
                 12.1: Generating Function / 739 \\
                 12.2: Recurrence Relations / 748 \\
                 12.3: Orthogonality / 755 \\
                 12.4: Alternate Definitions / 767 \\
                 12.5: Associated Legendre Functions / 771 \\
                 12.6G: Spherical Harmonics / 786 \\
                 12.7: Orbital Angular Momentum Operators / 792 \\
                 12.8: Addition Theorem for Spherical Harmonics / 796
                 \\
                 12.9: Integrals of Three Ys / 802 \\
                 12.10: Legendre Functions of the Second Kind / 806 \\
                 12.11: Vector Spherical Harmonics / 813 \\
                 13: Special Functions / 817 \\
                 13.1: Hermite Functions / 817 \\
                 13.2: Laguerre Functions / 828 \\
                 13.3: Chebyshev Polynomials / 839 \\
                 13.4: Hypergeometric Functions / 850 \\
                 13.5: Confluent Hypergeometric Functions / 855 \\
                 14: Fourier Series / 863 \\
                 14.1: General Properties / 863 \\
                 14.2: Advantages, Uses of Fouries Series / 870 \\
                 14.3: Applications of Fourier Series / 874 \\
                 14.4: Properties of Fourier Series / 886 \\
                 14.5: Gibbs Phenomenon / 893 \\
                 14.6: Discrete Fourier Transform / 898 \\
                 15: Integral Transforms / 905 \\
                 15.1: Integral Transforms / 905 \\
                 15.2: Development of the Fourier Integral / 909 \\
                 15.3: Fourier Transforms--Inversion Theorem / 911 \\
                 15.4: Fourier Transform of Derivatives / 920 \\
                 15.5: Convolution Theorem / 924 \\
                 15.6: Momentum Representation / 928 \\
                 15.7: Transfer Functions / 935 \\
                 15.8: Laplace Transforms / 938 \\
                 15.9: Laplace Transform of Derivatives / 946 \\
                 15.10: Other Properties / 953 \\
                 15.11: Convolution or Faltungs Theorem / 965 \\
                 15.12: Inverse Laplace Transform / 969 \\
                 16: Integral Equations / 983 \\
                 16.2: Integral Transforms, Generating Functions / 991
                 \\
                 16.3: Neumann Series, Separable Kernels / 997 \\
                 16.4: Hilbert--Schmidt Theory / 1009 \\
                 17: Calculus of Variations / 1017 \\
                 17.1: A Dependent and an Independent Variable / 1018
                 \\
                 17.2: Applications of the Euler Equation / 1023 \\
                 17.3: Several Dependent Variables / 1031 \\
                 17.4: Several Independent Variables / 1036 \\
                 17.5: Several Dependent and Independent Variables /
                 1038 \\
                 17.6: Lagrangian Multipliers / 1039 \\
                 17.7: Variation With Constraints / 1045 \\
                 17.8: Rayleigh--Ritz Variational Technique / 1052 \\
                 18: Nonlinear Methods and Chaos / 1059 \\
                 18.2: Logistic Map / 1060 \\
                 18.3: Sensitivity to Initial Conditions / 1064 \\
                 18.4: Nonlinear Differential Equations / 1068 \\
                 Appendix 1: Real Zeros of a Function / 1085 \\
                 Appendix 2: Gaussian Quadrature / 1089",
}


bibtype: book
filename: elefunt.bib
label: Askey:2001:SFG
editor: R. A. Askey and Tom H. Koornwinder and Walter J. Schempp
title: Special Functions: Group Theoretical Aspects and Applications
publisher: pub-SV
address: pub-SV:adr
pages: xxxiv + 311
year: 2001
ISBN: 90-277-1822-9 OR 9027718229
ISBN13: 978-90-277-1822-8 OR 9789027718228
LCCN: QA1 M428 v. 18 c.2
bibdate: Sat Oct 30 17:58:21 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 17:58:21 ???
series: Mathematics and Its Applications
acknowledgement: ack-nhfb
raweditor: R. A. Askey and Tom H. Koornwinder and Walter J. Schempp
rawtitle: Special Functions: Group Theoretical Aspects and Applications
TOC:
Editor's Preface / M. Hazewinkel / vii Preface / R. Askey / xi Jacobi functions and analysis on noncompact semisimple Lie groups / Tom H. Koornwinder / 1 Orthogonal polynomials and Chevalley groups / Dennis Stanton /87 Special functions and group theory in theoretical physics / L. C. Biedenharn, R. A. Gustafson, M. A. Lohe, J. D. Louck, S. C. Milne / 129 Lattice gauge theory, orthogonal polynomials and q-Hypergeometric functions / George E. Andrews, Enrico Onofri / 163 The Laguerre calculus on the Heisenberg group / R. W. Beals, P. C. Greiner, J. Vauthier / 189 Radar ambiguity functions, nilpotent harmonic analysis, and holomorphic theta series / Walter Schempp / 217 A factorization theorem for the Fourier transform of a separable locally compact Abelian group / Louis Auslander / 261 Band and time limiting, recursion relations and some nonlinear evolution equations / F. Alberto Grunbaum / 271 Harmonics and combinatorics / J. J. Seidel / 287 Subject Index / / 305

rawTOC:
Editor's Preface / M. Hazewinkel / vii \\ Preface / R. Askey / xi \\ Jacobi functions and analysis on noncompact semisimple Lie groups / Tom H. Koornwinder / 1 \\ Orthogonal polynomials and Chevalley groups / Dennis Stanton /87 \\ Special functions and group theory in theoretical physics / L. C. Biedenharn, R. A. Gustafson, M. A. Lohe, J. D. Louck, S. C. Milne / 129 \\ Lattice gauge theory, orthogonal polynomials and q-Hypergeometric functions / George E. Andrews, Enrico Onofri / 163 \\ The Laguerre calculus on the Heisenberg group / R. W. Beals, P. C. Greiner, J. Vauthier / 189 \\ Radar ambiguity functions, nilpotent harmonic analysis, and holomorphic theta series / Walter Schempp / 217 \\ A factorization theorem for the Fourier transform of a separable locally compact Abelian group / Louis Auslander / 261 \\ Band and time limiting, recursion relations and some nonlinear evolution equations / F. Alberto Gr{\"u}nbaum / 271 \\ Harmonics and combinatorics / J. J. Seidel / 287 \\ Subject Index / / 305

entry:
@Book{Askey:2001:SFG,
  editor =       "R. A. Askey and Tom H. Koornwinder and Walter J.
                 Schempp",
  title =        "Special Functions: Group Theoretical Aspects and
                 Applications",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "xxxiv + 311",
  year =         "2001",
  ISBN =         "90-277-1822-9",
  ISBN-13 =      "978-90-277-1822-8",
  LCCN =         "QA1 M428 v. 18 c.2",
  bibdate =      "Sat Oct 30 17:58:21 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Mathematics and Its Applications",
  acknowledgement = ack-nhfb,
  tableofcontents = "Editor's Preface / M. Hazewinkel / vii \\
                 Preface / R. Askey / xi \\
                 Jacobi functions and analysis on noncompact semisimple
                 Lie groups / Tom H. Koornwinder / 1 \\
                 Orthogonal polynomials and Chevalley groups / Dennis
                 Stanton /87 \\
                 Special functions and group theory in theoretical
                 physics / L. C. Biedenharn, R. A. Gustafson, M. A.
                 Lohe, J. D. Louck, S. C. Milne / 129 \\
                 Lattice gauge theory, orthogonal polynomials and
                 q-Hypergeometric functions / George E. Andrews, Enrico
                 Onofri / 163 \\
                 The Laguerre calculus on the Heisenberg group / R. W.
                 Beals, P. C. Greiner, J. Vauthier / 189 \\
                 Radar ambiguity functions, nilpotent harmonic analysis,
                 and holomorphic theta series / Walter Schempp / 217 \\
                 A factorization theorem for the Fourier transform of a
                 separable locally compact Abelian group / Louis
                 Auslander / 261 \\
                 Band and time limiting, recursion relations and some
                 nonlinear evolution equations / F. Alberto Gr{\"u}nbaum
                 / 271 \\
                 Harmonics and combinatorics / J. J. Seidel / 287 \\
                 Subject Index / / 305",
}


bibtype: article
filename: elefunt.bib
label: Bashagha:2001:NRS
author: A. E. Bashagha
title: Novel radix-$2$ $k$ square root module
volume: 148
number: 4
pages: 190--196
month: aug
monthnumber: 8
year: 2001
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
acknowledgement: ack-nhfb
rawauthor: A. E. Bashagha
rawtitle: Novel radix-$2$ $k$ square root module
journal:
Circuits, Devices and Systems, IEE Proceedings [see also IEE Proceedings G-Circuits, Devices and Systems]

entry:
@Article{Bashagha:2001:NRS,
  author =       "A. E. Bashagha",
  title =        "Novel radix-$2$ $k$ square root module",
  journal =      "Circuits, Devices and Systems, IEE Proceedings [see
                 also IEE Proceedings G-Circuits, Devices and Systems]",
  volume =       "148",
  number =       "4",
  pages =        "190--196",
  month =        aug,
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The conventional two's complement radix-$2$ $k$ square
                 root algorithm requires a set of $2^k$ full precision
                 comparisons to generate all the $2^k$ possible values
                 of the partial remainder. The correct remainder is the
                 minimum \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Berg:2001:CMF
author: Christian Berg and Henrik L. Pedersen
title: A completely monotone function related to the Gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 133
number: 1--2
pages: 219--230
day: 1
month: aug
monthnumber: 8
year: 2001
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:19 MST 2017
bibtimestamp: 2017.02.25 12:45:19 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700006440
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Christian Berg and Henrik L. Pedersen
rawtitle: A completely monotone function related to the Gamma function
entry:
@Article{Berg:2001:CMF,
  author =       "Christian Berg and Henrik L. Pedersen",
  title =        "A completely monotone function related to the Gamma
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "219--230",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700006440",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Berry:2001:WSF
author: Michael Berry
title: Why are special functions special?
journal: j-PHYS-TODAY
volume: 54
number: 4
pages: 11--12
month: apr
monthnumber: 4
year: 2001
CODEN: PHTOAD
DOI: https://doi.org/10.1063/1.1372098
ISSN: 0031-9228 (print), 1945-0699 (electronic) OR 00319228 (print), 19450699 (electronic)
ISSNL: 0031-9228 OR 00319228
bibdate: Sat Feb 19 13:23:33 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.02.19 13:23:33 ???
URL: http://www.physicstoday.org/resource/1/phtoad/v54/i4/p11_s1
fjournal: Physics Today
acknowledgement: ack-nhfb
journalURL: http://www.physicstoday.org/
rawauthor: Michael Berry
rawtitle: Why are special functions special?
entry:
@Article{Berry:2001:WSF,
  author =       "Michael Berry",
  title =        "Why are special functions special?",
  journal =      j-PHYS-TODAY,
  volume =       "54",
  number =       "4",
  pages =        "11--12",
  month =        apr,
  year =         "2001",
  CODEN =        "PHTOAD",
  DOI =          "https://doi.org/10.1063/1.1372098",
  ISSN =         "0031-9228 (print), 1945-0699 (electronic)",
  ISSN-L =       "0031-9228",
  bibdate =      "Sat Feb 19 13:23:33 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.physicstoday.org/resource/1/phtoad/v54/i4/p11_s1",
  acknowledgement = ack-nhfb,
  fjournal =     "Physics Today",
  journal-URL =  "http://www.physicstoday.org/",
}


bibtype: article
filename: elefunt.bib
label: Boisvert:2001:MM
author: Ronald F. Boisvert and M. J. Donahue and Daniel W. Lozier and R. McMichael and B. W. Rust
title: Mathematics and Measurement
journal: NIST Journal of Research
volume: 106
number: 1
pages: 293--313
month: jan
monthnumber: 1
year: 2001
bibdate: Fri Jul 09 06:26:11 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:26:11 ???
acknowledgement: ack-nhfb
rawauthor: Ronald F. Boisvert and M. J. Donahue and Daniel W. Lozier and R. McMichael and B. W. Rust
rawtitle: Mathematics and Measurement
entry:
@Article{Boisvert:2001:MM,
  author =       "Ronald F. Boisvert and M. J. Donahue and Daniel W.
                 Lozier and R. McMichael and B. W. Rust",
  title =        "Mathematics and Measurement",
  journal =      "NIST Journal of Research",
  volume =       "106",
  number =       "1",
  pages =        "293--313",
  month =        jan # "\slash " # feb,
  year =         "2001",
  bibdate =      "Fri Jul 09 06:26:11 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Boyd:2001:CFS
author: John Philip Boyd
title: Chebyshev and Fourier spectral methods
publisher: pub-DOVER
address: pub-DOVER:adr
edition: Second (revised).
pages: 1375
year: 2001
ISBN: 0-486-41183-4 (paperback), 0-486-14192-6 (e-book) OR 0486411834 (paperback), 0486141926 (ebook)
LCCN: QA404.5 .B69 2001
bibdate: Sat Feb 17 14:05:46 MST 2024
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2024.02.17 14:05:46 MST
series: Dover Books on Mathematics
URL: http://www.freading.com/ebooks/details/r:download/ZnJlYWQ6OTc4MDQ4NjE0MTkyMzpl
acknowledgement: ack-nhfb
authordates: 1951--
rawauthor: John Philip Boyd
rawtitle: {Chebyshev} and {Fourier} spectral methods
ISBN13:
978-0-486-41183-5 (paperback), 978-0-486-14192-3 (e-book) OR 9780486411835 (paperback), 9780486141923 (ebook)

abstract:
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, spherical and cylindrical geometry, and more. Includes 7 appendices and over 160 text figures.

subject:
Chebyshev polynomials; Fourier analysis; Spectral theory (Mathematics); Polynyomes de Tchebychev; Analyse de Fourier; Spectre (Mathyematiques); MATHEMATICS; General.; Chebyshev polynomials; Fourier analysis; Spectral theory (Mathematics)

TOC:
1. Introduction 2. Chebyshev and Fourier Series 3. Galerkin and Weighted Residual Methods 4. Interpolation, Collocation and All That 5. Cardinal Functions 6. Pseudospectral Methods for BVPs 7. Linear Eigenvalue Problems 8. Symmetry and Parity 9. Explicit Time-Integration Methods 10. Partial Summation, the FFT and MMT 11. Aliasing, Spectral Blocking, and Blow-Up 12. Implicit Schemes and the Slow Manifold 13. Splitting and its Cousins 14. Semi-Lagrangian Advection 15. Matrix-Solving Methods 16. Coordinate Transformations 17. Methods for Unbounded Intervals 18. Spherical and Cylindrical Geometry 19. Special Tricks 20. Symbolic Calculations 21. The Tau Method 22. Domain Decomposition Methods 23. Books and Reviews

rawabstract:
Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, spherical and cylindrical geometry, and more. Includes 7 appendices and over 160 text figures.

rawTOC:
1. Introduction \\ 2. Chebyshev and Fourier Series \\ 3. Galerkin and Weighted Residual Methods \\ 4. Interpolation, Collocation and All That \\ 5. Cardinal Functions \\ 6. Pseudospectral Methods for BVPs \\ 7. Linear Eigenvalue Problems \\ 8. Symmetry and Parity \\ 9. Explicit Time-Integration Methods \\ 10. Partial Summation, the FFT and MMT \\ 11. Aliasing, Spectral Blocking, and Blow-Up \\ 12. Implicit Schemes and the Slow Manifold \\ 13. Splitting and its Cousins \\ 14. Semi-Lagrangian Advection \\ 15. Matrix-Solving Methods \\ 16. Coordinate Transformations \\ 17. Methods for Unbounded Intervals \\ 18. Spherical and Cylindrical Geometry \\ 19. Special Tricks \\ 20. Symbolic Calculations \\ 21. The Tau Method \\ 22. Domain Decomposition Methods \\ 23. Books and Reviews

entry:
@Book{Boyd:2001:CFS,
  author =       "John Philip Boyd",
  title =        "{Chebyshev} and {Fourier} spectral methods",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  edition =      "Second (revised).",
  pages =        "1375",
  year =         "2001",
  ISBN =         "0-486-41183-4 (paperback), 0-486-14192-6 (e-book)",
  ISBN-13 =      "978-0-486-41183-5 (paperback), 978-0-486-14192-3
                 (e-book)",
  LCCN =         "QA404.5 .B69 2001",
  bibdate =      "Sat Feb 17 14:05:46 MST 2024",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Dover Books on Mathematics",
  URL =          "http://www.freading.com/ebooks/details/r:download/ZnJlYWQ6OTc4MDQ4NjE0MTkyMzpl",
  abstract =     "Completely revised text focuses on use of spectral
                 methods to solve boundary value, eigenvalue, and
                 time-dependent problems, but also covers Hermite,
                 Laguerre, rational Chebyshev, sinc, and spherical
                 harmonic functions, as well as cardinal functions,
                 linear eigenvalue problems, matrix-solving methods,
                 coordinate transformations, spherical and cylindrical
                 geometry, and more. Includes 7 appendices and over 160
                 text figures.",
  acknowledgement = ack-nhfb,
  author-dates = "1951--",
  subject =      "Chebyshev polynomials; Fourier analysis; Spectral
                 theory (Mathematics); Polyn{\'y}omes de Tchebychev;
                 Analyse de Fourier; Spectre (Math{\'y}ematiques);
                 MATHEMATICS; General.; Chebyshev polynomials; Fourier
                 analysis; Spectral theory (Mathematics)",
  tableofcontents = "1. Introduction \\
                 2. Chebyshev and Fourier Series \\
                 3. Galerkin and Weighted Residual Methods \\
                 4. Interpolation, Collocation and All That \\
                 5. Cardinal Functions \\
                 6. Pseudospectral Methods for BVPs \\
                 7. Linear Eigenvalue Problems \\
                 8. Symmetry and Parity \\
                 9. Explicit Time-Integration Methods \\
                 10. Partial Summation, the FFT and MMT \\
                 11. Aliasing, Spectral Blocking, and Blow-Up \\
                 12. Implicit Schemes and the Slow Manifold \\
                 13. Splitting and its Cousins \\
                 14. Semi-Lagrangian Advection \\
                 15. Matrix-Solving Methods \\
                 16. Coordinate Transformations \\
                 17. Methods for Unbounded Intervals \\
                 18. Spherical and Cylindrical Geometry \\
                 19. Special Tricks \\
                 20. Symbolic Calculations \\
                 21. The Tau Method \\
                 22. Domain Decomposition Methods \\
                 23. Books and Reviews",
}


bibtype: inproceedings
filename: elefunt.bib
label: Burgess:2001:DIR
author: N. Burgess and C. Hinds
booktitle: Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems and Computers, 2001
title: Design issues in radix-$4$ SRT square root & divide unit
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1646--1650
year: 2001
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: N. Burgess and C. Hinds
rawbooktitle: Conference Record of the Thirty-Fifth Asilomar Conference on Signals, Systems and Computers, 2001
rawtitle: Design issues in radix-$4$ {SRT} square root {\&} divide unit
entry:
@InProceedings{Burgess:2001:DIR,
  author =       "N. Burgess and C. Hinds",
  booktitle =    "Conference Record of the Thirty-Fifth Asilomar
                 Conference on Signals, Systems and Computers, 2001",
  title =        "Design issues in radix-$4$ {SRT} square root {\&}
                 divide unit",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1646--1650",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "This paper introduces a number of design issues not
                 covered in the open literature that arose during the
                 design of a radix-$4$ SRT divide/square root unit for a
                 vector processing chip. These include compression of
                 the partial remainder's m.s.b.'s, \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Bustoz:2001:SFC
editor: Joaquin Bustoz and Mourad Ismail and S. K. (Sergei Konstantinovich) Suslov
title: Special functions 2000: current perspective and future directions
volume: 30
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: xi + 520
year: 2001
ISBN: 0-7923-7119-4, 0-7923-7120-8 OR 0792371194, 0792371208
ISBN13: 978-0-7923-7119-9, 978-0-7923-7120-5 OR 9780792371199, 9780792371205
LCCN: QA351 .S694 2001
bibdate: Sat Oct 30 17:31:39 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager
bibtimestamp: 2010.10.30 17:31:39 MDT
series: NATO science series. Series II, Mathematics, physics, and chemistry
subject: functions, special; congresses
acknowledgement: ack-nhfb
raweditor: Joaquin Bustoz and Mourad Ismail and S. K. (Sergei Konstantinovich) Suslov
rawtitle: Special functions 2000: current perspective and future directions
TOC:
Preface Foreword Bailey's transform, lemma, chains and tree / George E. Andrews 1 Riemann--Hilbert problems for multiple orthogonal polynomials / Walter Van Assche, Jeffrey S. Geronimo, Arno B. J. Kuijlaars 23 Flowers which we cannot yet see growing in Ramanujan's garden of hypergeometric series, elliptic functions and $q$'s / Bruce C. Berndt 61 Orthogonal rational functions and continued fractions [et al.] 87 Orthogonal polynomials and reflection groups / Charles F. Dunkl 111 The bispectral problem: an overview / F. Alberto Grunbaum 129 The Bochner--Krall problem: some new perspectives / Luc Haine 141 Lectures on $q$-orthogonal polynomials / Mourad E. H. Ismail 179 The Askey--Wilson function transform scheme / Erik Koelink, Jasper V. Stokman 221 Arithmetic of the partition function / Ken Ono 243 The associated classical orthogonal polynomials / Mizan Rahman 255 Special functions defined by analytic difference equations / S. N. M. Ruijsenaars 281 The factorization method, self-similar potentials and quantum algebras / V. P. Spiridonov 335 Generalized eigenvalue problem and a new family of rational functions biorthogonal on elliptic grids / V. P. Spiridonov, A. S. Zhedanov 365 Orthogonal polynomials and combinatorics / Dennis Stanton 389 Basic exponential functions on a $q$-quadratic grid / Sergei K. Suslov 411 Projection operator method for quantum groups / V. N. Tolstoy 457 Uniform asymptotic expansions / R. Wong 489 Exponential asymptotics / R. Wong 505 Index 519

rawTOC:
Preface \\ Foreword \\ Bailey's transform, lemma, chains and tree / George E. Andrews 1 \\ Riemann--Hilbert problems for multiple orthogonal polynomials / Walter Van Assche, Jeffrey S. Geronimo, Arno B. J. Kuijlaars 23 \\ Flowers which we cannot yet see growing in Ramanujan's garden of hypergeometric series, elliptic functions and $q$'s / Bruce C. Berndt 61 \\ Orthogonal rational functions and continued fractions [et al.] 87 \\ Orthogonal polynomials and reflection groups / Charles F. Dunkl 111 \\ The bispectral problem: an overview / F. Alberto Grunbaum 129 \\ The Bochner--Krall problem: some new perspectives / Luc Haine 141 \\ Lectures on $q$-orthogonal polynomials / Mourad E. H. Ismail 179 \\ The Askey--Wilson function transform scheme / Erik Koelink, Jasper V. Stokman 221 \\ Arithmetic of the partition function / Ken Ono 243 \\ The associated classical orthogonal polynomials / Mizan Rahman 255 \\ Special functions defined by analytic difference equations / S. N. M. Ruijsenaars 281 \\ The factorization method, self-similar potentials and quantum algebras / V. P. Spiridonov 335 \\ Generalized eigenvalue problem and a new family of rational functions biorthogonal on elliptic grids / V. P. Spiridonov, A. S. Zhedanov 365 \\ Orthogonal polynomials and combinatorics / Dennis Stanton 389 \\ Basic exponential functions on a $q$-quadratic grid / Sergei K. Suslov 411 \\ Projection operator method for quantum groups / V. N. Tolstoy 457 \\ Uniform asymptotic expansions / R. Wong 489 \\ Exponential asymptotics / R. Wong 505 \\ Index 519

entry:
@Book{Bustoz:2001:SFC,
  editor =       "Joaquin Bustoz and Mourad Ismail and S. K. (Sergei
                 Konstantinovich) Suslov",
  title =        "Special functions 2000: current perspective and future
                 directions",
  volume =       "30",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "xi + 520",
  year =         "2001",
  ISBN =         "0-7923-7119-4, 0-7923-7120-8",
  ISBN-13 =      "978-0-7923-7119-9, 978-0-7923-7120-5",
  LCCN =         "QA351 .S694 2001",
  bibdate =      "Sat Oct 30 17:31:39 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "NATO science series. Series II, Mathematics, physics,
                 and chemistry",
  acknowledgement = ack-nhfb,
  subject =      "functions, special; congresses",
  tableofcontents = "Preface \\
                 Foreword \\
                 Bailey's transform, lemma, chains and tree / George E.
                 Andrews 1 \\
                 Riemann--Hilbert problems for multiple orthogonal
                 polynomials / Walter Van Assche, Jeffrey S. Geronimo,
                 Arno B. J. Kuijlaars 23 \\
                 Flowers which we cannot yet see growing in Ramanujan's
                 garden of hypergeometric series, elliptic functions and
                 $q$'s / Bruce C. Berndt 61 \\
                 Orthogonal rational functions and continued fractions
                 [et al.] 87 \\
                 Orthogonal polynomials and reflection groups / Charles
                 F. Dunkl 111 \\
                 The bispectral problem: an overview / F. Alberto
                 Grunbaum 129 \\
                 The Bochner--Krall problem: some new perspectives / Luc
                 Haine 141 \\
                 Lectures on $q$-orthogonal polynomials / Mourad E. H.
                 Ismail 179 \\
                 The Askey--Wilson function transform scheme / Erik
                 Koelink, Jasper V. Stokman 221 \\
                 Arithmetic of the partition function / Ken Ono 243 \\
                 The associated classical orthogonal polynomials / Mizan
                 Rahman 255 \\
                 Special functions defined by analytic difference
                 equations / S. N. M. Ruijsenaars 281 \\
                 The factorization method, self-similar potentials and
                 quantum algebras / V. P. Spiridonov 335 \\
                 Generalized eigenvalue problem and a new family of
                 rational functions biorthogonal on elliptic grids / V.
                 P. Spiridonov, A. S. Zhedanov 365 \\
                 Orthogonal polynomials and combinatorics / Dennis
                 Stanton 389 \\
                 Basic exponential functions on a $q$-quadratic grid /
                 Sergei K. Suslov 411 \\
                 Projection operator method for quantum groups / V. N.
                 Tolstoy 457 \\
                 Uniform asymptotic expansions / R. Wong 489 \\
                 Exponential asymptotics / R. Wong 505 \\
                 Index 519",
}


bibtype: incollection
filename: elefunt.bib
label: Corless:2001:RAE
author: Robert M. Corless and James H. Davenport and David J. Jeffrey and Gurjeet Litt and Stephen M. Watt
booktitle: Artificial intelligence and symbolic computation (Madrid, 2000)
title: Reasoning about the elementary functions of complex analysis
volume: 1930
publisher: pub-SV
address: pub-SV:adr
pages: 115--126
year: 2001
MRclass: 68W30 (30C35)
MRnumber: MR1882755 (2002m:68126)
bibdate: Wed Apr 13 06:46:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.13 06:46:35 ???
series: Lecture Notes in Comput. Sci.
acknowledgement: ack-nhfb
rawauthor: Robert M. Corless and James H. Davenport and David J. Jeffrey and Gurjeet Litt and Stephen M. Watt
rawbooktitle: Artificial intelligence and symbolic computation (Madrid, 2000)
rawtitle: Reasoning about the elementary functions of complex analysis
entry:
@InCollection{Corless:2001:RAE,
  author =       "Robert M. Corless and James H. Davenport and David J.
                 Jeffrey and Gurjeet Litt and Stephen M. Watt",
  booktitle =    "Artificial intelligence and symbolic computation
                 (Madrid, 2000)",
  title =        "Reasoning about the elementary functions of complex
                 analysis",
  volume =       "1930",
  publisher =    pub-SV,
  address =      pub-SV:adr,
  pages =        "115--126",
  year =         "2001",
  MRclass =      "68W30 (30C35)",
  MRnumber =     "MR1882755 (2002m:68126)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Lecture Notes in Comput. Sci.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Dunkl:2001:OPS
author: Charles F. Dunkl and Yuan Xu
title: Orthogonal Polynomials of Several Variables
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: xv + 390
year: 2001
DOI: https://doi.org/10.1017/CBO9780511565717
LCCN: QA404.5 .D86 2001
bibdate: Sat Nov 11 07:30:57 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.11.11 07:30:57 ???
remark: See also second edition cite Dunkl:2014:OPS
acknowledgement: ack-nhfb
rawauthor: Charles F. Dunkl and Yuan Xu
rawtitle: Orthogonal Polynomials of Several Variables
ISBN:
0-511-56571-2 (e-book), 0-521-80043-9 (hardcover), 1-107-09582-4 OR 0511565712 (ebook), 0521800439 (hardcover), 1107095824

ISBN13:
978-0-511-56571-7 (e-book), 978-0-521-80043-3 (hardcover), 978-1-107-09582-3 OR 9780511565717 (ebook), 9780521800433 (hardcover), 9781107095823

abstract:
This is the first modern book on orthogonal polynomials of several variables, which are valuable tools used in multivariate analysis, including approximations and numerical integration. The book presents the theory in elegant form and with modern concepts and notation. It introduces the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains such as the cube, the simplex, the sphere and the ball. It also focuses on those of Gaussian type, for which fairly explicit formulae exist. The authors' approach blends classical analysis and symmetry-group-theoretic methods.

TOC:
1. Background 2. Examples of Orthogonal Polynomials in Several Variables 3. General Properties of Orthogonal Polynomials in Several Variables 4. Root Systems and Coxeter groups 5. Spherical Harmonics Associated with Reflection Groups 6. Classical and Generalized Classical Orthogonal Polynomials 7. Summability of Orthogonal Expansions 8. Orthogonal Polynomials Associated with Symmetric Groups 9. Orthogonal Polynomials Associated with Octahedral Groups and Applications

rawabstract:
This is the first modern book on orthogonal polynomials of several variables, which are valuable tools used in multivariate analysis, including approximations and numerical integration. The book presents the theory in elegant form and with modern concepts and notation. It introduces the general theory and emphasizes the classical types of orthogonal polynomials whose weight functions are supported on standard domains such as the cube, the simplex, the sphere and the ball. It also focuses on those of Gaussian type, for which fairly explicit formulae exist. The authors' approach blends classical analysis and symmetry-group-theoretic methods.

rawTOC:
1. Background \\ 2. Examples of Orthogonal Polynomials in Several Variables \\ 3. General Properties of Orthogonal Polynomials in Several Variables \\ 4. Root Systems and Coxeter groups \\ 5. Spherical Harmonics Associated with Reflection Groups \\ 6. Classical and Generalized Classical Orthogonal Polynomials \\ 7. Summability of Orthogonal Expansions \\ 8. Orthogonal Polynomials Associated with Symmetric Groups \\ 9. Orthogonal Polynomials Associated with Octahedral Groups and Applications

entry:
@Book{Dunkl:2001:OPS,
  author =       "Charles F. Dunkl and Yuan Xu",
  title =        "Orthogonal Polynomials of Several Variables",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xv + 390",
  year =         "2001",
  DOI =          "https://doi.org/10.1017/CBO9780511565717",
  ISBN =         "0-511-56571-2 (e-book), 0-521-80043-9 (hardcover),
                 1-107-09582-4",
  ISBN-13 =      "978-0-511-56571-7 (e-book), 978-0-521-80043-3
                 (hardcover), 978-1-107-09582-3",
  LCCN =         "QA404.5 .D86 2001",
  bibdate =      "Sat Nov 11 07:30:57 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This is the first modern book on orthogonal
                 polynomials of several variables, which are valuable
                 tools used in multivariate analysis, including
                 approximations and numerical integration. The book
                 presents the theory in elegant form and with modern
                 concepts and notation. It introduces the general theory
                 and emphasizes the classical types of orthogonal
                 polynomials whose weight functions are supported on
                 standard domains such as the cube, the simplex, the
                 sphere and the ball. It also focuses on those of
                 Gaussian type, for which fairly explicit formulae
                 exist. The authors' approach blends classical analysis
                 and symmetry-group-theoretic methods.",
  acknowledgement = ack-nhfb,
  remark =       "See also second edition \cite{Dunkl:2014:OPS}",
  tableofcontents = "1. Background \\
                 2. Examples of Orthogonal Polynomials in Several
                 Variables \\
                 3. General Properties of Orthogonal Polynomials in
                 Several Variables \\
                 4. Root Systems and Coxeter groups \\
                 5. Spherical Harmonics Associated with Reflection
                 Groups \\
                 6. Classical and Generalized Classical Orthogonal
                 Polynomials \\
                 7. Summability of Orthogonal Expansions \\
                 8. Orthogonal Polynomials Associated with Symmetric
                 Groups \\
                 9. Orthogonal Polynomials Associated with Octahedral
                 Groups and Applications",
}


bibtype: article
filename: elefunt.bib
label: Eklund:2001:CEF
author: Neil Eklund
title: CORDIC: Elementary Function Computation Using Recursive Sequences
journal: j-COLLEGE-MATH-J
volume: 32
number: 5
pages: 330--333
month: nov
monthnumber: 11
year: 2001
DOI: https://doi.org/10.1080/07468342.2001.11921899
ISSN: 0746-8342 (print), 1931-1346 (electronic) OR 07468342 (print), 19311346 (electronic)
ISSNL: 0746-8342 OR 07468342
bibdate: Thu Feb 14 09:53:12 MST 2019
bibtimestamp: 2019.02.14 09:53:12 MST
URL: http://www.tandfonline.com/doi/abs/10.1080/07468342.2001.11921899
fjournal: College Mathematics Journal
acknowledgement: ack-nhfb
journalURL: https://maa.tandfonline.com/loi/ucmj20; https://www.jstor.org/journal/collmathj
onlinedate: 30 Jan 2018
rawauthor: Neil Eklund
rawtitle: {CORDIC}: Elementary Function Computation Using Recursive Sequences
entry:
@Article{Eklund:2001:CEF,
  author =       "Neil Eklund",
  title =        "{CORDIC}: Elementary Function Computation Using
                 Recursive Sequences",
  journal =      j-COLLEGE-MATH-J,
  volume =       "32",
  number =       "5",
  pages =        "330--333",
  month =        nov,
  year =         "2001",
  CODEN =        "????",
  DOI =          "https://doi.org/10.1080/07468342.2001.11921899",
  ISSN =         "0746-8342 (print), 1931-1346 (electronic)",
  ISSN-L =       "0746-8342",
  bibdate =      "Thu Feb 14 09:53:12 MST 2019",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/collegemathj.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.tandfonline.com/doi/abs/10.1080/07468342.2001.11921899",
  acknowledgement = ack-nhfb,
  fjournal =     "College Mathematics Journal",
  journal-URL =  "https://maa.tandfonline.com/loi/ucmj20;
                 https://www.jstor.org/journal/collmathj",
  onlinedate =   "30 Jan 2018",
}


bibtype: article
filename: elefunt.bib
label: Elbert:2001:CZB
author: Arpad Elbert and Andrea Laforgia
title: A conjecture on the zeros of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 133
number: 1--2
pages: 683--683
day: 1
month: aug
monthnumber: 8
year: 2001
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:19 MST 2017
bibtimestamp: 2017.02.25 12:45:19 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700007172
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: {\'A}rp{\'a}d Elbert and Andrea Laforgia
rawtitle: A conjecture on the zeros of {Bessel} functions
entry:
@Article{Elbert:2001:CZB,
  author =       "{\'A}rp{\'a}d Elbert and Andrea Laforgia",
  title =        "A conjecture on the zeros of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "683--683",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700007172",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Elbert:2001:SRR
author: A. Elbert
title: Some recent results on the zeros of Bessel functions and orthogonal polynomials
journal: j-J-COMPUT-APPL-MATH
volume: 133
number: 1--2
pages: 65--83
day: 1
month: aug
monthnumber: 8
year: 2001
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:19 MST 2017
bibtimestamp: 2017.02.25 12:45:19 MST
URL: http://www.sciencedirect.com/science/article/pii/S037704270000635X
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: {\'A}. Elbert
rawtitle: Some recent results on the zeros of {Bessel} functions and orthogonal polynomials
entry:
@Article{Elbert:2001:SRR,
  author =       "{\'A}. Elbert",
  title =        "Some recent results on the zeros of {Bessel} functions
                 and orthogonal polynomials",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "65--83",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270000635X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Giordano:2001:IMP
author: C. Giordano and A. Laforgia
title: Inequalities and monotonicity properties for the gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 133
number: 1--2
pages: 387--396
day: 1
month: aug
monthnumber: 8
year: 2001
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:19 MST 2017
bibtimestamp: 2017.02.25 12:45:19 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700006592
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: C. Giordano and A. Laforgia
rawtitle: Inequalities and monotonicity properties for the gamma function
entry:
@Article{Giordano:2001:IMP,
  author =       "C. Giordano and A. Laforgia",
  title =        "Inequalities and monotonicity properties for the gamma
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "387--396",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700006592",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: unpublished
filename: elefunt.bib
label: Godfrey:2001:NCC
author: P. Godfrey
title: A Note on the Computation of the Convergent Lanczos Complex Gamma Approximation
pages: 387--396
year: 2001
bibdate: Mon Nov 24 21:04:40 2008
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2008.11.24 21:04:40 ???
note: Unpublished Web file.
URL: http://my.fit.edu/~gabdo/gamma.txt
acknowledgement: ack-nhfb
rawauthor: P. Godfrey
rawnote: Unpublished Web file.
rawtitle: A Note on the Computation of the Convergent {Lanczos} Complex Gamma Approximation
entry:
@Unpublished{Godfrey:2001:NCC,
  author =       "P. Godfrey",
  title =        "A Note on the Computation of the Convergent {Lanczos}
                 Complex Gamma Approximation",
  year =         "2001",
  bibdate =      "Mon Nov 24 21:04:40 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Unpublished Web file.",
  URL =          "http://my.fit.edu/~gabdo/gamma.txt",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Harris:2001:KFL
author: Frank E. Harris
title: On Kryachko's formula for the leaky aquifer function
journal: j-IJQC
volume: 81
number: 5
pages: 332--334
year: 2001
CODEN: IJQCB2
DOI: https://doi.org/10.1002/1097-461X(2001)81:5<332::AID-QUA1002>3.0.CO%3B2-W
ISSN: 0020-7608 (print), 1097-461X (electronic) OR 00207608 (print), 1097461X (electronic)
ISSNL: 0020-7608 OR 00207608
bibdate: Wed Apr 4 11:48:33 MDT 2001
bibtimestamp: 2001.04.04 11:48:33 MDT
fjournal: International Journal of Quantum Chemistry
acknowledgement: ack-nhfb
ajournal: Int. J. Quantum Chem.
journalURL: http://www.interscience.wiley.com/jpages/0020-7608/
rawauthor: Frank E. Harris
rawtitle: On {Kryachko}'s formula for the leaky aquifer function
bibsource:
http://www.interscience.wiley.com/jpages/0020-7608; http://www3.interscience.wiley.com/journalfinder.html; https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/ijqc2000.bib

URL:
http://www3.interscience.wiley.com/cgi-bin/abstract/76507286/START; http://www3.interscience.wiley.com/cgi-bin/fulltext/76507286/FILE?TPL=ftx_start; http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=76507286&PLACEBO=IE.pdf

entry:
@Article{Harris:2001:KFL,
  author =       "Frank E. Harris",
  title =        "On {Kryachko}'s formula for the leaky aquifer
                 function",
  journal =      j-IJQC,
  volume =       "81",
  number =       "5",
  pages =        "332--334",
  month =        "????",
  year =         "2001",
  CODEN =        "IJQCB2",
  DOI =          "https://doi.org/10.1002/1097-461X(2001)81:5<332::AID-QUA1002>3.0.CO%3B2-W",
  ISSN =         "0020-7608 (print), 1097-461X (electronic)",
  ISSN-L =       "0020-7608",
  bibdate =      "Wed Apr 4 11:48:33 MDT 2001",
  bibsource =    "http://www.interscience.wiley.com/jpages/0020-7608;
                 http://www3.interscience.wiley.com/journalfinder.html;
                 https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/ijqc2000.bib",
  URL =          "http://www3.interscience.wiley.com/cgi-bin/abstract/76507286/START;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext/76507286/FILE?TPL=ftx_start;
                 http://www3.interscience.wiley.com/cgi-bin/fulltext?ID=76507286&PLACEBO=IE.pdf",
  acknowledgement = ack-nhfb,
  ajournal =     "Int. J. Quantum Chem.",
  fjournal =     "International Journal of Quantum Chemistry",
  journal-URL =  "http://www.interscience.wiley.com/jpages/0020-7608/",
}


bibtype: unpublished
filename: elefunt.bib
label: Kahan:2001:PDA
author: William Kahan
title: Pseudo-Division Algorithms for Floating-Point Logarithms and Exponentials
pages: 8
day: 20
month: may
monthnumber: 5
year: 2001
bibdate: Sat Aug 23 06:17:04 2025
bibtimestamp: 2025.08.23 06:17:04 ???
URL: https://ieeemilestones.ethw.org/w/images/3/30/Wk_pseudo_division_log_exp_may01.pdf
acknowledgement: ack-nhfb
rawauthor: William Kahan
rawtitle: Pseudo-Division Algorithms for Floating-Point Logarithms and Exponentials
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Among the CORDIC-like algorithms for computing elementary transcendental functions like log and exp, certain pseudo-division algorithms are peculiarly well suited to implementation in microcode or in conjunction with software-implemented floating-point arithmetic. These algorithms need tables of comparatively modest size; they are almost as fast as the fastest digit-by-digit algorithms known; and they can achieve accuracy to within a unit or two in the last sig. bit carried. Algorithms like these are used by the Intel 8087 family of numeric coprocessors. This document is for people who wish to imitate or surpass them.

rawabstract:
Among the CORDIC-like algorithms for computing elementary transcendental functions like log and exp, certain pseudo-division algorithms are peculiarly well suited to implementation in microcode or in conjunction with software-implemented floating-point arithmetic. These algorithms need tables of comparatively modest size; they are almost as fast as the fastest digit-by-digit algorithms known; and they can achieve accuracy to within a unit or two in the last sig. bit carried. Algorithms like these are used by the Intel 8087 family of numeric coprocessors. This document is for people who wish to imitate or surpass them.

entry:
@Unpublished{Kahan:2001:PDA,
  author =       "William Kahan",
  title =        "Pseudo-Division Algorithms for Floating-Point
                 Logarithms and Exponentials",
  pages =        "8",
  day =          "20",
  month =        may,
  year =         "2001",
  bibdate =      "Sat Aug 23 06:17:04 2025",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/k/kahan-william-m.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "https://ieeemilestones.ethw.org/w/images/3/30/Wk_pseudo_division_log_exp_may01.pdf",
  abstract =     "Among the CORDIC-like algorithms for computing
                 elementary transcendental functions like log and exp,
                 certain pseudo-division algorithms are peculiarly well
                 suited to implementation in microcode or in conjunction
                 with software-implemented floating-point arithmetic.
                 These algorithms need tables of comparatively modest
                 size; they are almost as fast as the fastest
                 digit-by-digit algorithms known; and they can achieve
                 accuracy to within a unit or two in the last sig. bit
                 carried. Algorithms like these are used by the Intel
                 8087 family of numeric coprocessors. This document is
                 for people who wish to imitate or surpass them.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Karatsuba:2001:ARE
author: Ekatherina A. Karatsuba
title: On the asymptotic representation of the Euler gamma function by Ramanujan
journal: j-J-COMPUT-APPL-MATH
volume: 135
number: 2
pages: 225--240
day: 15
month: oct
monthnumber: 10
year: 2001
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:20 MST 2017
bibtimestamp: 2017.02.25 12:45:20 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700005860
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Ekatherina A. Karatsuba
rawtitle: On the asymptotic representation of the {Euler} gamma function by {Ramanujan}
entry:
@Article{Karatsuba:2001:ARE,
  author =       "Ekatherina A. Karatsuba",
  title =        "On the asymptotic representation of the {Euler} gamma
                 function by {Ramanujan}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "135",
  number =       "2",
  pages =        "225--240",
  day =          "15",
  month =        oct,
  year =         "2001",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:20 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700005860",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Lang:2001:CRR
author: Tomas Lang and Elisardo Antelo
booktitle: Proceedings of the 15th IEEE Symposium on Computer Arithmetic, 11--13 June 2001
title: Correctly Rounded Reciprocal Square-Root by Digit Recurrence and Radix-$4$ Implementation
crossref: Burgess:2001:ISC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 83--93
year: 2001
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Tom{\'a}s Lang and Elisardo Antelo
rawbooktitle: Proceedings of the 15th {IEEE} Symposium on Computer Arithmetic, 11--13 June 2001
rawtitle: Correctly Rounded Reciprocal Square-Root by Digit Recurrence and Radix-$4$ Implementation
entry:
@InProceedings{Lang:2001:CRR,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  booktitle =    "Proceedings of the 15th {IEEE} Symposium on Computer
                 Arithmetic, 11--13 June 2001",
  title =        "Correctly Rounded Reciprocal Square-Root by Digit
                 Recurrence and Radix-$4$ Implementation",
  crossref =     "Burgess:2001:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "83--93",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "We present a reciprocal square-root algorithm by digit
                 recurrence and selection by a staircase function, and
                 the radix-$4$ implementation. As similar algorithms for
                 division and square-root, the results are obtained
                 correctly rounded in a \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Lether:2001:VPA
author: F. G. Lether
journal: j-J-SCI-COMPUT
volume: 16
number: 1
pages: 69--79
month: mar
monthnumber: 3
year: 2001
CODEN: JSCOEB
DOI: https://doi.org/10.1023/A:1011150530703
ISSN: 0885-7474 (print), 1573-7691 (electronic) OR 08857474 (print), 15737691 (electronic)
ISSNL: 0885-7474 OR 08857474
bibdate: Sat Dec 22 13:05:47 MST 2012
bibtimestamp: 2012.12.22 13:05:47 MST
fjournal: Journal of Scientific Computing
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10915
rawauthor: F. G. Lether
title:
Variable Precision Algorithm for the Numerical Computation of the Fermi--Dirac Function $ F_j(x) $ of Order $ j = - 3 / 2 $

bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0885-7474&volume=16&issue=1; https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib; https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jscicomput.bib

URL:
http://link.springer.com/content/pdf/10.1023/A%3A1011150530703; http://www.springerlink.com/openurl.asp?genre=article&issn=0885-7474&volume=16&issue=1&spage=69-79

rawtitle:
Variable Precision Algorithm for the Numerical Computation of the {Fermi--Dirac} Function {$ F_j(x) $} of Order $ j = - 3 / 2 $

entry:
@Article{Lether:2001:VPA,
  author =       "F. G. Lether",
  title =        "Variable Precision Algorithm for the Numerical
                 Computation of the {Fermi--Dirac} Function {$ F_j(x) $}
                 of Order $ j = - 3 / 2 $",
  journal =      j-J-SCI-COMPUT,
  volume =       "16",
  number =       "1",
  pages =        "69--79",
  month =        mar,
  year =         "2001",
  CODEN =        "JSCOEB",
  DOI =          "https://doi.org/10.1023/A:1011150530703",
  ISSN =         "0885-7474 (print), 1573-7691 (electronic)",
  ISSN-L =       "0885-7474",
  bibdate =      "Sat Dec 22 13:05:47 MST 2012",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0885-7474&volume=16&issue=1;
                 https://www.math.utah.edu/pub/bibnet/authors/d/dirac-p-a-m.bib;
                 https://www.math.utah.edu/pub/bibnet/authors/f/fermi-enrico.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jscicomput.bib",
  URL =          "http://link.springer.com/content/pdf/10.1023/A%3A1011150530703;
                 http://www.springerlink.com/openurl.asp?genre=article&issn=0885-7474&volume=16&issue=1&spage=69-79",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Scientific Computing",
  journal-URL =  "http://link.springer.com/journal/10915",
}


bibtype: techreport
filename: elefunt.bib
label: Li:2001:LLF
author: Ren-Cang Li and Peter Markstein and Jon P. Okada and James W. Thomas
title: The tt libm library and floating-point arithmetic for HP-UX on Itanium
type: Technical report
institution: pub-HP
address: pub-HP:adr
month: apr
monthnumber: 4
year: 2001
bibdate: Fri Jun 24 20:12:09 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.06.24 20:12:09 ???
acknowledgement: ack-nhfb
rawauthor: Ren-Cang Li and Peter Markstein and Jon P. Okada and James W. Thomas
rawtitle: The {\tt libm} library and floating-point arithmetic for {HP-UX} on {Itanium}
URL:
http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf; http://h21007.www2.hp.com/dspp/tech/tech_TechDocumentDetailPage_IDX/1,1701,981,00.html

entry:
@TechReport{Li:2001:LLF,
  author =       "Ren-Cang Li and Peter Markstein and Jon P. Okada and
                 James W. Thomas",
  title =        "The {\tt libm} library and floating-point arithmetic
                 for {HP-UX} on {Itanium}",
  type =         "Technical report",
  institution =  pub-HP,
  address =      pub-HP:adr,
  pages =        "??",
  month =        apr,
  year =         "2001",
  bibdate =      "Fri Jun 24 20:12:09 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://h21007.www2.hp.com/dspp/ddl/ddl_Download_File_TRX/1,1249,942,00.pdf;
                 http://h21007.www2.hp.com/dspp/tech/tech_TechDocumentDetailPage_IDX/1,1701,981,00.html",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Loenko:2001:CEF
author: M. Yu. Loenko
title: Computation of elementary functions with guaranteed accuracy
journal: j-PROGRAMMIROVANIE
volume: 2
pages: 68--80
year: 2001
CODEN: PROGD3
ISSN: 0132-3474, 0361-7688 OR 01323474, 03617688
MRclass: 65D15 (65G20)
MRnumber: MR1867584
bibdate: Wed Apr 13 06:46:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.13 06:46:35 ???
fjournal: Rossiui skaya Akademiya Nauk. Programmirovanie
acknowledgement: ack-nhfb
rawauthor: M. Yu. Loenko
rawtitle: Computation of elementary functions with guaranteed accuracy
entry:
@Article{Loenko:2001:CEF,
  author =       "M. Yu. Loenko",
  title =        "Computation of elementary functions with guaranteed
                 accuracy",
  journal =      j-PROGRAMMIROVANIE,
  volume =       "2",
  pages =        "68--80",
  year =         "2001",
  CODEN =        "PROGD3",
  ISSN =         "0132-3474, 0361-7688",
  MRclass =      "65D15 (65G20)",
  MRnumber =     "MR1867584",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Rossi\u\i skaya Akademiya Nauk. Programmirovanie",
}


bibtype: article
filename: elefunt.bib
label: Meyer:2001:JEF
author: Kenneth R. Meyer
title: Jacobi Elliptic Functions from a Dynamical Systems Point of View
journal: j-AMER-MATH-MONTHLY
volume: 108
number: 8
pages: 729--737
month: oct
monthnumber: 10
year: 2001
CODEN: AMMYAE
ISSN: 0002-9890 (print), 1930-0972 (electronic) OR 00029890 (print), 19300972 (electronic)
ISSNL: 0002-9890 OR 00029890
bibdate: Mon Jan 30 12:00:14 MST 2012
bibtimestamp: 2012.01.30 12:00:14 MST
URL: http://www.jstor.org/stable/2695616
fjournal: American Mathematical Monthly
acknowledgement: ack-nhfb
journalURL: https://www.jstor.org/journals/00029890.htm
rawauthor: Kenneth R. Meyer
rawtitle: {Jacobi} Elliptic Functions from a Dynamical Systems Point of View
bibsource:
http://www.jstor.org/journals/00029890.html; http://www.jstor.org/stable/i346008; https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Meyer:2001:JEF,
  author =       "Kenneth R. Meyer",
  title =        "{Jacobi} Elliptic Functions from a Dynamical Systems
                 Point of View",
  journal =      j-AMER-MATH-MONTHLY,
  volume =       "108",
  number =       "8",
  pages =        "729--737",
  month =        oct,
  year =         "2001",
  CODEN =        "AMMYAE",
  ISSN =         "0002-9890 (print), 1930-0972 (electronic)",
  ISSN-L =       "0002-9890",
  bibdate =      "Mon Jan 30 12:00:14 MST 2012",
  bibsource =    "http://www.jstor.org/journals/00029890.html;
                 http://www.jstor.org/stable/i346008;
                 https://www.math.utah.edu/pub/tex/bib/amermathmonthly2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.jstor.org/stable/2695616",
  acknowledgement = ack-nhfb,
  fjournal =     "American Mathematical Monthly",
  journal-URL =  "https://www.jstor.org/journals/00029890.htm",
}


bibtype: article
filename: elefunt.bib
label: Muller:2001:CCH
author: Keith E. Muller
title: Computing the confluent hypergeometric function, $ M(a, b, x) $
journal: j-NUM-MATH
volume: 90
number: 1
pages: 179--196
month: nov
monthnumber: 11
year: 2001
CODEN: NUMMA7
DOI: https://doi.org/10.1007/s002110100285
ISSN: 0029-599X (print), 0945-3245 (electronic) OR 0029599X (print), 09453245 (electronic)
ISSNL: 0029-599X OR 0029599X
bibdate: Sun Feb 3 10:07:57 MST 2002
bibtimestamp: 2002.02.03 10:07:57 MST
fjournal: Numerische Mathematik
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/211
rawauthor: Keith E. Muller
rawtitle: Computing the confluent hypergeometric function, {$ M(a, b, x) $}
bibsource:
http://link.springer-ny.com/link/service/journals/00211/tocs/t1090001.htm; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0029-599X; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/nummath2000.bib

URL:
http://link.springer-ny.com/link/service/journals/00211/bibs/1090001/10900179.htm; http://link.springer-ny.com/link/service/journals/00211/papers/1090001/10900179.pdf

entry:
@Article{Muller:2001:CCH,
  author =       "Keith E. Muller",
  title =        "Computing the confluent hypergeometric function, {$
                 M(a, b, x) $}",
  journal =      j-NUM-MATH,
  volume =       "90",
  number =       "1",
  pages =        "179--196",
  month =        nov,
  year =         "2001",
  CODEN =        "NUMMA7",
  DOI =          "https://doi.org/10.1007/s002110100285",
  ISSN =         "0029-599X (print), 0945-3245 (electronic)",
  ISSN-L =       "0029-599X",
  bibdate =      "Sun Feb 3 10:07:57 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/journals/00211/tocs/t1090001.htm;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0029-599X;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/nummath2000.bib",
  URL =          "http://link.springer-ny.com/link/service/journals/00211/bibs/1090001/10900179.htm;
                 http://link.springer-ny.com/link/service/journals/00211/papers/1090001/10900179.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerische Mathematik",
  journal-URL =  "http://link.springer.com/journal/211",
}


bibtype: article
filename: elefunt.bib
label: Nagel:2001:EHF
author: Bengt Nagel
title: An expansion of the hypergeometric function in Bessel functions
journal: j-J-MATH-PHYS
volume: 42
number: 12
pages: 5910--5914
month: dec
monthnumber: 12
year: 2001
CODEN: JMAPAQ
ISSNL: 0022-2488 OR 00222488
bibdate: Thu Mar 28 19:47:21 MST 2002
bibtimestamp: 2002.03.28 19:47:21 MST
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: Bengt Nagel
rawtitle: An expansion of the hypergeometric function in {Bessel} functions
bibsource:
http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib

entry:
@Article{Nagel:2001:EHF,
  author =       "Bengt Nagel",
  title =        "An expansion of the hypergeometric function in
                 {Bessel} functions",
  journal =      j-J-MATH-PHYS,
  volume =       "42",
  number =       "12",
  pages =        "5910--5914",
  month =        dec,
  year =         "2001",
  CODEN =        "JMAPAQ",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Thu Mar 28 19:47:21 MST 2002",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
}


bibtype: article
filename: elefunt.bib
label: Plagianakos:2001:LCP
author: V. P. Plagianakos and N. K. Nousis and M. N. Vrahatis
title: Locating and computing in parallel all the simple roots of special functions using PVM
journal: j-J-COMPUT-APPL-MATH
volume: 133
number: 1--2
pages: 545--554
day: 1
month: aug
monthnumber: 8
year: 2001
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(00)00675-0
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:45:19 MST 2017
bibtimestamp: 2017.02.25 12:45:19 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042700006750
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: V. P. Plagianakos and N. K. Nousis and M. N. Vrahatis
rawtitle: Locating and computing in parallel all the simple roots of special functions using {PVM}
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib; https://www.math.utah.edu/pub/tex/bib/pvm.bib

entry:
@Article{Plagianakos:2001:LCP,
  author =       "V. P. Plagianakos and N. K. Nousis and M. N.
                 Vrahatis",
  title =        "Locating and computing in parallel all the simple
                 roots of special functions using {PVM}",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "133",
  number =       "1--2",
  pages =        "545--554",
  day =          "1",
  month =        aug,
  year =         "2001",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(00)00675-0",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:45:19 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/pvm.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700006750",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Plofker:2001:EIT
author: Kim Plofker
title: The ``Error'' in the Indian ``Taylor Series Approximation'' to the Sine
journal: j-HIST-MATH
volume: 28
number: 4
pages: 283--295
month: nov
monthnumber: 11
year: 2001
CODEN: HIMADS
DOI: https://doi.org/10.1006/hmat.2001.2331
ISSN: 0315-0860 (print), 1090-249X (electronic) OR 03150860 (print), 1090249X (electronic)
ISSNL: 0315-0860 OR 03150860
bibdate: Wed Jun 26 06:20:02 MDT 2013
bibtimestamp: 2013.06.26 06:20:02 MDT
URL: http://www.sciencedirect.com/science/article/pii/S0315086001923316
fjournal: Historia Mathematica
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03150860
rawauthor: Kim Plofker
rawtitle: The {``Error''} in the {Indian} ``{Taylor} Series Approximation'' to the Sine
entry:
@Article{Plofker:2001:EIT,
  author =       "Kim Plofker",
  title =        "The {``Error''} in the {Indian} ``{Taylor} Series
                 Approximation'' to the Sine",
  journal =      j-HIST-MATH,
  volume =       "28",
  number =       "4",
  pages =        "283--295",
  month =        nov,
  year =         "2001",
  CODEN =        "HIMADS",
  DOI =          "https://doi.org/10.1006/hmat.2001.2331",
  ISSN =         "0315-0860 (print), 1090-249X (electronic)",
  ISSN-L =       "0315-0860",
  bibdate =      "Wed Jun 26 06:20:02 MDT 2013",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/histmath.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0315086001923316",
  acknowledgement = ack-nhfb,
  fjournal =     "Historia Mathematica",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03150860",
}


bibtype: article
filename: elefunt.bib
label: Rabi:2001:OCA
author: J. A. Rabi and M. J. S. de Lemos
journal: j-APPL-MATH-COMP
volume: 124
number: 2
pages: 215--226
day: 25
month: oct
monthnumber: 10
year: 2001
CODEN: AMHCBQ
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Sun Nov 18 09:58:00 MST 2001
bibsource: http://www.elsevier.com/locate/issn/00963003; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2001.11.18 09:58:00 MST
URL: http://www.elsevier.com/gej-ng/10/9/12/113/31/31/abstract.html
fjournal: Applied Mathematics and Computation
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: J. A. Rabi and M. J. S. de Lemos
title:
Optimization of convergence acceleration in multigrid numerical solutions of conductive-convective problems

rawtitle:
Optimization of convergence acceleration in multigrid numerical solutions of conductive-convective problems

entry:
@Article{Rabi:2001:OCA,
  author =       "J. A. Rabi and M. J. S. de Lemos",
  title =        "Optimization of convergence acceleration in multigrid
                 numerical solutions of conductive-convective problems",
  journal =      j-APPL-MATH-COMP,
  volume =       "124",
  number =       "2",
  pages =        "215--226",
  day =          "25",
  month =        oct,
  year =         "2001",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Sun Nov 18 09:58:00 MST 2001",
  bibsource =    "http://www.elsevier.com/locate/issn/00963003;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/gej-ng/10/9/12/113/31/31/abstract.html",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Rahavachary:2001:LSS
author: Saty Rahavachary
title: Letters: Setting the tt sqrt() record straight
journal: j-DDJ
volume: 26
number: 4
pages: 12--12
month: apr
monthnumber: 4
year: 2001
CODEN: DDJOEB
ISSN: 1044-789X OR 1044789X
bibdate: Tue Mar 13 15:22:36 MST 2001
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2001.03.13 15:22:36 MST
URL: http://www.ddj.com/
fjournal: Dr. Dobb's Journal of Software Tools
acknowledgement: ack-nhfb
rawauthor: Saty Rahavachary
rawtitle: Letters: Setting the {\tt sqrt()} record straight
entry:
@Article{Rahavachary:2001:LSS,
  author =       "Saty Rahavachary",
  title =        "Letters: Setting the {\tt sqrt()} record straight",
  journal =      j-DDJ,
  volume =       "26",
  number =       "4",
  pages =        "12--12",
  month =        apr,
  year =         "2001",
  CODEN =        "DDJOEB",
  ISSN =         "1044-789X",
  bibdate =      "Tue Mar 13 15:22:36 MST 2001",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ddj.com/",
  acknowledgement = ack-nhfb,
  fjournal =     "Dr. Dobb's Journal of Software Tools",
}


bibtype: article
filename: elefunt.bib
label: Rappoport:2001:CVP
author: J. M. Rappoport
journal: j-COMPUT-MATH-APPL
volume: 41
number: 3--4
pages: 399--406
month: feb
monthnumber: 2
year: 2001
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:49:14 MST 2017
bibtimestamp: 2017.03.01 21:49:14 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122100002820
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: J. M. Rappoport
title:
Canonical vector polynomials for the computation of complex order Bessel functions with the tau method

bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Canonical vector polynomials for the computation of complex order {Bessel} functions with the tau method

entry:
@Article{Rappoport:2001:CVP,
  author =       "J. M. Rappoport",
  title =        "Canonical vector polynomials for the computation of
                 complex order {Bessel} functions with the tau method",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "41",
  number =       "3--4",
  pages =        "399--406",
  month =        feb,
  year =         "2001",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:14 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122100002820",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Rump:2001:RPS
author: Siegfried M. Rump
title: Rigorous and Portable Standard Functions
journal: j-BIT-NUM-MATH
volume: 41
number: 3
pages: 540--562
month: jun
monthnumber: 6
year: 2001
CODEN: BITTEL, NBITAB
DOI: https://doi.org/10.1023/A:1021971313412
ISSN: 0006-3835 (print), 1572-9125 (electronic) OR 00063835 (print), 15729125 (electronic)
ISSNL: 0006-3835 OR 00063835
bibdate: Wed Jan 4 15:06:04 MST 2006
bibtimestamp: 2006.01.04 15:06:04 MST
URL: http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=540
keywords: elementary functions; floating-point arithmetic
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10543
rawauthor: Siegfried M. Rump
rawtitle: Rigorous and Portable Standard Functions
bibsource:
http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3; http://www.mai.liu.se/BIT/contents/bit41.html; https://www.math.utah.edu/pub/tex/bib/bit.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

abstract:
Today's floating point implementations of elementary transcendental functions are usually very accurate. However, with few exceptions, the actual accuracy is not known. In the present paper we describe a rigorous, accurate, fast and portable implementation of the elementary standard functions based on some existing approximate standard functions. The scheme is outlined for IEEE 754, but not difficult to adapt to other floating point formats. A Matlab implementation is available on the net. Accuracy of the proposed algorithms can be rigorously estimated. As an example we prove that the relative accuracy of the exponential function is better than 2.07 eps in a slightly reduced argument range (eps denoting the relative rounding error unit). Otherwise, extensive computational tests suggest for all elementary functions and all suitable arguments an accuracy better than about 3 eps.

rawabstract:
Today's floating point implementations of elementary transcendental functions are usually very accurate. However, with few exceptions, the actual accuracy is not known. In the present paper we describe a rigorous, accurate, fast and portable implementation of the elementary standard functions based on some existing approximate standard functions. The scheme is outlined for IEEE 754, but not difficult to adapt to other floating point formats. A Matlab implementation is available on the net. Accuracy of the proposed algorithms can be rigorously estimated. As an example we prove that the relative accuracy of the exponential function is better than 2.07 eps in a slightly reduced argument range (eps denoting the relative rounding error unit). Otherwise, extensive computational tests suggest for all elementary functions and all suitable arguments an accuracy better than about 3 eps.

entry:
@Article{Rump:2001:RPS,
  author =       "Siegfried M. Rump",
  title =        "Rigorous and Portable Standard Functions",
  journal =      j-BIT-NUM-MATH,
  volume =       "41",
  number =       "3",
  pages =        "540--562",
  month =        jun,
  year =         "2001",
  CODEN =        "BITTEL, NBITAB",
  DOI =          "https://doi.org/10.1023/A:1021971313412",
  ISSN =         "0006-3835 (print), 1572-9125 (electronic)",
  ISSN-L =       "0006-3835",
  bibdate =      "Wed Jan 4 15:06:04 MST 2006",
  bibsource =    "http://springerlink.metapress.com/openurl.asp?genre=issue&issn=0006-3835&volume=41&issue=3;
                 http://www.mai.liu.se/BIT/contents/bit41.html;
                 https://www.math.utah.edu/pub/tex/bib/bit.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.springerlink.com/openurl.asp?genre=article&issn=0006-3835&volume=41&issue=3&spage=540",
  abstract =     "Today's floating point implementations of elementary
                 transcendental functions are usually very accurate.
                 However, with few exceptions, the actual accuracy is
                 not known. In the present paper we describe a rigorous,
                 accurate, fast and portable implementation of the
                 elementary standard functions based on some existing
                 approximate standard functions. The scheme is outlined
                 for IEEE 754, but not difficult to adapt to other
                 floating point formats. A Matlab implementation is
                 available on the net. Accuracy of the proposed
                 algorithms can be rigorously estimated. As an example
                 we prove that the relative accuracy of the exponential
                 function is better than 2.07 eps in a slightly reduced
                 argument range (eps denoting the relative rounding
                 error unit). Otherwise, extensive computational tests
                 suggest for all elementary functions and all suitable
                 arguments an accuracy better than about 3 eps.",
  acknowledgement = ack-nhfb,
  journal-URL =  "http://link.springer.com/journal/10543",
  keywords =     "elementary functions; floating-point arithmetic",
}


bibtype: article
filename: elefunt.bib
label: Smith:2001:AFS
author: David M. Smith
journal: j-TOMS
volume: 27
number: 4
pages: 377--387
month: dec
monthnumber: 12
year: 2001
CODEN: ACMSCU
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Mar 13 08:49:29 MST 2002
bibtimestamp: 2002.03.13 08:49:29 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: David M. Smith
title:
Algorithm 814: Fortran 90 software for floating-point multiple precision arithmetic, gamma and related functions

rawtitle:
{Algorithm 814}: {Fortran 90} software for floating-point multiple precision arithmetic, gamma and related functions

entry:
@Article{Smith:2001:AFS,
  author =       "David M. Smith",
  title =        "{Algorithm 814}: {Fortran 90} software for
                 floating-point multiple precision arithmetic, gamma and
                 related functions",
  journal =      j-TOMS,
  volume =       "27",
  number =       "4",
  pages =        "377--387",
  month =        dec,
  year =         "2001",
  CODEN =        "ACMSCU",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Mar 13 08:49:29 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: book
filename: elefunt.bib
label: Srivastava:2001:SAZ
author: H. M. Srivastava and Choi Junesang
title: Series Associated with the Zeta and Related Functions
publisher: pub-KLUWER
address: pub-KLUWER:adr
pages: ix + 388
year: 2001
DOI: https://doi.org/10.1007/978-94-015-9672-5
ISBN: 0-7923-7054-6 OR 0792370546
ISBN13: 978-0-7923-7054-3 OR 9780792370543
LCCN: QA351 .S74 2001
bibdate: Wed Jun 10 16:22:26 MDT 2015
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2015.06.10 16:22:26 MDT
subject: Functions, Zeta; Series
acknowledgement: ack-nhfb
rawauthor: H. M. Srivastava and Choi Junesang
rawtitle: Series Associated with the Zeta and Related Functions
URL:
http://www.loc.gov/catdir/enhancements/fy0822/2001035764-d.html; http://www.loc.gov/catdir/enhancements/fy0822/2001035764-t.html

TOC:
Acknowledgements / ix 1. Introduction and Preliminaries 1.1. Gamma and Beta functions / 1 1.2. Polygamma functions / 13 1.3. The multiple Gamma functions / 24 1.4. The Gaussian hypergeometric function and its generalization / 44 1.5. Stirling numbers of the first and second kind / 56 1.6. Bernoulli and Euler polynomials and numbers / 59 Problems / 67 2. The Zeta and Related Functions 2.1. Multiple Hurwitz Zeta functions / 77 2.2. The Hurwitz (or generalized) Zeta function / 88 2.3. The Riemann Zeta function / 96 2.4. Polylogarithm functions / 106 2.5. Hurwitz--Lerch Zeta functions / 121 Problems / 128 3. Series Involving Zeta Functions 3.1. Historical introduction / 142 3.2. Use of the Binomial theorem / 143 3.3. Use of generating functions / 152 3.4. Use of multiple Gamma functions / 159 3.5. Use of hypergeometric identities / 250 3.6. Other methods and their applications / 260 Problems / 269 4. Evaluations and Series Representations 4.1. Evaluation of $zeta (2n)$ / 275 4.2. Rapidly convergent series for $zeta (2n + 1)$ / 280 4.3. Further series representations / 289 4.4. Computational results / 295 Problems / 304 5. Determinants of the Laplacians 5.1. The $n$-dimensional problem / 315 5.2. Computations using the simple and multiple Gamma functions / 318 5.3. Computations using series of Zeta functions / 325 5.4. Remarks and observations / 328 Problems / 329 6. Miscellaneous Results 6.1. Bernoulli and Euler polynomials at rational arguments / 335 6.2. Closed-form summation of trigonometric series / 341 6.3. Integrals associated with the use of the Euler--Maclaurin summation formula / 344 Problems / 350 Bibliography / 353 Author Index / 379 Subject Index / 383

rawTOC:
Acknowledgements / ix \\ 1. Introduction and Preliminaries \\ 1.1. Gamma and Beta functions / 1 \\ 1.2. Polygamma functions / 13 \\ 1.3. The multiple Gamma functions / 24 \\ 1.4. The Gaussian hypergeometric function and its generalization / 44 \\ 1.5. Stirling numbers of the first and second kind / 56 \\ 1.6. Bernoulli and Euler polynomials and numbers / 59 \\ Problems / 67 \\ 2. The Zeta and Related Functions \\ 2.1. Multiple Hurwitz Zeta functions / 77 \\ 2.2. The Hurwitz (or generalized) Zeta function / 88 \\ 2.3. The Riemann Zeta function / 96 \\ 2.4. Polylogarithm functions / 106 \\ 2.5. Hurwitz--Lerch Zeta functions / 121 \\ Problems / 128 \\ 3. Series Involving Zeta Functions \\ 3.1. Historical introduction / 142 \\ 3.2. Use of the Binomial theorem / 143 \\ 3.3. Use of generating functions / 152 \\ 3.4. Use of multiple Gamma functions / 159 \\ 3.5. Use of hypergeometric identities / 250 \\ 3.6. Other methods and their applications / 260 \\ Problems / 269 \\ 4. Evaluations and Series Representations \\ 4.1. Evaluation of $\zeta(2n)$ / 275 \\ 4.2. Rapidly convergent series for $\zeta(2n + 1)$ / 280 \\ 4.3. Further series representations / 289 \\ 4.4. Computational results / 295 \\ Problems / 304 \\ 5. Determinants of the Laplacians \\ 5.1. The $n$-dimensional problem / 315 \\ 5.2. Computations using the simple and multiple Gamma functions / 318 \\ 5.3. Computations using series of Zeta functions / 325 \\ 5.4. Remarks and observations / 328 \\ Problems / 329 \\ 6. Miscellaneous Results \\ 6.1. Bernoulli and Euler polynomials at rational arguments / 335 \\ 6.2. Closed-form summation of trigonometric series / 341 \\ 6.3. Integrals associated with the use of the Euler--Maclaurin summation formula / 344 \\ Problems / 350 \\ Bibliography / 353 \\ Author Index / 379 \\ Subject Index / 383

entry:
@Book{Srivastava:2001:SAZ,
  author =       "H. M. Srivastava and Choi Junesang",
  title =        "Series Associated with the Zeta and Related
                 Functions",
  publisher =    pub-KLUWER,
  address =      pub-KLUWER:adr,
  pages =        "ix + 388",
  year =         "2001",
  DOI =          "https://doi.org/10.1007/978-94-015-9672-5",
  ISBN =         "0-7923-7054-6",
  ISBN-13 =      "978-0-7923-7054-3",
  LCCN =         "QA351 .S74 2001",
  bibdate =      "Wed Jun 10 16:22:26 MDT 2015",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  URL =          "http://www.loc.gov/catdir/enhancements/fy0822/2001035764-d.html;
                 http://www.loc.gov/catdir/enhancements/fy0822/2001035764-t.html",
  acknowledgement = ack-nhfb,
  subject =      "Functions, Zeta; Series",
  tableofcontents = "Acknowledgements / ix \\
                 1. Introduction and Preliminaries \\
                 1.1. Gamma and Beta functions / 1 \\
                 1.2. Polygamma functions / 13 \\
                 1.3. The multiple Gamma functions / 24 \\
                 1.4. The Gaussian hypergeometric function and its
                 generalization / 44 \\
                 1.5. Stirling numbers of the first and second kind / 56
                 \\
                 1.6. Bernoulli and Euler polynomials and numbers / 59
                 \\
                 Problems / 67 \\
                 2. The Zeta and Related Functions \\
                 2.1. Multiple Hurwitz Zeta functions / 77 \\
                 2.2. The Hurwitz (or generalized) Zeta function / 88
                 \\
                 2.3. The Riemann Zeta function / 96 \\
                 2.4. Polylogarithm functions / 106 \\
                 2.5. Hurwitz--Lerch Zeta functions / 121 \\
                 Problems / 128 \\
                 3. Series Involving Zeta Functions \\
                 3.1. Historical introduction / 142 \\
                 3.2. Use of the Binomial theorem / 143 \\
                 3.3. Use of generating functions / 152 \\
                 3.4. Use of multiple Gamma functions / 159 \\
                 3.5. Use of hypergeometric identities / 250 \\
                 3.6. Other methods and their applications / 260 \\
                 Problems / 269 \\
                 4. Evaluations and Series Representations \\
                 4.1. Evaluation of $\zeta(2n)$ / 275 \\
                 4.2. Rapidly convergent series for $\zeta(2n + 1)$ /
                 280 \\
                 4.3. Further series representations / 289 \\
                 4.4. Computational results / 295 \\
                 Problems / 304 \\
                 5. Determinants of the Laplacians \\
                 5.1. The $n$-dimensional problem / 315 \\
                 5.2. Computations using the simple and multiple Gamma
                 functions / 318 \\
                 5.3. Computations using series of Zeta functions / 325
                 \\
                 5.4. Remarks and observations / 328 \\
                 Problems / 329 \\
                 6. Miscellaneous Results \\
                 6.1. Bernoulli and Euler polynomials at rational
                 arguments / 335 \\
                 6.2. Closed-form summation of trigonometric series /
                 341 \\
                 6.3. Integrals associated with the use of the
                 Euler--Maclaurin summation formula / 344 \\
                 Problems / 350 \\
                 Bibliography / 353 \\
                 Author Index / 379 \\
                 Subject Index / 383",
}


bibtype: inproceedings
filename: elefunt.bib
label: Takagi:2001:HAC
author: N. Takagi
booktitle: Proceedings of the 15th IEEE Symposium on Computer Arithmetic, 11--13 June 2001
title: A Hardware Algorithm for Computing Reciprocal Square Root
crossref: Burgess:2001:ISC
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 94--100
year: 2001
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; OCLC Proceedings database
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: N. Takagi
rawbooktitle: Proceedings of the 15th {IEEE} Symposium on Computer Arithmetic, 11--13 June 2001
rawtitle: A Hardware Algorithm for Computing Reciprocal Square Root
entry:
@InProceedings{Takagi:2001:HAC,
  author =       "N. Takagi",
  booktitle =    "Proceedings of the 15th {IEEE} Symposium on Computer
                 Arithmetic, 11--13 June 2001",
  title =        "A Hardware Algorithm for Computing Reciprocal Square
                 Root",
  crossref =     "Burgess:2001:ISC",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "94--100",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 OCLC Proceedings database",
  acknowledgement = ack-nhfb,
  summary =      "A hardware algorithm for computing the reciprocal
                 square root which appears frequently in multimedia and
                 graphics applications is proposed. The reciprocal
                 square root is computed by iteration of
                 carry-propagation-free additions, shifts, and
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Thorsley:2001:AEH
author: Michael D. Thorsley and Marita C. Chidichimo
title: An asymptotic expansion for the hypergeometric function $_2 F_1 (a, b; c; x)$
journal: j-J-MATH-PHYS
volume: 42
number: 4
pages: 1921--1930
month: apr
monthnumber: 4
year: 2001
CODEN: JMAPAQ
ISSNL: 0022-2488 OR 00222488
bibdate: Wed Apr 18 05:33:53 MDT 2001
bibtimestamp: 2001.04.18 05:33:53 MDT
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: Michael D. Thorsley and Marita C. Chidichimo
rawtitle: An asymptotic expansion for the hypergeometric function {$_2 F_1 (a, b; c; x)$}
bibsource:
http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib

entry:
@Article{Thorsley:2001:AEH,
  author =       "Michael D. Thorsley and Marita C. Chidichimo",
  title =        "An asymptotic expansion for the hypergeometric
                 function {$_2 F_1 (a, b; c; x)$}",
  journal =      j-J-MATH-PHYS,
  volume =       "42",
  number =       "4",
  pages =        "1921--1930",
  month =        apr,
  year =         "2001",
  CODEN =        "JMAPAQ",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Wed Apr 18 05:33:53 MDT 2001",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
}


bibtype: article
filename: elefunt.bib
label: Verdonk:2001:PRIa
author: Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren
journal: j-TOMS
volume: 27
number: 1
pages: 92--118
month: mar
monthnumber: 3
year: 2001
CODEN: ACMSCU
DOI: https://doi.org/10.1145/382043.382404
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Wed Feb 6 16:43:42 MST 2002
bibtimestamp: 2002.02.06 16:43:42 MST
URL: http://doi.acm.org/10.1145/382043.382404; http://www.win.ua.ac.be/~cant/ieeecc754.html
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Brigitte Verdonk and Annie Cuyt and Dennis Verschaeren
title:
A precision- and range-independent tool for testing floating-point arithmetic I: Basic operations, square root, and remainder

bibsource:
http://www.acm.org/pubs/contents/journals/toms/; https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/toms.bib

abstract:
This paper introduces a precision- and range-independent tool for testing the compliance of hardware or software implementations of (multiprecision) floating-point arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a driver program, offering many options to test only specific aspects of the IEEE standards, and a large set of test vectors, encoded in a precision-independent syntax to allow the testing of basic and extended hardware formats as well as multiprecision floating-point implementations. The suite of test vectors stems on one hand from the integration and fully precision- and range-independent generalization of existing hardware test sets, and on the other hand from the systematic testing of exact rounding for all combinations of round and sticky bits that can occur. The former constitutes only 50% of the resulting test set. In the latter we especially focus on hard-to-round cases. In addition, the test suite implicitly tests properties of floating-point operations, following the idea of Paranoia, and it reports which of the three IEEE-compliant underflow mechanisms is used by the floating-point implementation under consideration. We also check whether that underflow mechanism is used consistently. The tool is backward compatible with the UCBTEST package and with Coonen's test syntax.

keywords:
arithmetic; floating-point; floating-point testing; IEEE floating-point standard; multiprecision; validation; Verification

subject:
Primary Classification: G. Mathematics of Computing G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer arithmetic Additional Classification: D. Software D.3 PROGRAMMING LANGUAGES D.3.0 General Subjects: Standards

rawabstract:
This paper introduces a precision- and range-independent tool for testing the compliance of hardware or software implementations of (multiprecision) floating-point arithmetic with the principles of the IEEE standards 754 and 854. The tool consists of a driver program, offering many options to test only specific aspects of the IEEE standards, and a large set of test vectors, encoded in a precision-independent syntax to allow the testing of basic and extended hardware formats as well as multiprecision floating-point implementations. The suite of test vectors stems on one hand from the integration and fully precision- and range-independent generalization of existing hardware test sets, and on the other hand from the systematic testing of exact rounding for all combinations of round and sticky bits that can occur. The former constitutes only 50\% of the resulting test set. In the latter we especially focus on hard-to-round cases. In addition, the test suite implicitly tests properties of floating-point operations, following the idea of Paranoia, and it reports which of the three IEEE-compliant underflow mechanisms is used by the floating-point implementation under consideration. We also check whether that underflow mechanism is used consistently. The tool is backward compatible with the UCBTEST package and with Coonen's test syntax.

rawtitle:
A precision- and range-independent tool for testing floating-point arithmetic {I}: {Basic} operations, square root, and remainder

entry:
@Article{Verdonk:2001:PRIa,
  author =       "Brigitte Verdonk and Annie Cuyt and Dennis
                 Verschaeren",
  title =        "A precision- and range-independent tool for testing
                 floating-point arithmetic {I}: {Basic} operations,
                 square root, and remainder",
  journal =      j-TOMS,
  volume =       "27",
  number =       "1",
  pages =        "92--118",
  month =        mar,
  year =         "2001",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/382043.382404",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Wed Feb 6 16:43:42 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/bibnet/subjects/acc-stab-num-alg-2ed.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  URL =          "http://doi.acm.org/10.1145/382043.382404;
                 http://www.win.ua.ac.be/~cant/ieeecc754.html",
  abstract =     "This paper introduces a precision- and
                 range-independent tool for testing the compliance of
                 hardware or software implementations of
                 (multiprecision) floating-point arithmetic with the
                 principles of the IEEE standards 754 and 854. The tool
                 consists of a driver program, offering many options to
                 test only specific aspects of the IEEE standards, and a
                 large set of test vectors, encoded in a
                 precision-independent syntax to allow the testing of
                 basic and extended hardware formats as well as
                 multiprecision floating-point implementations. The
                 suite of test vectors stems on one hand from the
                 integration and fully precision- and range-independent
                 generalization of existing hardware test sets, and on
                 the other hand from the systematic testing of exact
                 rounding for all combinations of round and sticky bits
                 that can occur. The former constitutes only 50\% of the
                 resulting test set. In the latter we especially focus
                 on hard-to-round cases. In addition, the test suite
                 implicitly tests properties of floating-point
                 operations, following the idea of Paranoia, and it
                 reports which of the three IEEE-compliant underflow
                 mechanisms is used by the floating-point implementation
                 under consideration. We also check whether that
                 underflow mechanism is used consistently. The tool is
                 backward compatible with the UCBTEST package and with
                 Coonen's test syntax.",
  accepted =     "23 February 2001",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
  keywords =     "arithmetic; floating-point; floating-point testing;
                 IEEE floating-point standard; multiprecision;
                 validation; Verification",
  subject =      "Primary Classification: G. Mathematics of Computing
                 G.1 NUMERICAL ANALYSIS G.1.0 General Subjects: Computer
                 arithmetic\\
                 Additional Classification: D. Software D.3 PROGRAMMING
                 LANGUAGES D.3.0 General Subjects: Standards",
}


bibtype: article
filename: elefunt.bib
label: Weniger:2001:IID
author: Ernst Joachim Weniger
journal: j-COMP-PHYS-COMM
volume: 133
number: 2--3
pages: 202--228
day: 15
month: jan
monthnumber: 1
year: 2001
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(00)00175-2
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Thu Dec 01 09:12:48 2011
bibtimestamp: 2011.12.01 09:12:48 ???
fjournal: Computer Physics Communications
keywords: convergence acceleration
remark: This paper concentrates on $_2 F_1 (a, b; c; z)$.
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Ernst Joachim Weniger
title:
Irregular input data in convergence acceleration and summation processes: General considerations and some special Gaussian hypergeometric series as model problems

bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

rawtitle:
Irregular input data in convergence acceleration and summation processes: {General} considerations and some special {Gaussian} hypergeometric series as model problems

entry:
@Article{Weniger:2001:IID,
  author =       "Ernst Joachim Weniger",
  title =        "Irregular input data in convergence acceleration and
                 summation processes: {General} considerations and some
                 special {Gaussian} hypergeometric series as model
                 problems",
  journal =      j-COMP-PHYS-COMM,
  volume =       "133",
  number =       "2--3",
  pages =        "202--228",
  day =          "15",
  month =        jan,
  year =         "2001",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(00)00175-2",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Thu Dec 01 09:12:48 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
  keywords =     "convergence acceleration",
  remark =       "This paper concentrates on $_2 F_1 (a, b; c; z)$.",
}


bibtype: inproceedings
filename: elefunt.bib
label: Zheng:2001:ARE
author: Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui
booktitle: Proceedings of the 4th International Conference on ASIC
title: The application of redundant encoding in iterative implementation of division and square root
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 603--606
year: 2001
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui
rawbooktitle: Proceedings of the 4th International Conference on {ASIC}
rawtitle: The application of redundant encoding in iterative implementation of division and square root
entry:
@InProceedings{Zheng:2001:ARE,
  author =       "Liang Zheng and Shen Xu-Bang and Peng Zuo-Hui",
  booktitle =    "Proceedings of the 4th International Conference on
                 {ASIC}",
  title =        "The application of redundant encoding in iterative
                 implementation of division and square root",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "603--606",
  year =         "2001",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "The purpose of this paper is to discuss the speed
                 improvement in division and square root computation
                 with small area penalty. The digit recurrence SRT
                 algorithm and functional iteration Newton--Raphson
                 algorithm are generally used in modern \ldots{}",
}


bibtype: misc
filename: elefunt.bib
label: Ziv:2001:APM
author: Abraham Ziv and Moshe Olshansky and Ealan Henis and Anna Reitman
title: Accurate Portable Mathematical Library (IBM APMathLib)
publisher: pub-IBM
address: pub-IBM:adr
pages: 603--606
day: 20
month: dec
monthnumber: 12
year: 2001
bibdate: Wed Nov 24 08:06:54 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.11.24 08:06:54 ???
URL: ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz; http://oss.software.ibm.com/mathlib/
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: Abraham Ziv and Moshe Olshansky and Ealan Henis and Anna Reitman
rawtitle: Accurate Portable Mathematical Library ({IBM APMathLib})
entry:
@Misc{Ziv:2001:APM,
  author =       "Abraham Ziv and Moshe Olshansky and Ealan Henis and
                 Anna Reitman",
  title =        "Accurate Portable Mathematical Library ({IBM
                 APMathLib})",
  howpublished = "World-Wide Web document",
  publisher =    pub-IBM,
  address =      pub-IBM:adr,
  day =          "20",
  month =        dec,
  year =         "2001",
  bibdate =      "Wed Nov 24 08:06:54 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "ftp://www-126.ibm.com/pub/mathlib/mathlib12.20.2001.tar.gz;
                 http://oss.software.ibm.com/mathlib/",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Al-Jarrah:2002:GSB
author: A. Al-Jarrah and K. M. Dempsey and M. L. Glasser
title: Generalized series of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 143
number: 1
pages: 1--8
day: 1
month: jun
monthnumber: 6
year: 2002
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:28 MST 2017
bibtimestamp: 2017.02.25 12:52:28 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042701005052
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: A. Al-Jarrah and K. M. Dempsey and M. L. Glasser
rawtitle: Generalized series of {Bessel} functions
entry:
@Article{Al-Jarrah:2002:GSB,
  author =       "A. Al-Jarrah and K. M. Dempsey and M. L. Glasser",
  title =        "Generalized series of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "143",
  number =       "1",
  pages =        "1--8",
  day =          "1",
  month =        jun,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:28 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042701005052",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Bertot:2002:PGS
author: Yves Bertot and Nicolas Magaud and Paul Zimmermann
title: A Proof of GMP Square Root
journal: j-J-AUTOM-REASON
volume: 29
number: 3--4
pages: 225--252
month: sep
monthnumber: 9
year: 2002
CODEN: JAREEW
DOI: https://doi.org/10.1023/A:1021987403425
ISSN: 0168-7433 (print), 1573-0670 (electronic) OR 01687433 (print), 15730670 (electronic)
ISSNL: 0168-7433 OR 01687433
bibdate: Sat Feb 08 08:59:09 2020
bibtimestamp: 2020.02.08 08:59:09 ???
URL: https://link.springer.com/article/10.1023/A:1021987403425
fjournal: Journal of Automated Reasoning
keywords: GNU Multiple Precision library
acknowledgement: ack-nhfb
ajournal: J. Autom. Reason.
journalURL: http://link.springer.com/journal/10817
rawauthor: Yves Bertot and Nicolas Magaud and Paul Zimmermann
rawtitle: A Proof of {GMP} Square Root
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/gnu.bib; https://www.math.utah.edu/pub/tex/bib/jautomreason.bib

entry:
@Article{Bertot:2002:PGS,
  author =       "Yves Bertot and Nicolas Magaud and Paul Zimmermann",
  title =        "A Proof of {GMP} Square Root",
  journal =      j-J-AUTOM-REASON,
  volume =       "29",
  number =       "3--4",
  pages =        "225--252",
  month =        sep,
  year =         "2002",
  CODEN =        "JAREEW",
  DOI =          "https://doi.org/10.1023/A:1021987403425",
  ISSN =         "0168-7433 (print), 1573-0670 (electronic)",
  ISSN-L =       "0168-7433",
  bibdate =      "Sat Feb 08 08:59:09 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/gnu.bib;
                 https://www.math.utah.edu/pub/tex/bib/jautomreason.bib",
  URL =          "https://link.springer.com/article/10.1023/A:1021987403425",
  acknowledgement = ack-nhfb,
  ajournal =     "J. Autom. Reason.",
  fjournal =     "Journal of Automated Reasoning",
  journal-URL =  "http://link.springer.com/journal/10817",
  keywords =     "GNU Multiple Precision library",
}


bibtype: incollection
filename: elefunt.bib
label: Boisvert:2002:HMF
author: Ronald F. Boisvert and Daniel W. Lozier
title: Handbook of Mathematical Functions
crossref: Lide:2002:CEM
pages: 135--139
year: 2002
bibdate: Fri Jul 09 06:28:13 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:28:13 ???
note: Also printed as NIST Special Publication 958, Jan. 2001.
acknowledgement: ack-nhfb
rawauthor: Ronald F. Boisvert and Daniel W. Lozier
rawnote: Also printed as NIST Special Publication 958, Jan. 2001.
rawtitle: Handbook of Mathematical Functions
URL:
https://nvlpubs.nist.gov/nistpubs/sp958-lide/135-139.pdf; https://nvlpubs.nist.gov/nistpubs/sp958-lide/html/135-139.html

remark:
This article describes the history of the creation of the famous 1964 book by Milton Abramowitz and Irene Stegun named in the title.

entry:
@InCollection{Boisvert:2002:HMF,
  author =       "Ronald F. Boisvert and Daniel W. Lozier",
  title =        "Handbook of Mathematical Functions",
  crossref =     "Lide:2002:CEM",
  pages =        "135--139",
  year =         "2002",
  bibdate =      "Fri Jul 09 06:28:13 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Also printed as NIST Special Publication 958, Jan.
                 2001.",
  URL =          "https://nvlpubs.nist.gov/nistpubs/sp958-lide/135-139.pdf;
                 https://nvlpubs.nist.gov/nistpubs/sp958-lide/html/135-139.html",
  acknowledgement = ack-nhfb,
  remark =       "This article describes the history of the creation of
                 the famous 1964 book by Milton Abramowitz and Irene
                 Stegun named in the title.",
}


bibtype: article
filename: elefunt.bib
label: Bradford:2002:RAE
title: Reasoning about the elementary functions of complex analysis
journal: j-ANN-MATH-ARTIF-INTELL
volume: 36
number: 3
pages: 303--318
year: 2002
CODEN: AMAIEC
ISSN: 1012-2443 (print), 1573-7470 (electronic) OR 10122443 (print), 15737470 (electronic)
ISSNL: 1012-2443 OR 10122443
MRclass: 30-01 (03B35 68W30)
MRnumber: MR1950025 (2003m:30001)
bibdate: Wed Apr 13 06:46:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.13 06:46:35 ???
note: Artificial intelligence and symbolic computation (Madrid, 2000)
fjournal: Annals of Mathematics and Artificial Intelligence
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10472
rawnote: Artificial intelligence and symbolic computation (Madrid, 2000)
rawtitle: Reasoning about the elementary functions of complex analysis
author:
Russell Bradford and Robert M. Corless and James H. Davenport and David J. Jeffrey and Stephen M. Watt

rawauthor:
Russell Bradford and Robert M. Corless and James H. Davenport and David J. Jeffrey and Stephen M. Watt

entry:
@Article{Bradford:2002:RAE,
  author =       "Russell Bradford and Robert M. Corless and James H.
                 Davenport and David J. Jeffrey and Stephen M. Watt",
  title =        "Reasoning about the elementary functions of complex
                 analysis",
  journal =      j-ANN-MATH-ARTIF-INTELL,
  volume =       "36",
  number =       "3",
  pages =        "303--318",
  year =         "2002",
  CODEN =        "AMAIEC",
  ISSN =         "1012-2443 (print), 1573-7470 (electronic)",
  ISSN-L =       "1012-2443",
  MRclass =      "30-01 (03B35 68W30)",
  MRnumber =     "MR1950025 (2003m:30001)",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Artificial intelligence and symbolic computation
                 (Madrid, 2000)",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematics and Artificial Intelligence",
  journal-URL =  "http://link.springer.com/journal/10472",
}


bibtype: inproceedings
filename: elefunt.bib
label: Bradford:2002:TBS
author: Russell Bradford and James H. Davenport
booktitle: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation
title: Towards better simplification of elementary functions
publisher: pub-ACM
address: pub-ACM:adr
pages: 16--22 (electronic)
year: 2002
MRclass: 68W30 (33B10)
MRnumber: MR2035228
bibdate: Wed Apr 13 06:46:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.13 06:46:35 ???
acknowledgement: ack-nhfb
rawauthor: Russell Bradford and James H. Davenport
rawbooktitle: Proceedings of the 2002 International Symposium on Symbolic and Algebraic Computation
rawtitle: Towards better simplification of elementary functions
entry:
@InProceedings{Bradford:2002:TBS,
  author =       "Russell Bradford and James H. Davenport",
  booktitle =    "Proceedings of the 2002 International Symposium on
                 Symbolic and Algebraic Computation",
  title =        "Towards better simplification of elementary
                 functions",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "16--22 (electronic)",
  year =         "2002",
  MRclass =      "68W30 (33B10)",
  MRnumber =     "MR2035228",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Bryc:2002:UAR
author: W. Bryc
title: A uniform approximation to the right normal tail integral
journal: j-APPL-MATH-COMP
volume: 127
number: 2--3
pages: 365--374
day: 15
month: apr
monthnumber: 4
year: 2002
CODEN: AMHCBQ
DOI: https://doi.org/10.1016/S0096-3003(01)00015-7
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Wed Feb 27 08:48:29 MST 2002
bibtimestamp: 2002.02.27 08:48:29 MST
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003/
rawauthor: W. Bryc
rawtitle: A uniform approximation to the right normal tail integral
bibsource:
http://www.elsevier.com/locate/issn/00963003; https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://www.elsevier.com/gej-ng/10/9/12/123/27/44/abstract.html; http://www.sciencedirect.com/science/article/pii/S0096300301000157

entry:
@Article{Bryc:2002:UAR,
  author =       "W. Bryc",
  title =        "A uniform approximation to the right normal tail
                 integral",
  journal =      j-APPL-MATH-COMP,
  volume =       "127",
  number =       "2--3",
  pages =        "365--374",
  day =          "15",
  month =        apr,
  year =         "2002",
  CODEN =        "AMHCBQ",
  DOI =          "https://doi.org/10.1016/S0096-3003(01)00015-7",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Wed Feb 27 08:48:29 MST 2002",
  bibsource =    "http://www.elsevier.com/locate/issn/00963003;
                 https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.elsevier.com/gej-ng/10/9/12/123/27/44/abstract.html;
                 http://www.sciencedirect.com/science/article/pii/S0096300301000157",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003/",
}


bibtype: article
filename: elefunt.bib
label: Ceberio:2002:HRI
author: M. Ceberio and L. Granvilliers
title: Horner's Rule for Interval Evaluation Revisited
journal: j-COMPUTING
volume: 69
number: 1
pages: 51--81
month: mar
monthnumber: 3
year: 2002
CODEN: CMPTA2
DOI: https://doi.org/10.1007/s00607-002-1448-y
ISSN: 0010-485X (print), 1436-5057 (electronic) OR 0010485X (print), 14365057 (electronic)
ISSNL: 0010-485X OR 0010485X
bibdate: Tue Nov 5 07:12:39 MST 2002
bibtimestamp: 2002.11.05 07:12:39 MST
fjournal: Computing
keywords: interval arithmetic; number of multiplications to evaluate a polynomial
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/607
rawauthor: M. Ceberio and L. Granvilliers
rawtitle: {Horner}'s Rule for Interval Evaluation Revisited
bibsource:
http://link.springer-ny.com/link/service/journals/00607/tocs/t2069001.htm; http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X; https://www.math.utah.edu/pub/tex/bib/computing.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://link.springer.de/link/service/journals/00607/bibs/2069001/20690051.htm; http://link.springer.de/link/service/journals/00607/papers/2069001/20690051.pdf

entry:
@Article{Ceberio:2002:HRI,
  author =       "M. Ceberio and L. Granvilliers",
  title =        "{Horner}'s Rule for Interval Evaluation Revisited",
  journal =      j-COMPUTING,
  volume =       "69",
  number =       "1",
  pages =        "51--81",
  month =        mar,
  year =         "2002",
  CODEN =        "CMPTA2",
  DOI =          "https://doi.org/10.1007/s00607-002-1448-y",
  ISSN =         "0010-485X (print), 1436-5057 (electronic)",
  ISSN-L =       "0010-485X",
  bibdate =      "Tue Nov 5 07:12:39 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/journals/00607/tocs/t2069001.htm;
                 http://springerlink.metapress.com/openurl.asp?genre=journal&issn=0010-485X;
                 https://www.math.utah.edu/pub/tex/bib/computing.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.de/link/service/journals/00607/bibs/2069001/20690051.htm;
                 http://link.springer.de/link/service/journals/00607/papers/2069001/20690051.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Computing",
  journal-URL =  "http://link.springer.com/journal/607",
  keywords =     "interval arithmetic; number of multiplications to
                 evaluate a polynomial",
}


bibtype: inproceedings
filename: elefunt.bib
label: Chiani:2002:IEB
author: M. Chiani and D. Dardari
booktitle: Global Telecommunications Conference, 2002. GLOBECOM '02. IEEE
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 51--81
year: 2002
DOI: https://doi.org/10.1109/glocom.2002.1188428
bibdate: Sat Dec 16 16:54:47 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 16:54:47 ???
URL: http://ieeexplore.ieee.org/document/1188428/
acknowledgement: ack-nhfb
rawauthor: M. Chiani and D. Dardari
rawbooktitle: Global Telecommunications Conference, 2002. {GLOBECOM '02}. {IEEE}
title:
Improved exponential bounds and approximation for the $Q$-function with application to average error probability computation

rawtitle:
Improved exponential bounds and approximation for the {$Q$}-function with application to average error probability computation

entry:
@InProceedings{Chiani:2002:IEB,
  author =       "M. Chiani and D. Dardari",
  booktitle =    "Global Telecommunications Conference, 2002. {GLOBECOM
                 '02}. {IEEE}",
  title =        "Improved exponential bounds and approximation for the
                 {$Q$}-function with application to average error
                 probability computation",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  year =         "2002",
  DOI =          "https://doi.org/10.1109/glocom.2002.1188428",
  bibdate =      "Sat Dec 16 16:54:47 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/1188428/",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Fabijonas:2002:LMC
author: Bruce R. Fabijonas
journal: j-J-COMPUT-APPL-MATH
volume: 146
number: 2
pages: 323--342
day: 15
month: sep
monthnumber: 9
year: 2002
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:30 MST 2017
bibtimestamp: 2017.02.25 12:52:30 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042702003643
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Bruce R. Fabijonas
title:
Laplace's method on a computer algebra system with an application to the real valued modified Bessel functions

rawtitle:
{Laplace}'s method on a computer algebra system with an application to the real valued modified {Bessel} functions

entry:
@Article{Fabijonas:2002:LMC,
  author =       "Bruce R. Fabijonas",
  title =        "{Laplace}'s method on a computer algebra system with
                 an application to the real valued modified {Bessel}
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "146",
  number =       "2",
  pages =        "323--342",
  day =          "15",
  month =        sep,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:30 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702003643",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:2002:GQA
author: W. Gautschi
title: Gauss quadrature approximations to hypergeometric and confluent hypergeometric functions
journal: j-J-COMPUT-APPL-MATH
volume: 139
number: 1
pages: 173--187
day: 1
month: feb
monthnumber: 2
year: 2002
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 33F05 (33C05 33C15 65D20)
MRnumber: MR1876879 (2002m:33029)
bibdate: Thu Dec 01 09:11:13 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 09:11:13 ???
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: W. Gautschi
rawtitle: {Gauss} quadrature approximations to hypergeometric and confluent hypergeometric functions
remark:
The paper treats ordinary and confluent hypergeometric functions $_2 F_1$ and $_1 F_1$, using their integral representations to obtain Gaussian quadrature rules.

entry:
@Article{Gautschi:2002:GQA,
  author =       "W. Gautschi",
  title =        "{Gauss} quadrature approximations to hypergeometric
                 and confluent hypergeometric functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "139",
  number =       "1",
  pages =        "173--187",
  day =          "1",
  month =        feb,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "33F05 (33C05 33C15 65D20)",
  MRnumber =     "MR1876879 (2002m:33029)",
  bibdate =      "Thu Dec 01 09:11:13 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  remark =       "The paper treats ordinary and confluent hypergeometric
                 functions $_2 F_1$ and $_1 F_1$, using their integral
                 representations to obtain Gaussian quadrature rules.",
}


bibtype: article
filename: elefunt.bib
label: Gil:2002:AAB
author: Amparo Gil and Javier Segura and Nico M. Temme
title: Algorithm 819: AIZ, BIZ: two Fortran 77 routines for the computation of complex Airy functions
journal: j-TOMS
volume: 28
number: 3
pages: 325--336
month: sep
monthnumber: 9
year: 2002
CODEN: ACMSCU
DOI: https://doi.org/10.1145/569147.569150
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Sat Nov 9 11:16:50 MST 2002
bibtimestamp: 2002.11.09 11:16:50 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
abstract:
Two Fortran 77 routines for the evaluation of Airy functions of complex arguments $ A i(z) $, $ B i(z) $ and their derivatives are presented. The routines are based on the use of Gaussian quadrature, Maclaurin series and asymptotic expansions. Comparison with a previous code by D. E. Amos (ACM TOMS 12 (1986)) is provided.

rawabstract:
Two Fortran 77 routines for the evaluation of Airy functions of complex arguments $ A i(z) $, $ B i(z) $ and their derivatives are presented. The routines are based on the use of Gaussian quadrature, Maclaurin series and asymptotic expansions. Comparison with a previous code by D. E. Amos (ACM TOMS 12 (1986)) is provided.

rawtitle:
{Algorithm 819}: {AIZ}, {BIZ}: two {Fortran 77} routines for the computation of complex {Airy} functions

entry:
@Article{Gil:2002:AAB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 819}: {AIZ}, {BIZ}: two {Fortran 77}
                 routines for the computation of complex {Airy}
                 functions",
  journal =      j-TOMS,
  volume =       "28",
  number =       "3",
  pages =        "325--336",
  month =        sep,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/569147.569150",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Sat Nov 9 11:16:50 MST 2002",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Two Fortran 77 routines for the evaluation of Airy
                 functions of complex arguments $ A i(z) $, $ B i(z) $
                 and their derivatives are presented. The routines are
                 based on the use of Gaussian quadrature, Maclaurin
                 series and asymptotic expansions. Comparison with a
                 previous code by D. E. Amos (ACM TOMS 12 (1986)) is
                 provided.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: article
filename: elefunt.bib
label: Gil:2002:AGH
author: Amparo Gil and Javier Segura and Nico M. Temme
title: Algorithm 822: GIZ, HIZ: two Fortran 77 routines for the computation of complex Scorer functions
journal: j-TOMS
volume: 28
number: 4
pages: 436--447
month: dec
monthnumber: 12
year: 2002
CODEN: ACMSCU
DOI: https://doi.org/10.1145/592843.592847
ISSN: 0098-3500 (print), 1557-7295 (electronic) OR 00983500 (print), 15577295 (electronic)
ISSNL: 0098-3500 OR 00983500
bibdate: Fri Mar 28 08:17:55 MST 2003
bibtimestamp: 2003.03.28 08:17:55 MST
fjournal: ACM Transactions on Mathematical Software (TOMS)
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/toms
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
abstract:
Two Fortran 77 routines for the evaluation of Scorer functions of complex arguments $ G i(z) $, $ H i(z) $ and their derivatives are presented. The routines are based on the use of quadrature, Maclaurin series and asymptotic expansions. For real $z$ comparison with a previous code by A. J. Macleod (J. Comput. Appl. Math. 53 (1994)) is provided.

rawabstract:
Two Fortran 77 routines for the evaluation of Scorer functions of complex arguments $ G i(z) $, $ H i(z) $ and their derivatives are presented. The routines are based on the use of quadrature, Maclaurin series and asymptotic expansions. For real $z$ comparison with a previous code by A. J. Macleod (J. Comput. Appl. Math. 53 (1994)) is provided.

rawtitle:
{Algorithm 822}: {GIZ}, {HIZ}: two {Fortran} 77 routines for the computation of complex {Scorer} functions

entry:
@Article{Gil:2002:AGH,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "{Algorithm 822}: {GIZ}, {HIZ}: two {Fortran} 77
                 routines for the computation of complex {Scorer}
                 functions",
  journal =      j-TOMS,
  volume =       "28",
  number =       "4",
  pages =        "436--447",
  month =        dec,
  year =         "2002",
  CODEN =        "ACMSCU",
  DOI =          "https://doi.org/10.1145/592843.592847",
  ISSN =         "0098-3500 (print), 1557-7295 (electronic)",
  ISSN-L =       "0098-3500",
  bibdate =      "Fri Mar 28 08:17:55 MST 2003",
  bibsource =    "http://www.acm.org/pubs/contents/journals/toms/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/toms.bib",
  abstract =     "Two Fortran 77 routines for the evaluation of Scorer
                 functions of complex arguments $ G i(z) $, $ H i(z) $
                 and their derivatives are presented. The routines are
                 based on the use of quadrature, Maclaurin series and
                 asymptotic expansions. For real $z$ comparison with a
                 previous code by A. J. Macleod (J. Comput. Appl. Math.
                 53 (1994)) is provided.",
  acknowledgement = ack-nhfb,
  fjournal =     "ACM Transactions on Mathematical Software (TOMS)",
  journal-URL =  "https://dl.acm.org/loi/toms",
}


bibtype: techreport
filename: elefunt.bib
label: Gil:2002:CSF
author: A. Gil and J. Segura and N. M. Temme
title: Computing special functions by using quadrature rules
type: Report
number: MAS-R0230
institution: pub-CWI
address: pub-CWI:adr
pages: 11
year: 2002
LCCN: QA9.A1 R426 MAS-R0230
bibdate: Sat Oct 30 19:13:12 2010
bibsource: http://cat.cisti-icist.nrc-cnrc.gc.ca/; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 19:13:12 ???
note: Published in cite Gil:2003:CSF.
acknowledgement: ack-nhfb
rawauthor: A. Gil and J. Segura and N. M. Temme
rawnote: Published in \cite{Gil:2003:CSF}.
rawtitle: Computing special functions by using quadrature rules
entry:
@TechReport{Gil:2002:CSF,
  author =       "A. Gil and J. Segura and N. M. Temme",
  title =        "Computing special functions by using quadrature
                 rules",
  type =         "Report",
  number =       "MAS-R0230",
  institution =  pub-CWI,
  address =      pub-CWI:adr,
  pages =        "11",
  year =         "2002",
  LCCN =         "QA9.A1 R426 MAS-R0230",
  bibdate =      "Sat Oct 30 19:13:12 2010",
  bibsource =    "http://cat.cisti-icist.nrc-cnrc.gc.ca/;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Published in \cite{Gil:2003:CSF}.",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Gil:2002:EMB
author: Amparo Gil and Javier Segura and Nico M. Temme
title: Evaluation of the Modified Bessel Function of the Third Kind of Imaginary Orders
journal: j-J-COMPUT-PHYS
volume: 175
number: 2
pages: 398--411
day: 20
month: jan
monthnumber: 1
year: 2002
CODEN: JCTPAH
DOI: https://doi.org/10.1006/jcph.2001.6894
ISSN: 0021-9991 (print), 1090-2716 (electronic) OR 00219991 (print), 10902716 (electronic)
ISSNL: 0021-9991 OR 00219991
bibdate: Mon Jan 2 22:12:13 MST 2012
bibtimestamp: 2012.01.02 22:12:13 MST
URL: http://www.sciencedirect.com/science/article/pii/S0021999101968949
fjournal: Journal of Computational Physics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00219991/
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
rawtitle: Evaluation of the Modified {Bessel} Function of the Third Kind of Imaginary Orders
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib

abstract:
The evaluation of the modified Bessel function of the third kind of purely imaginary order $ mathrm K_ia(x) $ is discussed; we also present analogous results for the derivative. The methods are based on the use of Maclaurin series, nonoscillatory integral representations, asymptotic expansions, and a continued fraction method, depending on the ranges of x and a. We discuss the range of applicability of the different approaches considered and conclude that power series, the continued fraction method, and the nonoscillatory integral representation can be used to accurately compute the function $ mathrm K_ia(x) $ in the range $ 0 leq a leq 200 $, $ 0 leq x leq 100 $; using a similar scheme the derivative $ mathrm K'_ia(x) $ can also be computed within these ranges.

rawabstract:
The evaluation of the modified Bessel function of the third kind of purely imaginary order $ \mathrm {K}_{ia}(x) $ is discussed; we also present analogous results for the derivative. The methods are based on the use of Maclaurin series, nonoscillatory integral representations, asymptotic expansions, and a continued fraction method, depending on the ranges of x and a. We discuss the range of applicability of the different approaches considered and conclude that power series, the continued fraction method, and the nonoscillatory integral representation can be used to accurately compute the function $ \mathrm {K}_{ia}(x) $ in the range $ 0 \leq a \leq 200 $, $ 0 \leq x \leq 100 $; using a similar scheme the derivative $ \mathrm {K}'_{ia(x)} $ can also be computed within these ranges.

entry:
@Article{Gil:2002:EMB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Evaluation of the Modified {Bessel} Function of the
                 Third Kind of Imaginary Orders",
  journal =      j-J-COMPUT-PHYS,
  volume =       "175",
  number =       "2",
  pages =        "398--411",
  day =          "20",
  month =        jan,
  year =         "2002",
  CODEN =        "JCTPAH",
  DOI =          "https://doi.org/10.1006/jcph.2001.6894",
  ISSN =         "0021-9991 (print), 1090-2716 (electronic)",
  ISSN-L =       "0021-9991",
  bibdate =      "Mon Jan 2 22:12:13 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputphys2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0021999101968949",
  abstract =     "The evaluation of the modified Bessel function of the
                 third kind of purely imaginary order $ \mathrm
                 {K}_{ia}(x) $ is discussed; we also present analogous
                 results for the derivative. The methods are based on
                 the use of Maclaurin series, nonoscillatory integral
                 representations, asymptotic expansions, and a continued
                 fraction method, depending on the ranges of x and a. We
                 discuss the range of applicability of the different
                 approaches considered and conclude that power series,
                 the continued fraction method, and the nonoscillatory
                 integral representation can be used to accurately
                 compute the function $ \mathrm {K}_{ia}(x) $ in the
                 range $ 0 \leq a \leq 200 $, $ 0 \leq x \leq 100 $;
                 using a similar scheme the derivative $ \mathrm
                 {K}'_{ia(x)} $ can also be computed within these
                 ranges.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational Physics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00219991/",
}


bibtype: article
filename: elefunt.bib
label: Gray:2002:ARE
author: Norman Gray
title: Automatic reduction of elliptic integrals using Carlson's relations
journal: j-MATH-COMPUT
volume: 71
number: 237
pages: 311--318
month: jan
monthnumber: 1
year: 2002
CODEN: MCMPAF
ISSN: 0025-5718 (print), 1088-6842 (electronic) OR 00255718 (print), 10886842 (electronic)
ISSNL: 0025-5718 OR 00255718
bibdate: Thu Jan 31 06:16:28 MST 2002
bibsource: http://www.ams.org/mcom/2002-71-237; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2002.01.31 06:16:28 MST
fjournal: Mathematics of Computation
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/mcom/
rawauthor: Norman Gray
rawtitle: Automatic reduction of elliptic integrals using {Carlson}'s relations
URL:
http://www.ams.org/journal-getitem?pii=S0025-5718-01-01333-3; http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.dvi; http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.pdf; http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.ps; http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.tex

entry:
@Article{Gray:2002:ARE,
  author =       "Norman Gray",
  title =        "Automatic reduction of elliptic integrals using
                 {Carlson}'s relations",
  journal =      j-MATH-COMPUT,
  volume =       "71",
  number =       "237",
  pages =        "311--318",
  month =        jan,
  year =         "2002",
  CODEN =        "MCMPAF",
  ISSN =         "0025-5718 (print), 1088-6842 (electronic)",
  ISSN-L =       "0025-5718",
  bibdate =      "Thu Jan 31 06:16:28 MST 2002",
  bibsource =    "http://www.ams.org/mcom/2002-71-237;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.ams.org/journal-getitem?pii=S0025-5718-01-01333-3;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.dvi;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.pdf;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.ps;
                 http://www.ams.org/mcom/2002-71-237/S0025-5718-01-01333-3/S0025-5718-01-01333-3.tex",
  acknowledgement = ack-nhfb,
  fjournal =     "Mathematics of Computation",
  journal-URL =  "http://www.ams.org/mcom/",
}


bibtype: article
filename: elefunt.bib
label: Hassenpflug:2002:EAS
author: W. C. Hassenpflug
title: Error analysis in the series evaluation of the exponential type integral $ e^z E_1 (z) $
journal: j-COMPUT-MATH-APPL
volume: 43
number: 1--2
pages: 207--266
month: jan
monthnumber: 1
year: 2002
CODEN: CMAPDK
ISSN: 0898-1221 (print), 1873-7668 (electronic) OR 08981221 (print), 18737668 (electronic)
ISSNL: 0898-1221 OR 08981221
bibdate: Wed Mar 1 21:49:20 MST 2017
bibtimestamp: 2017.03.01 21:49:20 MST
URL: http://www.sciencedirect.com/science/article/pii/S0898122101002838
fjournal: Computers and Mathematics with Applications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08981221
rawauthor: W. C. Hassenpflug
rawtitle: Error analysis in the series evaluation of the exponential type integral {$ e^z E_1 (z) $}
bibsource:
https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Hassenpflug:2002:EAS,
  author =       "W. C. Hassenpflug",
  title =        "Error analysis in the series evaluation of the
                 exponential type integral {$ e^z E_1 (z) $}",
  journal =      j-COMPUT-MATH-APPL,
  volume =       "43",
  number =       "1--2",
  pages =        "207--266",
  month =        jan,
  year =         "2002",
  CODEN =        "CMAPDK",
  ISSN =         "0898-1221 (print), 1873-7668 (electronic)",
  ISSN-L =       "0898-1221",
  bibdate =      "Wed Mar 1 21:49:20 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/computmathappl2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0898122101002838",
  acknowledgement = ack-nhfb,
  fjournal =     "Computers and Mathematics with Applications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08981221",
}


bibtype: article
filename: elefunt.bib
label: Kilbas:2002:ARH
author: Anatoly A. Kilbas and Luis Rodriguez and Juan J. Trujillo
title: Asymptotic representations for hypergeometric-Bessel type function and fractional integrals
journal: j-J-COMPUT-APPL-MATH
volume: 149
number: 2
pages: 469--487
day: 15
month: dec
monthnumber: 12
year: 2002
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:32 MST 2017
bibtimestamp: 2017.02.25 12:52:32 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042702005629
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Anatoly A. Kilbas and Luis Rodr{\'\i}guez and Juan J. Trujillo
rawtitle: Asymptotic representations for hypergeometric-{Bessel} type function and fractional integrals
entry:
@Article{Kilbas:2002:ARH,
  author =       "Anatoly A. Kilbas and Luis Rodr{\'\i}guez and Juan J.
                 Trujillo",
  title =        "Asymptotic representations for hypergeometric-{Bessel}
                 type function and fractional integrals",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "149",
  number =       "2",
  pages =        "469--487",
  day =          "15",
  month =        dec,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:32 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702005629",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: book
filename: elefunt.bib
label: Korenev:2002:BFT
author: B. G. (Boris Grigorevich) Korenev
title: Bessel Functions and Their Applications
publisher: pub-TAYLOR-FRANCIS
address: pub-TAYLOR-FRANCIS:adr
pages: ix + 276
year: 2002
ISBN: 0-415-28130-X (hardcover) OR 041528130X (hardcover)
ISBN13: 978-0-415-28130-0 (hardcover) OR 9780415281300 (hardcover)
LCCN: QA408 .K67 2002
bibdate: Sat Oct 30 17:01:51 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager
bibtimestamp: 2010.10.30 17:01:51 MDT
series: Analytical methods and special functions
subject: Bessel functions
acknowledgement: ack-nhfb
rawauthor: B. G. (Boris Grigorevich) Korenev
rawtitle: {Bessel} Functions and Their Applications
TOC:
Part 1. Foundation of the theory of Bessel functions 1. The Bessel equation Properties of Bessel functions 2. Definite and improper integrals Series in Bessel functions Part 2. Applications of Bessel functions 3. Problems of the theory of plates and shells 4. Problems of the theory of oscillations, hydrodynamics and heat transfer Appendix A. Brief information on gamma functions

rawTOC:
Part 1. Foundation of the theory of Bessel functions \\ 1. The Bessel equation \\ Properties of Bessel functions \\ 2. Definite and improper integrals \\ Series in Bessel functions \\ Part 2. Applications of Bessel functions \\ 3. Problems of the theory of plates and shells \\ 4. Problems of the theory of oscillations, hydrodynamics and heat transfer \\ Appendix A. Brief information on gamma functions

entry:
@Book{Korenev:2002:BFT,
  author =       "B. G. (Boris Grigorevich) Korenev",
  title =        "{Bessel} Functions and Their Applications",
  publisher =    pub-TAYLOR-FRANCIS,
  address =      pub-TAYLOR-FRANCIS:adr,
  pages =        "ix + 276",
  year =         "2002",
  ISBN =         "0-415-28130-X (hardcover)",
  ISBN-13 =      "978-0-415-28130-0 (hardcover)",
  LCCN =         "QA408 .K67 2002",
  bibdate =      "Sat Oct 30 17:01:51 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "Analytical methods and special functions",
  acknowledgement = ack-nhfb,
  subject =      "Bessel functions",
  tableofcontents = "Part 1. Foundation of the theory of Bessel
                 functions \\
                 1. The Bessel equation \\
                 Properties of Bessel functions \\
                 2. Definite and improper integrals \\
                 Series in Bessel functions \\
                 Part 2. Applications of Bessel functions \\
                 3. Problems of the theory of plates and shells \\
                 4. Problems of the theory of oscillations,
                 hydrodynamics and heat transfer \\
                 Appendix A. Brief information on gamma functions",
  xxaddress =    pub-CRC:adr,
  xxpublisher =  pub-CRC,
}


bibtype: book
filename: elefunt.bib
label: Li:2002:SWF
author: Le-Wei Li and Xiao-Kang Kang and Mook-Seng Leong
title: Spheroidal Wave Functions in Electromagnetic Theory
publisher: pub-WILEY
address: pub-WILEY:adr
pages: xiii + 295
year: 2002
ISBN: 0-471-03170-4 (hardcover) OR 0471031704 (hardcover)
ISBN13: 978-0-471-03170-3 (hardcover) OR 9780471031703 (hardcover)
LCCN: QC670 .L49 2002
bibdate: Sat Apr 1 14:32:29 MDT 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2017.04.01 14:32:29 MDT
series: Wiley series in microwave and optical engineering
subject: Electromagnetic theory; Spheroidal functions
acknowledgement: ack-nhfb
rawauthor: Le-Wei Li and Xiao-Kang Kang and Mook-Seng Leong
rawtitle: Spheroidal Wave Functions in Electromagnetic Theory
URL:
http://www.loc.gov/catdir/bios/wiley043/2001045399.html; http://www.loc.gov/catdir/description/wiley036/2001045399.html; http://www.loc.gov/catdir/toc/onix07/2001045399.html

TOC:
Preface Acknowledgments Introduction Spheroidal Coordinates and Wave Functions Dyadic Green's Functions in Spheroidal Systems EM Scattering by a Conducting Spheroid EM Scattering by a Coated Dielectric Spheroid Spheroidal Antennas SAR Distributions in a Spheroidal Head Model Analysis of Rainfall Attenuation Using Oblate Raindrops EM Eigenfrequencies in a Spheroidal Cavity Appendix A: Expressions of Spheroidal Vector Wave Functions Appendix B: Intermediates $I_t,ell ^mn(c)$ in Closed Form Appendix C: $cal U^q(i),t$ and $cal V^(i),t$ Used in the Matrix Equation System References Index

rawTOC:
Preface \\ Acknowledgments \\ Introduction \\ Spheroidal Coordinates and Wave Functions \\ Dyadic Green's Functions in Spheroidal Systems \\ EM Scattering by a Conducting Spheroid \\ EM Scattering by a Coated Dielectric Spheroid \\ Spheroidal Antennas \\ SAR Distributions in a Spheroidal Head Model \\ Analysis of Rainfall Attenuation Using Oblate Raindrops \\ EM Eigenfrequencies in a Spheroidal Cavity \\ Appendix A: Expressions of Spheroidal Vector Wave Functions \\ Appendix B: Intermediates $I_{t,\ell}^{mn}(c)$ in Closed Form \\ Appendix C: ${\cal U}^{q(i),t}$ and ${\cal V}^{(i),t}$ Used in the Matrix Equation System \\ References \\ Index

entry:
@Book{Li:2002:SWF,
  author =       "Le-Wei Li and Xiao-Kang Kang and Mook-Seng Leong",
  title =        "Spheroidal Wave Functions in Electromagnetic Theory",
  publisher =    pub-WILEY,
  address =      pub-WILEY:adr,
  pages =        "xiii + 295",
  year =         "2002",
  ISBN =         "0-471-03170-4 (hardcover)",
  ISBN-13 =      "978-0-471-03170-3 (hardcover)",
  LCCN =         "QC670 .L49 2002",
  bibdate =      "Sat Apr 1 14:32:29 MDT 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Wiley series in microwave and optical engineering",
  URL =          "http://www.loc.gov/catdir/bios/wiley043/2001045399.html;
                 http://www.loc.gov/catdir/description/wiley036/2001045399.html;
                 http://www.loc.gov/catdir/toc/onix07/2001045399.html",
  acknowledgement = ack-nhfb,
  subject =      "Electromagnetic theory; Spheroidal functions",
  tableofcontents = "Preface \\
                 Acknowledgments \\
                 Introduction \\
                 Spheroidal Coordinates and Wave Functions \\
                 Dyadic Green's Functions in Spheroidal Systems \\
                 EM Scattering by a Conducting Spheroid \\
                 EM Scattering by a Coated Dielectric Spheroid \\
                 Spheroidal Antennas \\
                 SAR Distributions in a Spheroidal Head Model \\
                 Analysis of Rainfall Attenuation Using Oblate Raindrops
                 \\
                 EM Eigenfrequencies in a Spheroidal Cavity \\
                 Appendix A: Expressions of Spheroidal Vector Wave
                 Functions \\
                 Appendix B: Intermediates $I_{t,\ell}^{mn}(c)$ in
                 Closed Form \\
                 Appendix C: ${\cal U}^{q(i),t}$ and ${\cal V}^{(i),t}$
                 Used in the Matrix Equation System \\
                 References \\
                 Index",
}


bibtype: article
filename: elefunt.bib
label: McCluskey:2002:MLF
author: Glen McCluskey
title: Math Library Functions in C9X
journal: j-LOGIN
volume: 27
number: 2
pages: 8--13
month: apr
monthnumber: 4
year: 2002
CODEN: LOGNEM
ISSN: 1044-6397 OR 10446397
bibdate: Tue Apr 11 10:52:14 MDT 2006
bibtimestamp: 2006.04.11 10:52:14 MDT
URL: http://www.usenix.org/publications/login/2002-04/pdfs/mccluskey.pdf
fjournal: ;login: the USENIX Association newsletter
remark: This is a short tutorial on some of the new math library functions in C99.
acknowledgement: ack-nhfb
rawauthor: Glen McCluskey
rawtitle: Math Library Functions in {C9X}
bibsource:
http://www.usenix.org/publications/login/2002-04/index.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{McCluskey:2002:MLF,
  author =       "Glen McCluskey",
  title =        "Math Library Functions in {C9X}",
  journal =      j-LOGIN,
  volume =       "27",
  number =       "2",
  pages =        "8--13",
  month =        apr,
  year =         "2002",
  CODEN =        "LOGNEM",
  ISSN =         "1044-6397",
  bibdate =      "Tue Apr 11 10:52:14 MDT 2006",
  bibsource =    "http://www.usenix.org/publications/login/2002-04/index.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www.usenix.org/publications/login/2002-04/pdfs/mccluskey.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     ";login: the USENIX Association newsletter",
  remark =       "This is a short tutorial on some of the new math
                 library functions in C99.",
}


bibtype: article
filename: elefunt.bib
label: Paris:2002:EBU
author: R. B. Paris
title: Error bounds for the uniform asymptotic expansion of the incomplete gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 147
number: 1
pages: 215--231
day: 1
month: oct
monthnumber: 10
year: 2002
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:30 MST 2017
bibtimestamp: 2017.02.25 12:52:30 MST
URL: http://www.sciencedirect.com/science/article/pii/S037704270200434X
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: R. B. Paris
rawtitle: Error bounds for the uniform asymptotic expansion of the incomplete gamma function
entry:
@Article{Paris:2002:EBU,
  author =       "R. B. Paris",
  title =        "Error bounds for the uniform asymptotic expansion of
                 the incomplete gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "147",
  number =       "1",
  pages =        "215--231",
  day =          "1",
  month =        oct,
  year =         "2002",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:30 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S037704270200434X",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Paris:2002:UAE
author: R. B. Paris
title: A uniform asymptotic expansion for the incomplete gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 148
number: 2
pages: 323--339
month: nov
monthnumber: 11
year: 2002
CODEN: JCAMDI
DOI: https://doi.org/10.1016/s0377-0427(02)00553-8
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 18 09:18:08 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.02.18 09:18:08 ???
note: See related work cite Paris:2016:UAE.
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: R. B. Paris
rawnote: See related work \cite{Paris:2016:UAE}.
rawtitle: A uniform asymptotic expansion for the incomplete gamma function
entry:
@Article{Paris:2002:UAE,
  author =       "R. B. Paris",
  title =        "A uniform asymptotic expansion for the incomplete
                 gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "148",
  number =       "2",
  pages =        "323--339",
  month =        nov,
  year =         "2002",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/s0377-0427(02)00553-8",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 18 09:18:08 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "See related work \cite{Paris:2016:UAE}.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Pineiro:2002:HRL
author: J.-A. Pineiro and M. D. Ercegovac and J. D. Bruguera
title: High-radix logarithm with selection by rounding
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 101--110
year: 2002
bibdate: Sat Jul 16 11:25:05 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 11:25:05 MDT
acknowledgement: ack-nhfb
rawauthor: J.-A. Pineiro and M. D. Ercegovac and J. D. Bruguera
rawtitle: High-radix logarithm with selection by rounding
booktitle:
The IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2002. Proceedings. 17--19 July 2002

rawbooktitle:
{The IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2002. Proceedings. 17--19 July 2002}

entry:
@InProceedings{Pineiro:2002:HRL,
  author =       "J.-A. Pineiro and M. D. Ercegovac and J. D. Bruguera",
  booktitle =    "{The IEEE International Conference on
                 Application-Specific Systems, Architectures and
                 Processors, 2002. Proceedings. 17--19 July 2002}",
  title =        "High-radix logarithm with selection by rounding",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "101--110",
  year =         "2002",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "A high-radix digit-recurrence algorithm or the
                 computation of the logarithm is presented in this
                 paper. Selection by rounding is used in iterations
                 j/spl ges/2, and selection by table in the first
                 iteration is combined with a restricted digit-set
                 \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Pineiro:2002:HSD
author: J. A. Pineiro and J. D. Bruguera
journal: j-IEEE-TRANS-COMPUT
volume: 51
number: 12
pages: 1377--1388
month: dec
monthnumber: 12
year: 2002
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2002.1146704
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibtimestamp: 2005.07.16 15:28:13 MDT
URL: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1146704
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: J. A. Pi{\~n}eiro and J. D. Bruguera
title:
High-Speed Double Precision Computation of Reciprocal, Division, Square Root, and Inverse Square Root

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib

rawtitle:
High-Speed Double Precision Computation of Reciprocal, Division, Square Root, and Inverse Square Root

entry:
@Article{Pineiro:2002:HSD,
  author =       "J. A. Pi{\~n}eiro and J. D. Bruguera",
  title =        "High-Speed Double Precision Computation of Reciprocal,
                 Division, Square Root, and Inverse Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "51",
  number =       "12",
  pages =        "1377--1388",
  month =        dec,
  year =         "2002",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2002.1146704",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/ieeetranscomput2000.bib",
  URL =          "http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1146704",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
  summary =      "A new method for the high-speed computation of
                 double-precision floating-point reciprocal, division,
                 square root, and inverse square root operations is
                 presented in this paper. This method employs a
                 second-degree minimax polynomial approximation to
                 \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Samko:2002:HIT
author: S. G. (Stefan Grigorevich) Samko
title: Hypersingular Integrals and Their Applications
volume: 5
publisher: pub-TAYLOR-FRANCIS
address: pub-TAYLOR-FRANCIS:adr
pages: xvii + 359
year: 2002
DOI: https://doi.org/10.1201/9781482264968
ISBN: 0-415-27268-8 OR 0415272688
ISBN13: 978-0-415-27268-1 OR 9780415272681
LCCN: QA403.5 .S26 2002
bibdate: Sat Oct 30 17:22:10 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager
bibtimestamp: 2010.10.30 17:22:10 MDT
series: Analytical methods and special functions
subject: singular integrals
acknowledgement: ack-nhfb
rawauthor: S. G. (Stefan Grigorevich) Samko
rawtitle: Hypersingular Integrals and Their Applications
TOC:
Part 1: Hypersingular integrals 1: Some basics from the theory of special functions and operator theory 2: The Riesz potential operator and Lizorkin type invariant spaces $Phi _v$ 3: Hypersingular integrals with constant characteristics 4: Potentials and hypersingular integrals with homogeneous characteristics 5: Hypersingular integrals with non-homogeneous characteristics 6: Hypersingular integrals on the unit sphere Part 2: Applications of hypersingular integrals 7: Characterization of some function spaces in terms of hypersingular integrals 8: Solution of multidimensional integral equations of the first kind with a potential type kernel 9: Hypersingular operators as positive fractional powers of some operators of mathematical physics 10: Regularization of multidimensional integral equations of the first kind with a potential type kernel 11: Some modifications of hypersingular integrals and their applications

rawTOC:
Part 1: Hypersingular integrals \\ 1: Some basics from the theory of special functions and operator theory \\ 2: The Riesz potential operator and Lizorkin type invariant spaces $\Phi_v$ \\ 3: Hypersingular integrals with constant characteristics \\ 4: Potentials and hypersingular integrals with homogeneous characteristics \\ 5: Hypersingular integrals with non-homogeneous characteristics \\ 6: Hypersingular integrals on the unit sphere \\ Part 2: Applications of hypersingular integrals \\ 7: Characterization of some function spaces in terms of hypersingular integrals \\ 8: Solution of multidimensional integral equations of the first kind with a potential type kernel \\ 9: Hypersingular operators as positive fractional powers of some operators of mathematical physics \\ 10: Regularization of multidimensional integral equations of the first kind with a potential type kernel \\ 11: Some modifications of hypersingular integrals and their applications

entry:
@Book{Samko:2002:HIT,
  author =       "S. G. (Stefan Grigorevich) Samko",
  title =        "Hypersingular Integrals and Their Applications",
  volume =       "5",
  publisher =    pub-TAYLOR-FRANCIS,
  address =      pub-TAYLOR-FRANCIS:adr,
  pages =        "xvii + 359",
  year =         "2002",
  DOI =          "https://doi.org/10.1201/9781482264968",
  ISBN =         "0-415-27268-8",
  ISBN-13 =      "978-0-415-27268-1",
  LCCN =         "QA403.5 .S26 2002",
  bibdate =      "Sat Oct 30 17:22:10 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "Analytical methods and special functions",
  acknowledgement = ack-nhfb,
  subject =      "singular integrals",
  tableofcontents = "Part 1: Hypersingular integrals \\
                 1: Some basics from the theory of special functions and
                 operator theory \\
                 2: The Riesz potential operator and Lizorkin type
                 invariant spaces $\Phi_v$ \\
                 3: Hypersingular integrals with constant
                 characteristics \\
                 4: Potentials and hypersingular integrals with
                 homogeneous characteristics \\
                 5: Hypersingular integrals with non-homogeneous
                 characteristics \\
                 6: Hypersingular integrals on the unit sphere \\
                 Part 2: Applications of hypersingular integrals \\
                 7: Characterization of some function spaces in terms of
                 hypersingular integrals \\
                 8: Solution of multidimensional integral equations of
                 the first kind with a potential type kernel \\
                 9: Hypersingular operators as positive fractional
                 powers of some operators of mathematical physics \\
                 10: Regularization of multidimensional integral
                 equations of the first kind with a potential type
                 kernel \\
                 11: Some modifications of hypersingular integrals and
                 their applications",
}


bibtype: inproceedings
filename: elefunt.bib
label: Sawada:2002:FVD
author: J. Sawada
title: Formal verification of divide and square root algorithms using series calculation
crossref: Borrione:2002:TIW
pages: 31--49
year: 2002
bibdate: Fri Jun 24 15:14:00 2005
bibtimestamp: 2005.06.24 15:14:00 ???
acknowledgement: ack-nhfb
rawauthor: J. Sawada
rawtitle: Formal verification of divide and square root algorithms using series calculation
entry:
@InProceedings{Sawada:2002:FVD,
  author =       "J. Sawada",
  title =        "Formal verification of divide and square root
                 algorithms using series calculation",
  crossref =     "Borrione:2002:TIW",
  pages =        "31--49",
  year =         "2002",
  bibdate =      "Fri Jun 24 15:14:00 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Sawada:2002:MVS
author: Jun Sawada and Ruben Gamboa
title: Mechanical Verification of a Square Root Algorithm Using Taylor's Theorem
journal: j-LECT-NOTES-COMP-SCI
volume: 2517
pages: 274--??
year: 2002
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Sat Nov 30 20:58:00 MST 2002
bibtimestamp: 2002.11.30 20:58:00 MST
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Jun Sawada and Ruben Gamboa
rawtitle: Mechanical Verification of a Square Root Algorithm Using {Taylor}'s Theorem
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2517.htm; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

URL:
http://link.springer.de/link/service/series/0558/bibs/2517/25170274.htm; http://link.springer.de/link/service/series/0558/papers/2517/25170274.pdf

entry:
@Article{Sawada:2002:MVS,
  author =       "Jun Sawada and Ruben Gamboa",
  title =        "Mechanical Verification of a Square Root Algorithm
                 Using {Taylor}'s Theorem",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2517",
  pages =        "274--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Sat Nov 30 20:58:00 MST 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2517.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://link.springer.de/link/service/series/0558/bibs/2517/25170274.htm;
                 http://link.springer.de/link/service/series/0558/papers/2517/25170274.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: misc
filename: elefunt.bib
label: Sebah:2002:IGF
author: Pascal Sebah and Xavier Gourdon
title: Introduction to the Gamma Function
pages: 274--??
day: 4
month: feb
monthnumber: 2
year: 2002
bibdate: Sat May 01 16:07:51 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.05.01 16:07:51 ???
acknowledgement: ack-nhfb
howpublished: World-Wide Web document
rawauthor: Pascal Sebah and Xavier Gourdon
rawtitle: Introduction to the Gamma Function
URL:
http://numbers.computation.free.fr/Constants/constants.html; http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.ps

entry:
@Misc{Sebah:2002:IGF,
  author =       "Pascal Sebah and Xavier Gourdon",
  title =        "Introduction to the Gamma Function",
  howpublished = "World-Wide Web document",
  day =          "4",
  month =        feb,
  year =         "2002",
  bibdate =      "Sat May 01 16:07:51 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://numbers.computation.free.fr/Constants/constants.html;
                 http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.ps",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Shore:2002:RMM
author: Haim Shore
title: Response Modeling Methodology (RMM)-Exploring the Properties of the Implied Error Distribution
journal: j-COMMUN-STAT-THEORY-METH
volume: 31
number: 12
pages: 2225--2249
year: 2002
CODEN: CSTMDC
DOI: https://doi.org/10.1081/STA-120017223
ISSN: 0361-0926 (print), 1532-415X (electronic) OR 03610926 (print), 1532415X (electronic)
ISSNL: 0361-0926 OR 03610926
bibdate: Wed Jan 27 05:41:30 MST 2016
bibtimestamp: 2016.01.27 05:41:30 MST
fjournal: Communications in Statistics: Theory and Methods
acknowledgement: ack-nhfb
journalURL: http://www.tandfonline.com/loi/lsta20
rawauthor: Haim Shore
rawtitle: Response Modeling Methodology ({RMM})-Exploring the Properties of the Implied Error Distribution
bibsource:
https://www.math.utah.edu/pub/tex/bib/communstattheorymeth2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Shore:2002:RMM,
  author =       "Haim Shore",
  title =        "Response Modeling Methodology ({RMM})-Exploring the
                 Properties of the Implied Error Distribution",
  journal =      j-COMMUN-STAT-THEORY-METH,
  volume =       "31",
  number =       "12",
  pages =        "2225--2249",
  year =         "2002",
  CODEN =        "CSTMDC",
  DOI =          "https://doi.org/10.1081/STA-120017223",
  ISSN =         "0361-0926 (print), 1532-415X (electronic)",
  ISSN-L =       "0361-0926",
  bibdate =      "Wed Jan 27 05:41:30 MST 2016",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/communstattheorymeth2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Communications in Statistics: Theory and Methods",
  journal-URL =  "http://www.tandfonline.com/loi/lsta20",
}


bibtype: article
filename: elefunt.bib
label: Tornaria:2002:SRM
author: Gonzalo Tornaria
title: Square Roots Modulo $p$
journal: j-LECT-NOTES-COMP-SCI
volume: 2286
pages: 430--??
year: 2002
CODEN: LNCSD9
ISSN: 0302-9743 (print), 1611-3349 (electronic) OR 03029743 (print), 16113349 (electronic)
ISSNL: 0302-9743 OR 03029743
bibdate: Tue Sep 10 19:09:12 MDT 2002
bibtimestamp: 2002.09.10 19:09:12 MDT
fjournal: Lecture Notes in Computer Science
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/bookseries/558
rawauthor: Gonzalo Tornar{\'\i}a
rawtitle: Square Roots Modulo $p$
bibsource:
http://link.springer-ny.com/link/service/series/0558/tocs/t2286.htm; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://link.springer-ny.com/link/service/series/0558/bibs/2286/22860430.htm; http://link.springer-ny.com/link/service/series/0558/papers/2286/22860430.pdf

entry:
@Article{Tornaria:2002:SRM,
  author =       "Gonzalo Tornar{\'\i}a",
  title =        "Square Roots Modulo $p$",
  journal =      j-LECT-NOTES-COMP-SCI,
  volume =       "2286",
  pages =        "430--??",
  year =         "2002",
  CODEN =        "LNCSD9",
  ISSN =         "0302-9743 (print), 1611-3349 (electronic)",
  ISSN-L =       "0302-9743",
  bibdate =      "Tue Sep 10 19:09:12 MDT 2002",
  bibsource =    "http://link.springer-ny.com/link/service/series/0558/tocs/t2286.htm;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://link.springer-ny.com/link/service/series/0558/bibs/2286/22860430.htm;
                 http://link.springer-ny.com/link/service/series/0558/papers/2286/22860430.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Lecture Notes in Computer Science",
  journal-URL =  "http://link.springer.com/bookseries/558",
}


bibtype: book
filename: elefunt.bib
label: Vladimirov:2002:MTG
author: V. S. (Vasilii Sergeevich) Vladimirov
title: Methods of the Theory of Generalized Functions
volume: 6
publisher: pub-TAYLOR-FRANCIS
address: pub-TAYLOR-FRANCIS:adr
pages: xiv + 311
year: 2002
DOI: https://doi.org/10.1201/9781482288162
ISBN: 0-415-27356-0 OR 0415273560
ISBN13: 978-0-415-27356-5 OR 9780415273565
LCCN: QC20.7.T45 V53 2002
bibdate: Sat Oct 30 17:22:15 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; prodorbis.library.yale.edu:7090/voyager
bibtimestamp: 2010.10.30 17:22:15 MDT
series: Analytical methods and special functions
subject: Theory of distributions (Functional analysis); Integral transforms; Mathematical physics
acknowledgement: ack-nhfb
rawauthor: V. S. (Vasilii Sergeevich) Vladimirov
rawtitle: Methods of the Theory of Generalized Functions
TOC:
Preface / xi Symbols and Definitions / 1 1. Generalized Functions and their Properties / 5 1. Test and Generalized Functions / 5 1.1. Introduction / 5 1.2. The space of test functions $mathcal D(mathcal O)$ / 6 1.3. The space of generalized functions $mathcal D'(mathcal O)$ / 10 1.4. The completeness of the space of generalized functions $mathcal D'(mathcal O)$ / 12 1.5. The support of a generalized function / 13 1.6. Regular generalized functions / 15 1.7. Measures / 16 1.8. Sochozki formulae / 19 1.9. Change of variables in generalized functions / 21 1.10. Multiplication of generalized functions / 23 2. Differentiation of Generalized Functions / 25 2.1. Derivatives of generalized functions / 25 2.2. The antiderivative (primitive) of a generalized function / 27 2.3. Examples / 29 2.4. The local structure of generalized functions / 35 2.5. Generalized functions with compact support / 36 2.6. Generalized functions with point support / 37 2.7. Generalized functions $mathcal P(pi _nu|x|^alpha - 1)$ / 39 3. Direct Product of Generalized Functions / 41 3.1. The definition of a direct product / 41 3.2. The properties of a direct product / 43 3.3. Some applications / 56 3.4. Generalized functions that are smooth with respect to some of the variables / 48 4. The Convolution of Generalized Functions / 50 4.1. The definition of convolution / 50 4.2. The properties of a convolution / 53 4.3. The existence of a convolution / 57 4.4. Cones in $mathcal R^n$ / 59 4.5. Convolution algebras $mathcal D'(Gamma +)$ and $mathcal D'(Gamma )$ / 63 4.6. Mean functions of generalized functions / 64 4.7. Multiplication of generalized functions / 66 4.8. Convolution as a continuous linear translation invariant operator / 66 4.9. Some applications / 68 5. Tempered Generalized Functions / 74 5.1. The space $S$ of test (rapidly decreasing) functions / 74 5.2. The space $S'$ of tempered generalized functions / 77 5.3. Examples of tempered generalized functions and elementary operations in $S$ /' 78 5.4. The structure of tempered generalized functions / 80 5.5. The direct product of tempered generalized functions / 81 5.6. The convolution of tempered generalized functions / 82 5.7. Homogeneous generalized functions / 85 2. Integral Transformations of Generalized Functions / 89 6. The Fourier Transform of Tempered Generalized Functions / 89 6.1. The Fourier transform of test functions in $S$ / 89 6.2. The Fourier transform of tempered generalized functions / 90 6.3. Properties of the Fourier transform / 92 6.4. The Fourier transform of generalized functions with compact support / 93 6.5. The Fourier transform of a convolution / 94 6.6. Examples / 96 6.7. The Mellin transform / 109 7. Fourier Series of Periodic Generalized Functions / 113 7.1. The definition and elementary properties of periodic generalized functions / 113 7.2. Fourier series of periodic generalized functions / 116 7.3. The convolution algebra $mathcal D'_T$ / 117 7.4. Examples / 119 8. Positive Definite Generalized Functions / 121 8.1. The definition and elementary properties of positive definite generalized functions / 121 8.2. The Bochner--Schwartz theorem / 123 8.3. Examples / 125 9. The Laplace Transform of Tempered Generalized Functions / 126 9.1. Definition of the Laplace transform / 126 9.2. Properties of the Laplace transform / 128 9.3. Examples / 130 10. The Cauchy Kernel and the Transforms of Cauchy--Bochner and Hilbert / 133 10.1. The space $mathcal H_s$ / 133 10.2. The Cauchy kernel $mathcal K_(z)$ / 138 10.3. The Cauchy--Bochner transform / 144 10.4. The Hilbert transform / 146 10.5. Holomorphic functions of the class $mathcal H_a^(s)(C)$ / 147 10.6. The generalized Cauchy--Bochner representation / 151 11. Poisson Kernel and Poisson Transform / 152 11.1. The definition and properties of the Poisson kernel / 152 11.2. The Poisson transform and Poisson representation / 155 11.3. Boundary values of the Poisson integral / 157 12. Algebras of Holomorphic Functions / 159 12.1. The definition of the $H_+(C)$ and $H(C)$ algebras / 160 12.2. Isomorphism of the algebras $S'(C*+) sim H_+(C)$ and $S'(C*) sim H(C)$ / 160 12.3. The Paley--Wiener--Schwartz theorem and its generalizations / 165 12.4. The space $H_a(C)$ is the projective limit of the spaces $H_a'(C)$ / 166 12.5. The Schwartz representation / 168 12.6. A generalization of the Phragmen--Lindelof theorem / 171 13. Equations in Convolution Algebras / 171 13.1. Divisors of unity in the $H_+(C)$ and $H(C)$ algebras / 171 13.2. On division by a polynomial in the $H(C)$ algebra / 172 13.3. Estimates for holomorphic functions with nonnegative imaginary part in $T^C$ / 174 13.4. Divisors of unity in the algebra $W(C)$ / 177 13.5. Example / 177 14. Tauberian Theorems for Generalized Functions / 179 14.1. Preliminary results / 179 14.2. General Tauberian theorem / 183 14.3. One-dimensional Tauberian theorems / 186 14.4. Tauberian and Abelian theorems for nonnegative measures / 187 14.5. Tauberian theorems for holomorphic functions of bounded argument / 188 3. Some Applications in Mathematical Physics / 191 15. Differential Operators with Constant Coefficients / 191 15.1. Fundamental solutions in $mathcal D'$ / 191 15.2. Tempered fundamental solutions / 194 15.3. A descent method / 196 15.4. Examples / 199 15.5. A comparison of differential operators / 207 15.6. Elliptic and hypoelliptic operators / 210 15.7. Hyperbolic operators / 212 15.8. The sweeping principle / 212 16. The Cauchy Problem / 213 16.1. The generalized Cauchy problem for a hyperbolic equation / 213 16.2. Wave potential / 216 16.3. Surface wave potentials / 220 16.4. The Cauchy problem for the wave equation / 222 16.5. A statement of the generalized Cauchy problem for the heat equation / 224 16.6. Heat potential / 224 16.7. Solution of the Cauchy problem for the heat equation / 228 17. Holomorphic Functions with Nonnegative Imaginary Part in $T^C$ / 229 17.1. Preliminary remarks / 229 17.2. Properties of functions of the class $mathcal P_+(T^C)$ / 231 17.3. Estimates of the growth of functions of the class $H_+(T^C)$ / 238 17.4. Smoothness of the spectral function / 240 17.5. Indicator of growth of functions of the class $mathcal P_+T^C$ / 242 17.6. An integral representation of functions of the class $H_+(T^C)$ / 245 18. Holomorphic Functions with Nonnegative Imaginary Part in $T^n$ / 249 18.1. Lemmas / 249 18.2. Functions of the classes $H_+(T^1)$ and $mathcal P_+(T^1)$ / 254 18.3. Functions of the class $mathcal P_+(T^n)$ / 258 18.4. Functions of the class $H_+(T^n)$ / 263 19. Positive Real Matrix Functions in $T^C$ / 266 19.1. Positive real functions in $T^C$ / 267 19.2. Positive real matrix functions in $T^C$ / 269 20. Linear Passive Systems / 271 20.1. Introduction / 271 20.2. Corollaries to the condition of passivity / 273 20.3. The necessary and sufficient conditions for passivity / 277 20.4. Multidimensional dispersion relations / 282 20.5. The fundamental solution and the Cauchy problem / 285 20.6. What differential and difference operators are passive operators? / 287 20.7. Examples / 290 20.8. Quasiasymptotics of the solutions of systems of equations in convolutions / 294 21. Abstract Scattering Operator / 295 21.1. The definition and properties of an abstract scattering matrix / 295 21.2. A description of abstract scattering matrices / 298 21.3. The relationship between passive operators and scattering operators / 299 Bibliography / 303 Index / 309

rawTOC:
Preface / xi \\ Symbols and Definitions / 1 \\ \\ 1. Generalized Functions and their Properties / 5 \\ 1. Test and Generalized Functions / 5 \\ 1.1. Introduction / 5 \\ 1.2. The space of test functions $\mathcal{D}(\mathcal{O})$ / 6 \\ 1.3. The space of generalized functions $\mathcal{D}'(\mathcal{O})$ / 10 \\ 1.4. The completeness of the space of generalized functions $\mathcal{D}'(\mathcal{O})$ / 12 \\ 1.5. The support of a generalized function / 13 \\ 1.6. Regular generalized functions / 15 \\ 1.7. Measures / 16 \\ 1.8. Sochozki formulae / 19 \\ 1.9. Change of variables in generalized functions / 21 \\ 1.10. Multiplication of generalized functions / 23 \\ \\ 2. Differentiation of Generalized Functions / 25 \\ 2.1. Derivatives of generalized functions / 25 \\ 2.2. The antiderivative (primitive) of a generalized function / 27 \\ 2.3. Examples / 29 \\ 2.4. The local structure of generalized functions / 35 \\ 2.5. Generalized functions with compact support / 36 \\ 2.6. Generalized functions with point support / 37 \\ 2.7. Generalized functions $\mathcal{P}(\pi_nu|x|^{\alpha - 1})$ / 39 \\ \\ 3. Direct Product of Generalized Functions / 41 \\ 3.1. The definition of a direct product / 41 \\ 3.2. The properties of a direct product / 43 \\ 3.3. Some applications / 56 \\ 3.4. Generalized functions that are smooth with respect to some of the variables / 48 \\ \\ 4. The Convolution of Generalized Functions / 50 \\ 4.1. The definition of convolution / 50 \\ 4.2. The properties of a convolution / 53 \\ 4.3. The existence of a convolution / 57 \\ 4.4. Cones in $\mathcal{R}^n$ / 59 \\ 4.5. Convolution algebras $\mathcal{D}'(\Gamma+)$ and $\mathcal{D}'(\Gamma)$ / 63 \\ 4.6. Mean functions of generalized functions / 64 \\ 4.7. Multiplication of generalized functions / 66 \\ 4.8. Convolution as a continuous linear translation invariant operator / 66 \\ 4.9. Some applications / 68 \\ \\ 5. Tempered Generalized Functions / 74 \\ 5.1. The space $S$ of test (rapidly decreasing) functions / 74 \\ 5.2. The space $S'$ of tempered generalized functions / 77 \\ 5.3. Examples of tempered generalized functions and elementary operations in $S$ /' 78 \\ 5.4. The structure of tempered generalized functions / 80 \\ 5.5. The direct product of tempered generalized functions / 81 \\ 5.6. The convolution of tempered generalized functions / 82 \\ 5.7. Homogeneous generalized functions / 85 \\ 2. Integral Transformations of Generalized Functions / 89 \\ \\ 6. The Fourier Transform of Tempered Generalized Functions / 89 \\ 6.1. The Fourier transform of test functions in $S$ / 89 \\ 6.2. The Fourier transform of tempered generalized functions / 90 \\ 6.3. Properties of the Fourier transform / 92 \\ 6.4. The Fourier transform of generalized functions with compact support / 93 \\ 6.5. The Fourier transform of a convolution / 94 \\ 6.6. Examples / 96 \\ 6.7. The Mellin transform / 109 \\ \\ 7. Fourier Series of Periodic Generalized Functions / 113 \\ 7.1. The definition and elementary properties of periodic generalized functions / 113 \\ 7.2. Fourier series of periodic generalized functions / 116 \\ 7.3. The convolution algebra $\mathcal{D}'_T$ / 117 \\ 7.4. Examples / 119 \\ \\ 8. Positive Definite Generalized Functions / 121 \\ 8.1. The definition and elementary properties of positive definite generalized functions / 121 \\ 8.2. The Bochner--Schwartz theorem / 123 \\ 8.3. Examples / 125 \\ \\ 9. The Laplace Transform of Tempered Generalized Functions / 126 \\ 9.1. Definition of the Laplace transform / 126 \\ 9.2. Properties of the Laplace transform / 128 \\ 9.3. Examples / 130 \\ \\ 10. The Cauchy Kernel and the Transforms of Cauchy--Bochner and Hilbert / 133 \\ 10.1. The space $\mathcal{H}_s$ / 133 \\ 10.2. The Cauchy kernel $\mathcal{K}_(z)$ / 138 \\ 10.3. The Cauchy--Bochner transform / 144 \\ 10.4. The Hilbert transform / 146 \\ 10.5. Holomorphic functions of the class $\mathcal{H}_a^{(s)}(C)$ / 147 \\ 10.6. The generalized Cauchy--Bochner representation / 151 \\ \\ 11. Poisson Kernel and Poisson Transform / 152 \\ 11.1. The definition and properties of the Poisson kernel / 152 \\ 11.2. The Poisson transform and Poisson representation / 155 \\ 11.3. Boundary values of the Poisson integral / 157 \\ \\ 12. Algebras of Holomorphic Functions / 159 \\ 12.1. The definition of the $H_+(C)$ and $H(C)$ algebras / 160 \\ 12.2. Isomorphism of the algebras $S'(C*+) \sim H_+(C)$ and $S'(C*) \sim H(C)$ / 160 \\ 12.3. The Paley--Wiener--Schwartz theorem and its generalizations / 165 \\ 12.4. The space $H_a(C)$ is the projective limit of the spaces $H_{a'}(C)$ / 166 \\ 12.5. The Schwartz representation / 168 \\ 12.6. A generalization of the Phragmen--Lindelof theorem / 171 \\ \\ 13. Equations in Convolution Algebras / 171 \\ 13.1. Divisors of unity in the $H_+(C)$ and $H(C)$ algebras / 171 \\ 13.2. On division by a polynomial in the $H(C)$ algebra / 172 \\ 13.3. Estimates for holomorphic functions with nonnegative imaginary part in $T^C$ / 174 \\ 13.4. Divisors of unity in the algebra $W(C)$ / 177 \\ 13.5. Example / 177 \\ \\ 14. Tauberian Theorems for Generalized Functions / 179 \\ 14.1. Preliminary results / 179 \\ 14.2. General Tauberian theorem / 183 \\ 14.3. One-dimensional Tauberian theorems / 186 \\ 14.4. Tauberian and Abelian theorems for nonnegative measures / 187 \\ 14.5. Tauberian theorems for holomorphic functions of bounded argument / 188 \\ 3. Some Applications in Mathematical Physics / 191 \\ \\ 15. Differential Operators with Constant Coefficients / 191 \\ 15.1. Fundamental solutions in $\mathcal{D}'$ / 191 \\ 15.2. Tempered fundamental solutions / 194 \\ 15.3. A descent method / 196 \\ 15.4. Examples / 199 \\ 15.5. A comparison of differential operators / 207 \\ 15.6. Elliptic and hypoelliptic operators / 210 \\ 15.7. Hyperbolic operators / 212 \\ 15.8. The sweeping principle / 212 \\ \\ 16. The Cauchy Problem / 213 \\ 16.1. The generalized Cauchy problem for a hyperbolic equation / 213 \\ 16.2. Wave potential / 216 \\ 16.3. Surface wave potentials / 220 \\ 16.4. The Cauchy problem for the wave equation / 222 \\ 16.5. A statement of the generalized Cauchy problem for the heat equation / 224 \\ 16.6. Heat potential / 224 \\ 16.7. Solution of the Cauchy problem for the heat equation / 228 \\ \\ 17. Holomorphic Functions with Nonnegative Imaginary Part in $T^C$ / 229 \\ 17.1. Preliminary remarks / 229 \\ 17.2. Properties of functions of the class $\mathcal{P}_+(T^C)$ / 231 \\ 17.3. Estimates of the growth of functions of the class $H_+(T^C)$ / 238 \\ 17.4. Smoothness of the spectral function / 240 \\ 17.5. Indicator of growth of functions of the class $\mathcal{P}_+T^C$ / 242 \\ 17.6. An integral representation of functions of the class $H_+(T^C)$ / 245 \\ \\ 18. Holomorphic Functions with Nonnegative Imaginary Part in $T^n$ / 249 \\ 18.1. Lemmas / 249 \\ 18.2. Functions of the classes $H_+(T^1)$ and $\mathcal{P}_+(T^1)$ / 254 \\ 18.3. Functions of the class $\mathcal{P}_+(T^n)$ / 258 \\ 18.4. Functions of the class $H_+(T^n)$ / 263 \\ \\ 19. Positive Real Matrix Functions in $T^C$ / 266 \\ 19.1. Positive real functions in $T^C$ / 267 \\ 19.2. Positive real matrix functions in $T^C$ / 269 \\ \\ 20. Linear Passive Systems / 271 \\ 20.1. Introduction / 271 \\ 20.2. Corollaries to the condition of passivity / 273 \\ 20.3. The necessary and sufficient conditions for passivity / 277 \\ 20.4. Multidimensional dispersion relations / 282 \\ 20.5. The fundamental solution and the Cauchy problem / 285 \\ 20.6. What differential and difference operators are passive operators? / 287 \\ 20.7. Examples / 290 \\ 20.8. Quasiasymptotics of the solutions of systems of equations in convolutions / 294 \\ \\ 21. Abstract Scattering Operator / 295 \\ 21.1. The definition and properties of an abstract scattering matrix / 295 \\ 21.2. A description of abstract scattering matrices / 298 \\ 21.3. The relationship between passive operators and scattering operators / 299 \\ \\ Bibliography / 303 \\ Index / 309

entry:
@Book{Vladimirov:2002:MTG,
  author =       "V. S. (Vasilii Sergeevich) Vladimirov",
  title =        "Methods of the Theory of Generalized Functions",
  volume =       "6",
  publisher =    pub-TAYLOR-FRANCIS,
  address =      pub-TAYLOR-FRANCIS:adr,
  pages =        "xiv + 311",
  year =         "2002",
  DOI =          "https://doi.org/10.1201/9781482288162",
  ISBN =         "0-415-27356-0",
  ISBN-13 =      "978-0-415-27356-5",
  LCCN =         "QC20.7.T45 V53 2002",
  bibdate =      "Sat Oct 30 17:22:15 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  series =       "Analytical methods and special functions",
  acknowledgement = ack-nhfb,
  subject =      "Theory of distributions (Functional analysis);
                 Integral transforms; Mathematical physics",
  tableofcontents = "Preface / xi \\
                 Symbols and Definitions / 1 \\
                 \\
                 1. Generalized Functions and their Properties / 5 \\
                 1. Test and Generalized Functions / 5 \\
                 1.1. Introduction / 5 \\
                 1.2. The space of test functions
                 $\mathcal{D}(\mathcal{O})$ / 6 \\
                 1.3. The space of generalized functions
                 $\mathcal{D}'(\mathcal{O})$ / 10 \\
                 1.4. The completeness of the space of generalized
                 functions $\mathcal{D}'(\mathcal{O})$ / 12 \\
                 1.5. The support of a generalized function / 13 \\
                 1.6. Regular generalized functions / 15 \\
                 1.7. Measures / 16 \\
                 1.8. Sochozki formulae / 19 \\
                 1.9. Change of variables in generalized functions / 21
                 \\
                 1.10. Multiplication of generalized functions / 23 \\
                 \\
                 2. Differentiation of Generalized Functions / 25 \\
                 2.1. Derivatives of generalized functions / 25 \\
                 2.2. The antiderivative (primitive) of a generalized
                 function / 27 \\
                 2.3. Examples / 29 \\
                 2.4. The local structure of generalized functions / 35
                 \\
                 2.5. Generalized functions with compact support / 36
                 \\
                 2.6. Generalized functions with point support / 37 \\
                 2.7. Generalized functions
                 $\mathcal{P}(\pi_nu|x|^{\alpha - 1})$ / 39 \\
                 \\
                 3. Direct Product of Generalized Functions / 41 \\
                 3.1. The definition of a direct product / 41 \\
                 3.2. The properties of a direct product / 43 \\
                 3.3. Some applications / 56 \\
                 3.4. Generalized functions that are smooth with respect
                 to some of the variables / 48 \\
                 \\
                 4. The Convolution of Generalized Functions / 50 \\
                 4.1. The definition of convolution / 50 \\
                 4.2. The properties of a convolution / 53 \\
                 4.3. The existence of a convolution / 57 \\
                 4.4. Cones in $\mathcal{R}^n$ / 59 \\
                 4.5. Convolution algebras $\mathcal{D}'(\Gamma+)$ and
                 $\mathcal{D}'(\Gamma)$ / 63 \\
                 4.6. Mean functions of generalized functions / 64 \\
                 4.7. Multiplication of generalized functions / 66 \\
                 4.8. Convolution as a continuous linear translation
                 invariant operator / 66 \\
                 4.9. Some applications / 68 \\
                 \\
                 5. Tempered Generalized Functions / 74 \\
                 5.1. The space $S$ of test (rapidly decreasing)
                 functions / 74 \\
                 5.2. The space $S'$ of tempered generalized functions /
                 77 \\
                 5.3. Examples of tempered generalized functions and
                 elementary operations in $S$ /' 78 \\
                 5.4. The structure of tempered generalized functions /
                 80 \\
                 5.5. The direct product of tempered generalized
                 functions / 81 \\
                 5.6. The convolution of tempered generalized functions
                 / 82 \\
                 5.7. Homogeneous generalized functions / 85 \\
                 2. Integral Transformations of Generalized Functions /
                 89 \\
                 \\
                 6. The Fourier Transform of Tempered Generalized
                 Functions / 89 \\
                 6.1. The Fourier transform of test functions in $S$ /
                 89 \\
                 6.2. The Fourier transform of tempered generalized
                 functions / 90 \\
                 6.3. Properties of the Fourier transform / 92 \\
                 6.4. The Fourier transform of generalized functions
                 with compact support / 93 \\
                 6.5. The Fourier transform of a convolution / 94 \\
                 6.6. Examples / 96 \\
                 6.7. The Mellin transform / 109 \\
                 \\
                 7. Fourier Series of Periodic Generalized Functions /
                 113 \\
                 7.1. The definition and elementary properties of
                 periodic generalized functions / 113 \\
                 7.2. Fourier series of periodic generalized functions /
                 116 \\
                 7.3. The convolution algebra $\mathcal{D}'_T$ / 117 \\
                 7.4. Examples / 119 \\
                 \\
                 8. Positive Definite Generalized Functions / 121 \\
                 8.1. The definition and elementary properties of
                 positive definite generalized functions / 121 \\
                 8.2. The Bochner--Schwartz theorem / 123 \\
                 8.3. Examples / 125 \\
                 \\
                 9. The Laplace Transform of Tempered Generalized
                 Functions / 126 \\
                 9.1. Definition of the Laplace transform / 126 \\
                 9.2. Properties of the Laplace transform / 128 \\
                 9.3. Examples / 130 \\
                 \\
                 10. The Cauchy Kernel and the Transforms of
                 Cauchy--Bochner and Hilbert / 133 \\
                 10.1. The space $\mathcal{H}_s$ / 133 \\
                 10.2. The Cauchy kernel $\mathcal{K}_(z)$ / 138 \\
                 10.3. The Cauchy--Bochner transform / 144 \\
                 10.4. The Hilbert transform / 146 \\
                 10.5. Holomorphic functions of the class
                 $\mathcal{H}_a^{(s)}(C)$ / 147 \\
                 10.6. The generalized Cauchy--Bochner representation /
                 151 \\
                 \\
                 11. Poisson Kernel and Poisson Transform / 152 \\
                 11.1. The definition and properties of the Poisson
                 kernel / 152 \\
                 11.2. The Poisson transform and Poisson representation
                 / 155 \\
                 11.3. Boundary values of the Poisson integral / 157 \\
                 \\
                 12. Algebras of Holomorphic Functions / 159 \\
                 12.1. The definition of the $H_+(C)$ and $H(C)$
                 algebras / 160 \\
                 12.2. Isomorphism of the algebras $S'(C*+) \sim H_+(C)$
                 and $S'(C*) \sim H(C)$ / 160 \\
                 12.3. The Paley--Wiener--Schwartz theorem and its
                 generalizations / 165 \\
                 12.4. The space $H_a(C)$ is the projective limit of the
                 spaces $H_{a'}(C)$ / 166 \\
                 12.5. The Schwartz representation / 168 \\
                 12.6. A generalization of the Phragmen--Lindelof
                 theorem / 171 \\
                 \\
                 13. Equations in Convolution Algebras / 171 \\
                 13.1. Divisors of unity in the $H_+(C)$ and $H(C)$
                 algebras / 171 \\
                 13.2. On division by a polynomial in the $H(C)$ algebra
                 / 172 \\
                 13.3. Estimates for holomorphic functions with
                 nonnegative imaginary part in $T^C$ / 174 \\
                 13.4. Divisors of unity in the algebra $W(C)$ / 177 \\
                 13.5. Example / 177 \\
                 \\
                 14. Tauberian Theorems for Generalized Functions / 179
                 \\
                 14.1. Preliminary results / 179 \\
                 14.2. General Tauberian theorem / 183 \\
                 14.3. One-dimensional Tauberian theorems / 186 \\
                 14.4. Tauberian and Abelian theorems for nonnegative
                 measures / 187 \\
                 14.5. Tauberian theorems for holomorphic functions of
                 bounded argument / 188 \\
                 3. Some Applications in Mathematical Physics / 191 \\
                 \\
                 15. Differential Operators with Constant Coefficients /
                 191 \\
                 15.1. Fundamental solutions in $\mathcal{D}'$ / 191 \\
                 15.2. Tempered fundamental solutions / 194 \\
                 15.3. A descent method / 196 \\
                 15.4. Examples / 199 \\
                 15.5. A comparison of differential operators / 207 \\
                 15.6. Elliptic and hypoelliptic operators / 210 \\
                 15.7. Hyperbolic operators / 212 \\
                 15.8. The sweeping principle / 212 \\
                 \\
                 16. The Cauchy Problem / 213 \\
                 16.1. The generalized Cauchy problem for a hyperbolic
                 equation / 213 \\
                 16.2. Wave potential / 216 \\
                 16.3. Surface wave potentials / 220 \\
                 16.4. The Cauchy problem for the wave equation / 222
                 \\
                 16.5. A statement of the generalized Cauchy problem for
                 the heat equation / 224 \\
                 16.6. Heat potential / 224 \\
                 16.7. Solution of the Cauchy problem for the heat
                 equation / 228 \\
                 \\
                 17. Holomorphic Functions with Nonnegative Imaginary
                 Part in $T^C$ / 229 \\
                 17.1. Preliminary remarks / 229 \\
                 17.2. Properties of functions of the class
                 $\mathcal{P}_+(T^C)$ / 231 \\
                 17.3. Estimates of the growth of functions of the class
                 $H_+(T^C)$ / 238 \\
                 17.4. Smoothness of the spectral function / 240 \\
                 17.5. Indicator of growth of functions of the class
                 $\mathcal{P}_+T^C$ / 242 \\
                 17.6. An integral representation of functions of the
                 class $H_+(T^C)$ / 245 \\
                 \\
                 18. Holomorphic Functions with Nonnegative Imaginary
                 Part in $T^n$ / 249 \\
                 18.1. Lemmas / 249 \\
                 18.2. Functions of the classes $H_+(T^1)$ and
                 $\mathcal{P}_+(T^1)$ / 254 \\
                 18.3. Functions of the class $\mathcal{P}_+(T^n)$ / 258
                 \\
                 18.4. Functions of the class $H_+(T^n)$ / 263 \\
                 \\
                 19. Positive Real Matrix Functions in $T^C$ / 266 \\
                 19.1. Positive real functions in $T^C$ / 267 \\
                 19.2. Positive real matrix functions in $T^C$ / 269 \\
                 \\
                 20. Linear Passive Systems / 271 \\
                 20.1. Introduction / 271 \\
                 20.2. Corollaries to the condition of passivity / 273
                 \\
                 20.3. The necessary and sufficient conditions for
                 passivity / 277 \\
                 20.4. Multidimensional dispersion relations / 282 \\
                 20.5. The fundamental solution and the Cauchy problem /
                 285 \\
                 20.6. What differential and difference operators are
                 passive operators? / 287 \\
                 20.7. Examples / 290 \\
                 20.8. Quasiasymptotics of the solutions of systems of
                 equations in convolutions / 294 \\
                 \\
                 21. Abstract Scattering Operator / 295 \\
                 21.1. The definition and properties of an abstract
                 scattering matrix / 295 \\
                 21.2. A description of abstract scattering matrices /
                 298 \\
                 21.3. The relationship between passive operators and
                 scattering operators / 299 \\
                 \\
                 Bibliography / 303 \\
                 Index / 309",
}


bibtype: article
filename: elefunt.bib
label: Aarts:2003:ASF
author: Ronald M. Aarts and Augustus J. E. M. Janssen
title: Approximation of the Struve function $ H_1 $ occurring in impedance calculations
journal: j-J-ACOUST-SOC-AM
volume: 113
number: 5
pages: 2635--2637
month: may
monthnumber: 5
year: 2003
CODEN: JASMAN
DOI: https://doi.org/10.1121/1.1564019
ISSN: 0001-4966 OR 00014966
ISSNL: 0001-4966 OR 00014966
bibdate: Tue Mar 28 07:23:10 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.28 07:23:10 ???
fjournal: Journal of the Acoustical Society of America
acknowledgement: ack-nhfb
journalURL: http://scitation.aip.org/content/asa/journal/jasa
rawauthor: Ronald M. Aarts and Augustus J. E. M. Janssen
rawtitle: Approximation of the {Struve} function {$ H_1 $} occurring in impedance calculations
entry:
@Article{Aarts:2003:ASF,
  author =       "Ronald M. Aarts and Augustus J. E. M. Janssen",
  title =        "Approximation of the {Struve} function {$ H_1 $}
                 occurring in impedance calculations",
  journal =      j-J-ACOUST-SOC-AM,
  volume =       "113",
  number =       "5",
  pages =        "2635--2637",
  month =        may,
  year =         "2003",
  CODEN =        "JASMAN",
  DOI =          "https://doi.org/10.1121/1.1564019",
  ISSN =         "0001-4966",
  ISSN-L =       "0001-4966",
  bibdate =      "Tue Mar 28 07:23:10 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of the Acoustical Society of America",
  journal-URL =  "http://scitation.aip.org/content/asa/journal/jasa",
}


bibtype: article
filename: elefunt.bib
label: Abad:2003:AEQ
author: J. Abad and J. Sesma
title: Asymptotic expansion of the quasiconfluent hypergeometric function
journal: j-J-MATH-PHYS
volume: 44
number: 4
pages: 1723--1729
month: apr
monthnumber: 4
year: 2003
CODEN: JMAPAQ
ISSNL: 0022-2488 OR 00222488
bibdate: Tue Dec 16 11:36:01 MST 2003
bibtimestamp: 2003.12.16 11:36:01 MST
fjournal: Journal of Mathematical Physics
acknowledgement: ack-nhfb
journalURL: http://jmp.aip.org/
rawauthor: J. Abad and J. Sesma
rawtitle: Asymptotic expansion of the quasiconfluent hypergeometric function
bibsource:
http://www.aip.org/ojs/jmp.html; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib

entry:
@Article{Abad:2003:AEQ,
  author =       "J. Abad and J. Sesma",
  title =        "Asymptotic expansion of the quasiconfluent
                 hypergeometric function",
  journal =      j-J-MATH-PHYS,
  volume =       "44",
  number =       "4",
  pages =        "1723--1729",
  month =        apr,
  year =         "2003",
  CODEN =        "JMAPAQ",
  ISSN =         "0022-2488 (print), 1089-7658 (electronic), 1527-2427",
  ISSN-L =       "0022-2488",
  bibdate =      "Tue Dec 16 11:36:01 MST 2003",
  bibsource =    "http://www.aip.org/ojs/jmp.html;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jmathphys2000.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Mathematical Physics",
  journal-URL =  "http://jmp.aip.org/",
}


bibtype: article
filename: elefunt.bib
label: Agou:2003:SPR
author: Simon Joseph Agou and Marc Deleglise and Jean-Louis Nicolas
title: Short Polynomial Representations for Square Roots Modulo $p$
journal: j-DESIGNS-CODES-CRYPTOGR
volume: 28
number: 1
pages: 33--44
month: jan
monthnumber: 1
year: 2003
CODEN: DCCREC
ISSN: 0925-1022 (print), 1573-7586 (electronic) OR 09251022 (print), 15737586 (electronic)
ISSNL: 0925-1022 OR 09251022
bibdate: Thu Dec 11 06:27:20 MST 2003
bibtimestamp: 2003.12.11 06:27:20 MST
fjournal: Designs, codes, and cryptography
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10623
rawauthor: Simon Joseph Agou and Marc Del{\'e}glise and Jean-Louis Nicolas
rawtitle: Short Polynomial Representations for Square Roots Modulo $p$
bibsource:
http://www.wkap.nl/jrnltoc.htm/0925-1022; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib

URL:
http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/fulltext.pdf

entry:
@Article{Agou:2003:SPR,
  author =       "Simon Joseph Agou and Marc Del{\'e}glise and
                 Jean-Louis Nicolas",
  title =        "Short Polynomial Representations for Square Roots
                 Modulo $p$",
  journal =      j-DESIGNS-CODES-CRYPTOGR,
  volume =       "28",
  number =       "1",
  pages =        "33--44",
  month =        jan,
  year =         "2003",
  CODEN =        "DCCREC",
  ISSN =         "0925-1022 (print), 1573-7586 (electronic)",
  ISSN-L =       "0925-1022",
  bibdate =      "Thu Dec 11 06:27:20 MST 2003",
  bibsource =    "http://www.wkap.nl/jrnltoc.htm/0925-1022;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/4630/45/2/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Designs, codes, and cryptography",
  journal-URL =  "http://link.springer.com/journal/10623",
}


bibtype: article
filename: elefunt.bib
label: Alzer:2003:GHM
author: Horst Alzer
title: On Gautschi's harmonic mean inequality for the gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 157
number: 1
pages: 243--249
day: 1
month: aug
monthnumber: 8
year: 2003
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:37 MST 2017
bibtimestamp: 2017.02.25 12:52:37 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042703004564
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Horst Alzer
rawtitle: On {Gautschi}'s harmonic mean inequality for the gamma function
entry:
@Article{Alzer:2003:GHM,
  author =       "Horst Alzer",
  title =        "On {Gautschi}'s harmonic mean inequality for the gamma
                 function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "157",
  number =       "1",
  pages =        "243--249",
  day =          "1",
  month =        aug,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:37 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042703004564",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Beaumont:2003:BSE
author: James Beaumont and Russell Bradford and James H. Davenport
booktitle: Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation
title: Better simplification of elementary functions through power series
publisher: pub-ACM
address: pub-ACM:adr
pages: 30--36 (electronic)
year: 2003
MRclass: 33F10 (68W30)
MRnumber: MR2035192 (2005e:33018)
MRreviewer: Ekatherina A. Karatsuba
bibdate: Wed Apr 13 06:46:35 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.04.13 06:46:35 ???
acknowledgement: ack-nhfb
rawauthor: James Beaumont and Russell Bradford and James H. Davenport
rawbooktitle: Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation
rawtitle: Better simplification of elementary functions through power series
remark:
A new algorithm testing the correctness of simplifications of elementary functions in the presence of branch cuts is proposed.

entry:
@InProceedings{Beaumont:2003:BSE,
  author =       "James Beaumont and Russell Bradford and James H.
                 Davenport",
  booktitle =    "Proceedings of the 2003 International Symposium on
                 Symbolic and Algebraic Computation",
  title =        "Better simplification of elementary functions through
                 power series",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  pages =        "30--36 (electronic)",
  year =         "2003",
  MRclass =      "33F10 (68W30)",
  MRnumber =     "MR2035192 (2005e:33018)",
  MRreviewer =   "Ekatherina A. Karatsuba",
  bibdate =      "Wed Apr 13 06:46:35 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  remark =       "A new algorithm testing the correctness of
                 simplifications of elementary functions in the presence
                 of branch cuts is proposed.",
}


bibtype: article
filename: elefunt.bib
label: Buhring:2003:PSH
author: Wolfgang Buhring
title: Partial sums of hypergeometric functions of unit argument
journal: j-PROC-AM-MATH-SOC
volume: 132
number: 2
pages: 407--415
year: 2003
CODEN: PAMYAR
ISSN: 0002-9939 (print), 1088-6826 (electronic) OR 00029939 (print), 10886826 (electronic)
ISSNL: 0002-9939 OR 00029939
MRclass: 33C20
MRnumber: MR2022363 (2005f:33011)
bibdate: Thu Dec 01 09:53:54 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.12.01 09:53:54 ???
fjournal: Proceedings of the American Mathematical Society
acknowledgement: ack-nhfb
journalURL: http://www.ams.org/journals/proc
rawauthor: Wolfgang B{\"u}hring
rawtitle: Partial sums of hypergeometric functions of unit argument
entry:
@Article{Buhring:2003:PSH,
  author =       "Wolfgang B{\"u}hring",
  title =        "Partial sums of hypergeometric functions of unit
                 argument",
  journal =      j-PROC-AM-MATH-SOC,
  volume =       "132",
  number =       "2",
  pages =        "407--415",
  month =        "????",
  year =         "2003",
  CODEN =        "PAMYAR",
  ISSN =         "0002-9939 (print), 1088-6826 (electronic)",
  ISSN-L =       "0002-9939",
  MRclass =      "33C20",
  MRnumber =     "MR2022363 (2005f:33011)",
  bibdate =      "Thu Dec 01 09:53:54 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Proceedings of the American Mathematical Society",
  journal-URL =  "http://www.ams.org/journals/proc",
}


bibtype: article
filename: elefunt.bib
label: Chiani:2003:NEB
author: M. Chiani and D. Dardari and M. K. Simon
journal: j-IEEE-TRANS-WIREL-COMMUN
volume: 24
number: 5
pages: 840--845
month: may
monthnumber: 5
year: 2003
CODEN: ITWCAX
DOI: https://doi.org/10.1109/twc.2003.814350
ISSN: 1536-1276 (print), 1558-2248 (electronic) OR 15361276 (print), 15582248 (electronic)
ISSNL: 1536-1276 OR 15361276
bibdate: Sat Dec 16 15:47:42 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.12.16 15:47:42 ???
URL: http://ieeexplore.ieee.org/document/1210748/
fjournal: IEEE Transactions on Wireless Communications
acknowledgement: ack-nhfb
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7693
rawauthor: M. Chiani and D. Dardari and M. K. Simon
title:
New exponential bounds and approximations for the computation of error probability in fading channels

rawtitle:
New exponential bounds and approximations for the computation of error probability in fading channels

entry:
@Article{Chiani:2003:NEB,
  author =       "M. Chiani and D. Dardari and M. K. Simon",
  title =        "New exponential bounds and approximations for the
                 computation of error probability in fading channels",
  journal =      j-IEEE-TRANS-WIREL-COMMUN,
  volume =       "24",
  number =       "5",
  pages =        "840--845",
  month =        may,
  year =         "2003",
  CODEN =        "ITWCAX",
  DOI =          "https://doi.org/10.1109/twc.2003.814350",
  ISSN =         "1536-1276 (print), 1558-2248 (electronic)",
  ISSN-L =       "1536-1276",
  bibdate =      "Sat Dec 16 15:47:42 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ieeexplore.ieee.org/document/1210748/",
  acknowledgement = ack-nhfb,
  fjournal =     "IEEE Transactions on Wireless Communications",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7693",
}


bibtype: techreport
filename: elefunt.bib
label: Cornea:2003:DSR
author: M. Cornea and J. Harrison and C. Iordache and B. Norin and S. Story
title: Division, Square Root and Remainder Algorithms for the Intel Itanium Architecture
type: Report
institution: pub-INTEL
address: pub-INTEL:adr
pages: 840--845
month: nov
monthnumber: 11
year: 2003
bibdate: Fri Jun 24 12:05:58 2005
bibtimestamp: 2005.06.24 12:05:58 ???
acknowledgement: ack-nhfb
rawauthor: M. Cornea and J. Harrison and C. Iordache and B. Norin and S. Story
rawtitle: Division, Square Root and Remainder Algorithms for the {Intel Itanium} Architecture
entry:
@TechReport{Cornea:2003:DSR,
  author =       "M. Cornea and J. Harrison and C. Iordache and B. Norin
                 and S. Story",
  title =        "Division, Square Root and Remainder Algorithms for the
                 {Intel Itanium} Architecture",
  type =         "Report",
  institution =  pub-INTEL,
  address =      pub-INTEL:adr,
  month =        nov,
  year =         "2003",
  bibdate =      "Fri Jun 24 12:05:58 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Coussement:2003:AMO
author: Els Coussement and Walter Van Assche
journal: j-J-COMPUT-APPL-MATH
volume: 153
number: 1--2
pages: 141--149
day: 1
month: apr
monthnumber: 4
year: 2003
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:34 MST 2017
bibtimestamp: 2017.02.25 12:52:34 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042702005964
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Els Coussement and Walter {Van Assche}
title:
Asymptotics of multiple orthogonal polynomials associated with the modified Bessel functions of the first kind

rawtitle:
Asymptotics of multiple orthogonal polynomials associated with the modified {Bessel} functions of the first kind

entry:
@Article{Coussement:2003:AMO,
  author =       "Els Coussement and Walter {Van Assche}",
  title =        "Asymptotics of multiple orthogonal polynomials
                 associated with the modified {Bessel} functions of the
                 first kind",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "153",
  number =       "1--2",
  pages =        "141--149",
  day =          "1",
  month =        apr,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:34 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702005964",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Dominici:2003:NDS
author: Diego Dominici
title: Nested derivatives: a simple method for computing series expansions of inverse functions
journal: j-INT-J-MATH-MATH-SCI
volume: 58
pages: 3699--3715
year: 2003
ISSN: 0161-1712 (print), 1687-0425 (electronic) OR 01611712 (print), 16870425 (electronic)
ISSNL: 0161-1712 OR 01611712
MRclass: 41A58 (33F10)
MRnumber: MR2031140 (2005f:41079)
MRreviewer: Tord H. Ganelius
bibdate: Mon Oct 24 11:37:20 2011
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2011.10.24 11:37:20 ???
URL: http://www2.newpaltz.edu/~dominicd/NESTED14.pdf
fjournal: International Journal of Mathematics and Mathematical Sciences
acknowledgement: ack-nhfb
journalURL: https://www.hindawi.com/journals/ijmms/
rawauthor: Diego Dominici
rawtitle: Nested derivatives: a simple method for computing series expansions of inverse functions
abstract:
We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating the inverses of some special functions.

keywords:
error function, erf(x); incomplete beta function, B(nu,mu,x); incomplete gamma function, gamma(nu,x); logarithm integral, li(x); Maple; sine integral, Si(x)

rawabstract:
We give an algorithm to compute the series expansion for the inverse of a given function. The algorithm is extremely easy to implement and gives the first $N$ terms of the series. We show several examples of its application in calculating the inverses of some special functions.

entry:
@Article{Dominici:2003:NDS,
  author =       "Diego Dominici",
  title =        "Nested derivatives: a simple method for computing
                 series expansions of inverse functions",
  journal =      j-INT-J-MATH-MATH-SCI,
  volume =       "58",
  pages =        "3699--3715",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "0161-1712 (print), 1687-0425 (electronic)",
  ISSN-L =       "0161-1712",
  MRclass =      "41A58 (33F10)",
  MRnumber =     "MR2031140 (2005f:41079)",
  MRreviewer =   "Tord H. Ganelius",
  bibdate =      "Mon Oct 24 11:37:20 2011",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://www2.newpaltz.edu/~dominicd/NESTED14.pdf",
  abstract =     "We give an algorithm to compute the series expansion
                 for the inverse of a given function. The algorithm is
                 extremely easy to implement and gives the first $N$
                 terms of the series. We show several examples of its
                 application in calculating the inverses of some special
                 functions.",
  acknowledgement = ack-nhfb,
  fjournal =     "International Journal of Mathematics and Mathematical
                 Sciences",
  journal-URL =  "https://www.hindawi.com/journals/ijmms/",
  keywords =     "error function, erf(x); incomplete beta function,
                 B(nu,mu,x); incomplete gamma function, gamma(nu,x);
                 logarithm integral, li(x); Maple; sine integral,
                 Si(x)",
}


bibtype: inproceedings
filename: elefunt.bib
label: Ercegovac:2003:DRA
author: M. D. Ercegovac and J.-M. Muller
booktitle: Conference Record of the Thirty-Seventh Asilomar Conference on Signals, Systems and Computers, 2003
title: Digit-recurrence algorithms for division and square root with limited precision primitives
volume: 2
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 1440--1444
year: 2003
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
acknowledgement: ack-nhfb
rawauthor: M. D. Ercegovac and J.-M. Muller
rawbooktitle: Conference Record of the Thirty-Seventh Asilomar Conference on Signals, Systems and Computers, 2003
rawtitle: Digit-recurrence algorithms for division and square root with limited precision primitives
entry:
@InProceedings{Ercegovac:2003:DRA,
  author =       "M. D. Ercegovac and J.-M. Muller",
  booktitle =    "Conference Record of the Thirty-Seventh Asilomar
                 Conference on Signals, Systems and Computers, 2003",
  title =        "Digit-recurrence algorithms for division and square
                 root with limited precision primitives",
  volume =       "2",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "1440--1444",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "We propose a digit-recurrence algorithm for square
                 root using limited-precision multipliers, adders, and
                 table-lookups. The algorithm, except in the
                 initialization, uses the digit-recurrence algorithm for
                 division with limited-precision primitives \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Fabijonas:2003:ACM
author: B. R. Fabijonas and Daniel W. Lozier and J. M. Rappoport
title: Algorithms and Codes for the Macdonald Function: Recent Progress and Comparisons
journal: j-J-COMPUT-APPL-MATH
volume: 161
number: 1
pages: 179--192
year: 2003
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
MRclass: 33F05 (33C10 65D20)
MRnumber: MR2018582
bibdate: Fri Jul 09 06:21:51 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:21:51 ???
URL: http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6596.ps
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: B. R. Fabijonas and Daniel W. Lozier and J. M. Rappoport
rawtitle: Algorithms and Codes for the {Macdonald} Function: Recent Progress and Comparisons
entry:
@Article{Fabijonas:2003:ACM,
  author =       "B. R. Fabijonas and Daniel W. Lozier and J. M.
                 Rappoport",
  title =        "Algorithms and Codes for the {Macdonald} Function:
                 Recent Progress and Comparisons",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "161",
  number =       "1",
  pages =        "179--192",
  month =        "????",
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "33F05 (33C10 65D20)",
  MRnumber =     "MR2018582",
  bibdate =      "Fri Jul 09 06:21:51 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/nistir6596.ps",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Galue:2003:FRG
author: L. Galue and A. Al-Zamel and Shyam L. Kalla
title: Further results on generalized hypergeometric functions
journal: j-APPL-MATH-COMP
volume: 136
number: 1
pages: 17--25
day: 25
month: mar
monthnumber: 3
year: 2003
CODEN: AMHCBQ
ISSN: 0096-3003 (print), 1873-5649 (electronic) OR 00963003 (print), 18735649 (electronic)
ISSNL: 0096-3003 OR 00963003
bibdate: Fri Jan 9 08:40:52 MST 2004
bibtimestamp: 2004.01.09 08:40:52 MST
fjournal: Applied Mathematics and Computation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00963003
rawauthor: L. Galu{\'e} and A. Al-Zamel and Shyam L. Kalla
rawtitle: Further results on generalized hypergeometric functions
bibsource:
https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Galue:2003:FRG,
  author =       "L. Galu{\'e} and A. Al-Zamel and Shyam L. Kalla",
  title =        "Further results on generalized hypergeometric
                 functions",
  journal =      j-APPL-MATH-COMP,
  volume =       "136",
  number =       "1",
  pages =        "17--25",
  day =          "25",
  month =        mar,
  year =         "2003",
  CODEN =        "AMHCBQ",
  ISSN =         "0096-3003 (print), 1873-5649 (electronic)",
  ISSN-L =       "0096-3003",
  bibdate =      "Fri Jan 9 08:40:52 MST 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/applmathcomput2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics and Computation",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00963003",
}


bibtype: article
filename: elefunt.bib
label: Gautschi:2003:EEI
author: W. Gautschi and F. E. Harris and N. M. Temme
title: Expansions of the exponential integral in incomplete gamma functions
journal: j-APPL-MATH-LETT
volume: 16
number: 7
pages: 1095--1099
month: oct
monthnumber: 10
year: 2003
CODEN: AMLEEL
DOI: https://doi.org/10.1016/S0893-9659(03)90100-5
ISSN: 0893-9659 (print), 1873-5452 (electronic) OR 08939659 (print), 18735452 (electronic)
ISSNL: 0893-9659 OR 08939659
MRclass: 33B20
bibdate: Wed Dec 4 10:29:43 2013
bibtimestamp: 2013.12.04 10:29:43 ???
fjournal: Applied Mathematics Letters
ZMnumber: 1058.33002
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/08939659
rawauthor: W. Gautschi and F. E. Harris and N. M. Temme
rawtitle: Expansions of the exponential integral in incomplete gamma functions
bibsource:
https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib

entry:
@Article{Gautschi:2003:EEI,
  author =       "W. Gautschi and F. E. Harris and N. M. Temme",
  title =        "Expansions of the exponential integral in incomplete
                 gamma functions",
  journal =      j-APPL-MATH-LETT,
  volume =       "16",
  number =       "7",
  pages =        "1095--1099",
  month =        oct,
  year =         "2003",
  CODEN =        "AMLEEL",
  DOI =          "https://doi.org/10.1016/S0893-9659(03)90100-5",
  ISSN =         "0893-9659 (print), 1873-5452 (electronic)",
  ISSN-L =       "0893-9659",
  MRclass =      "33B20",
  bibdate =      "Wed Dec 4 10:29:43 2013",
  bibsource =    "https://www.math.utah.edu/pub/bibnet/authors/h/harris-frank-e.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  ZMnumber =     "1058.33002",
  acknowledgement = ack-nhfb,
  fjournal =     "Applied Mathematics Letters",
  journal-URL =  "http://www.sciencedirect.com/science/journal/08939659",
}


bibtype: article
filename: elefunt.bib
label: Gil:2003:CMB
author: Amparo Gil and Javier Segura and Nico M. Temme
journal: j-J-COMPUT-APPL-MATH
volume: 153
number: 1--2
pages: 225--234
day: 1
month: apr
monthnumber: 4
year: 2003
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:34 MST 2017
bibtimestamp: 2017.02.25 12:52:34 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042702006088
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
title:
Computation of the modified Bessel function of the third kind of imaginary orders: uniform Airy-type asymptotic expansion

rawtitle:
Computation of the modified {Bessel} function of the third kind of imaginary orders: uniform {Airy}-type asymptotic expansion

entry:
@Article{Gil:2003:CMB,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computation of the modified {Bessel} function of the
                 third kind of imaginary orders: uniform {Airy}-type
                 asymptotic expansion",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "153",
  number =       "1--2",
  pages =        "225--234",
  day =          "1",
  month =        apr,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:34 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702006088",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Gil:2003:CSF
author: Amparo Gil and Javier Segura and Nico M. Temme
title: Computing Special Functions by Using Quadrature Rules
journal: j-NUMER-ALGORITHMS
volume: 33
number: 1--4
pages: 265--275
month: aug
monthnumber: 8
year: 2003
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Sep 29 08:37:11 MDT 2003
bibsource: http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2003.09.29 08:37:11 MDT
fjournal: Numerical Algorithms
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Amparo Gil and Javier Segura and Nico M. Temme
rawtitle: Computing Special Functions by Using Quadrature Rules
URL:
http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/fulltext.pdf

entry:
@Article{Gil:2003:CSF,
  author =       "Amparo Gil and Javier Segura and Nico M. Temme",
  title =        "Computing Special Functions by Using Quadrature
                 Rules",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "33",
  number =       "1--4",
  pages =        "265--275",
  month =        aug,
  year =         "2003",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Sep 29 08:37:11 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/46/22/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
}


bibtype: article
filename: elefunt.bib
label: Harrison:2003:FVS
author: John Harrison
title: Formal verification of square root algorithms
journal: j-FORM-METHODS-SYST-DES
volume: 22
number: 2
pages: 143--153
month: mar
monthnumber: 3
year: 2003
CODEN: FMSDE6
DOI: https://doi.org/10.1023/A:1022973506233
ISSN: 0925-9856 (print), 1572-8102 (electronic) OR 09259856 (print), 15728102 (electronic)
ISSNL: 0925-9856 OR 09259856
bibdate: Sat Feb 08 08:47:21 2020
bibtimestamp: 2020.02.08 08:47:21 ???
URL: https://dl.acm.org/doi/abs/10.1023/A:1022973506233
fjournal: Formal Methods in System Design
acknowledgement: ack-nhfb
journalURL: https://dl.acm.org/loi/fmsd
rawauthor: John Harrison
rawtitle: Formal verification of square root algorithms
bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/fparith.bib; https://www.math.utah.edu/pub/tex/bib/intel-ia-64.bib

abstract:
We discuss the formal verification of some low-level mathematical software for the Intel Itanium architecture. A number of important algorithms have been proven correct using the HOL Light theorem prover. After briefly surveying some of our formal verification work, we discuss in more detail the verification of a square root algorithm, which helps to illustrate why some features of HOL Light, in particular programmability, make it especially suitable for these applications.

rawabstract:
We discuss the formal verification of some low-level mathematical software for the Intel Itanium architecture. A number of important algorithms have been proven correct using the HOL Light theorem prover. After briefly surveying some of our formal verification work, we discuss in more detail the verification of a square root algorithm, which helps to illustrate why some features of HOL Light, in particular programmability, make it especially suitable for these applications.

entry:
@Article{Harrison:2003:FVS,
  author =       "John Harrison",
  title =        "Formal verification of square root algorithms",
  journal =      j-FORM-METHODS-SYST-DES,
  volume =       "22",
  number =       "2",
  pages =        "143--153",
  month =        mar,
  year =         "2003",
  CODEN =        "FMSDE6",
  DOI =          "https://doi.org/10.1023/A:1022973506233",
  ISSN =         "0925-9856 (print), 1572-8102 (electronic)",
  ISSN-L =       "0925-9856",
  bibdate =      "Sat Feb 08 08:47:21 2020",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib;
                 https://www.math.utah.edu/pub/tex/bib/intel-ia-64.bib",
  URL =          "https://dl.acm.org/doi/abs/10.1023/A:1022973506233",
  abstract =     "We discuss the formal verification of some low-level
                 mathematical software for the Intel Itanium
                 architecture. A number of important algorithms have
                 been proven correct using the HOL Light theorem prover.
                 After briefly surveying some of our formal verification
                 work, we discuss in more detail the verification of a
                 square root algorithm, which helps to illustrate why
                 some features of HOL Light, in particular
                 programmability, make it especially suitable for these
                 applications.",
  acknowledgement = ack-nhfb,
  fjournal =     "Formal Methods in System Design",
  journal-URL =  "https://dl.acm.org/loi/fmsd",
}


bibtype: misc
filename: elefunt.bib
label: Intel:2003:DSR
author: Intel
title: Divide, Square Root, and Remainder Algorithms for the Itanium Architecture
pages: 143--153
day: 18
month: dec
monthnumber: 12
year: 2003
bibdate: Tue Nov 18 16:23:36 2008
bibtimestamp: 2008.11.18 16:23:36 ???
URL: http://www.intel.com/cd/software/products/asmo-na/eng/219863.htm
acknowledgement: ack-nhfb
howpublished: Intel Software Development Products
rawauthor: {Intel}
rawtitle: Divide, Square Root, and Remainder Algorithms for the {Itanium} Architecture
entry:
@Misc{Intel:2003:DSR,
  author =       "{Intel}",
  title =        "Divide, Square Root, and Remainder Algorithms for the
                 {Itanium} Architecture",
  howpublished = "Intel Software Development Products",
  day =          "18",
  month =        dec,
  year =         "2003",
  bibdate =      "Tue Nov 18 16:23:36 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.intel.com/cd/software/products/asmo-na/eng/219863.htm",
  acknowledgement = ack-nhfb,
}


bibtype: misc
filename: elefunt.bib
label: Intel:2003:NID
author: Intel
pages: 143--153
day: 18
month: dec
monthnumber: 12
year: 2003
bibdate: Tue Nov 18 16:23:36 2008
bibtimestamp: 2008.11.18 16:23:36 ???
URL: http://www.intel.com/cd/software/products/asmo-na/eng/219864.htm
acknowledgement: ack-nhfb
howpublished: Intel Software Development Products
rawauthor: {Intel}
title:
Non-IEEE Division, Square Root, Reciprocal, and Reciprocal Square Root Algorithms for the Intel Itanium Architecture

rawtitle:
Non-{IEEE} Division, Square Root, Reciprocal, and Reciprocal Square Root Algorithms for the {Intel Itanium} Architecture

entry:
@Misc{Intel:2003:NID,
  author =       "{Intel}",
  title =        "Non-{IEEE} Division, Square Root, Reciprocal, and
                 Reciprocal Square Root Algorithms for the {Intel
                 Itanium} Architecture",
  howpublished = "Intel Software Development Products",
  day =          "18",
  month =        dec,
  year =         "2003",
  bibdate =      "Tue Nov 18 16:23:36 2008",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/fparith.bib",
  URL =          "http://www.intel.com/cd/software/products/asmo-na/eng/219864.htm",
  acknowledgement = ack-nhfb,
}


bibtype: article
filename: elefunt.bib
label: Kzaz:2003:CAG
author: M. Kzaz and M. Prevost
title: Convergence Acceleration of Gauss--Chebyshev Quadrature Formulae
journal: j-NUMER-ALGORITHMS
volume: 34
number: 2--4
pages: 379--391
month: dec
monthnumber: 12
year: 2003
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Tue Jan 13 17:32:50 MST 2004
bibsource: http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.01.13 17:32:50 MST
fjournal: Numerical Algorithms
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: M. Kzaz and M. Pr{\'e}vost
rawtitle: Convergence Acceleration of {Gauss--Chebyshev} Quadrature Formulae
URL:
http://ipsapp007.kluweronline.com/content/getfile/5058/48/6/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/48/6/fulltext.pdf

entry:
@Article{Kzaz:2003:CAG,
  author =       "M. Kzaz and M. Pr{\'e}vost",
  title =        "Convergence Acceleration of {Gauss--Chebyshev}
                 Quadrature Formulae",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "34",
  number =       "2--4",
  pages =        "379--391",
  month =        dec,
  year =         "2003",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Tue Jan 13 17:32:50 MST 2004",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/48/6/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/48/6/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Lang:2003:RRS
author: Tomas Lang and Elisardo Antelo
title: Radix-$4$ Reciprocal Square-root and Its Combination with Division and Square Root
journal: j-IEEE-TRANS-COMPUT
volume: 52
number: 9
pages: 1100--1114
month: sep
monthnumber: 9
year: 2003
CODEN: ITCOB4
DOI: https://doi.org/10.1109/TC.2003.1228508
ISSN: 0018-9340 (print), 1557-9956 (electronic) OR 00189340 (print), 15579956 (electronic)
ISSNL: 0018-9340 OR 00189340
bibdate: Sat Jul 16 15:28:13 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:13 MDT
fjournal: IEEE Transactions on Computers
acknowledgement: ack-nhfb
ajournal: IEEE Trans. Comput.
journalURL: http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12
rawauthor: Tom{\'a}s Lang and Elisardo Antelo
rawtitle: Radix-$4$ Reciprocal Square-root and Its Combination with Division and Square Root
abstract:
In this work, we present a reciprocal square root algorithm by digit recurrence and selection by a staircase function and the radix-$4$ implementation. As in similar algorithms for division and square root, the results are obtained correctly rounded in a straightforward manner (in contrast to existing methods to compute the reciprocal square root). Although, apparently, a single selection function can only be used for $ j geq 2 $ (the selection constants are different for $ j = 0 $, $ j = 1 $, and $ j geq 2 $ ), we show that it is possible to use a single selection function for all iterations. We perform a rough comparison with existing methods and we conclude that our implementation is a low hardware complexity solution with moderate latency, especially for exactly rounded results. We also extend the unit to support division and square root with the same selection function and with slight modifications in the initialization of the reciprocal square root unit.

rawabstract:
In this work, we present a reciprocal square root algorithm by digit recurrence and selection by a staircase function and the radix-$4$ implementation. As in similar algorithms for division and square root, the results are obtained correctly rounded in a straightforward manner (in contrast to existing methods to compute the reciprocal square root). Although, apparently, a single selection function can only be used for $ j \geq 2 $ (the selection constants are different for $ j = 0 $, $ j = 1 $, and $ j \geq 2 $ ), we show that it is possible to use a single selection function for all iterations. We perform a rough comparison with existing methods and we conclude that our implementation is a low hardware complexity solution with moderate latency, especially for exactly rounded results. We also extend the unit to support division and square root with the same selection function and with slight modifications in the initialization of the reciprocal square root unit.

entry:
@Article{Lang:2003:RRS,
  author =       "Tom{\'a}s Lang and Elisardo Antelo",
  title =        "Radix-$4$ Reciprocal Square-root and Its Combination
                 with Division and Square Root",
  journal =      j-IEEE-TRANS-COMPUT,
  volume =       "52",
  number =       "9",
  pages =        "1100--1114",
  month =        sep,
  year =         "2003",
  CODEN =        "ITCOB4",
  DOI =          "https://doi.org/10.1109/TC.2003.1228508",
  ISSN =         "0018-9340 (print), 1557-9956 (electronic)",
  ISSN-L =       "0018-9340",
  bibdate =      "Sat Jul 16 15:28:13 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "In this work, we present a reciprocal square root
                 algorithm by digit recurrence and selection by a
                 staircase function and the radix-$4$ implementation. As
                 in similar algorithms for division and square root, the
                 results are obtained correctly rounded in a
                 straightforward manner (in contrast to existing methods
                 to compute the reciprocal square root). Although,
                 apparently, a single selection function can only be
                 used for $ j \geq 2 $ (the selection constants are
                 different for $ j = 0 $, $ j = 1 $, and $ j \geq 2 $ ),
                 we show that it is possible to use a single selection
                 function for all iterations. We perform a rough
                 comparison with existing methods and we conclude that
                 our implementation is a low hardware complexity
                 solution with moderate latency, especially for exactly
                 rounded results. We also extend the unit to support
                 division and square root with the same selection
                 function and with slight modifications in the
                 initialization of the reciprocal square root unit.",
  acknowledgement = ack-nhfb,
  ajournal =     "IEEE Trans. Comput.",
  fjournal =     "IEEE Transactions on Computers",
  journal-URL =  "http://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=12",
}


bibtype: techreport
filename: elefunt.bib
label: Lefevre:2003:WCC
author: Vincent Lefevre and Jean-Michel Muller
title: Worst Cases for Correct Rounding for the Elementary Functions in Double Precision
type: Technical report
institution: INRIA, Projet Spaces, LORIA, Campus Scientifique
address: B.P. 239, 54506 Vandoeuvre-les-Nancy Cedex, France
pages: 1100--1114
day: 14
month: aug
monthnumber: 8
year: 2003
bibdate: Thu Jul 08 08:27:53 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.08 08:27:53 ???
URL: http://perso.ens-lyon.fr/jean-michel.muller/TMDworstcases.pdf
keywords: computer arithmetic; elementary functions; floating-point arithmetic; Table Maker's Dilemma
acknowledgement: ack-nhfb
rawauthor: Vincent Lef{\`e}vre and Jean-Michel Muller
rawtitle: Worst Cases for Correct Rounding for the Elementary Functions in Double Precision
abstract:
We give the results of our search for the worst cases for correct rounding of the major elementary functions in double precision floating-point arithmetic. These results allow the design of reasonably fast routines that will compute these functions with correct rounding, at least in some interval, for any of the four rounding modes specified by the IEEE-754 standard. They will also allow one to easily test libraries that are claimed to provide correctly rounded functions.

rawabstract:
We give the results of our search for the worst cases for correct rounding of the major elementary functions in double precision floating-point arithmetic. These results allow the design of reasonably fast routines that will compute these functions with correct rounding, at least in some interval, for any of the four rounding modes specified by the IEEE-754 standard. They will also allow one to easily test libraries that are claimed to provide correctly rounded functions.

entry:
@TechReport{Lefevre:2003:WCC,
  author =       "Vincent Lef{\`e}vre and Jean-Michel Muller",
  title =        "Worst Cases for Correct Rounding for the Elementary
                 Functions in Double Precision",
  type =         "Technical report",
  institution =  "INRIA, Projet Spaces, LORIA, Campus Scientifique",
  address =      "B.P. 239, 54506 Vandoeuvre-l{\`e}s-Nancy Cedex,
                 France",
  day =          "14",
  month =        aug,
  year =         "2003",
  bibdate =      "Thu Jul 08 08:27:53 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://perso.ens-lyon.fr/jean-michel.muller/TMDworstcases.pdf",
  abstract =     "We give the results of our search for the worst cases
                 for correct rounding of the major elementary functions
                 in double precision floating-point arithmetic. These
                 results allow the design of reasonably fast routines
                 that will compute these functions with correct
                 rounding, at least in some interval, for any of the
                 four rounding modes specified by the IEEE-754 standard.
                 They will also allow one to easily test libraries that
                 are claimed to provide correctly rounded functions.",
  acknowledgement = ack-nhfb,
  keywords =     "computer arithmetic; elementary functions;
                 floating-point arithmetic; Table Maker's Dilemma",
}


bibtype: article
filename: elefunt.bib
label: Lozier:2003:NDL
author: Daniel W. Lozier
title: NIST Digital Library of Mathematical Functions
journal: j-ANN-MATH-ARTIF-INTELL
volume: 38
number: 1--3
pages: 105--119
month: may
monthnumber: 5
year: 2003
CODEN: AMAIEC
ISSN: 1012-2443 (print), 1573-7470 (electronic) OR 10122443 (print), 15737470 (electronic)
ISSNL: 1012-2443 OR 10122443
bibdate: Fri Jul 09 06:23:08 2004
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2004.07.09 06:23:08 ???
URL: http://math.nist.gov/acmd/Staff/DLozier/publications/Linz01.ps
fjournal: Annals of Mathematics and Artificial Intelligence
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/10472
rawauthor: Daniel W. Lozier
rawtitle: {NIST Digital Library of Mathematical Functions}
entry:
@Article{Lozier:2003:NDL,
  author =       "Daniel W. Lozier",
  title =        "{NIST Digital Library of Mathematical Functions}",
  journal =      j-ANN-MATH-ARTIF-INTELL,
  volume =       "38",
  number =       "1--3",
  pages =        "105--119",
  month =        may,
  year =         "2003",
  CODEN =        "AMAIEC",
  ISSN =         "1012-2443 (print), 1573-7470 (electronic)",
  ISSN-L =       "1012-2443",
  bibdate =      "Fri Jul 09 06:23:08 2004",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://math.nist.gov/acmd/Staff/DLozier/publications/Linz01.ps",
  acknowledgement = ack-nhfb,
  fjournal =     "Annals of Mathematics and Artificial Intelligence",
  journal-URL =  "http://link.springer.com/journal/10472",
}


bibtype: inproceedings
filename: elefunt.bib
label: Markstein:2003:FQP
author: Peter Markstein
title: A fast quad precision elementary function library for Itanium
crossref: Anonymous:2003:CRN
pages: 5--12
year: 2003
bibdate: Fri Jun 24 20:14:39 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.06.24 20:14:39 ???
acknowledgement: ack-nhfb
rawauthor: Peter Markstein
rawtitle: A fast quad precision elementary function library for {Itanium}
abstract:
This talk will describe Itanium's floating point architecture and how it has been used to produce a high performance, highly accurate quad precision elementary function library.par Itanium's floating-point features will first be described, from the point of view of a computer architect. Many conflicting requirements vie for consideration during the design of a new computer architecture. These include instruction word size, number of registers, the set of operations, arithmetic precisions supported, and memory access. Some of the trade-offs during the design phase will be discussed.par One of the objectives of the original Itanium design was to accelerate quad precision arithmetic. The talk will describe how the Itanium elementary function library was constructed, with attention to performance and accuracy. Because a pair of double-extended floating point words are used for internal operations involving quad precision numbers, intermediate results, holding 128 bits, provide 15 guard bits during intermediate calculations, resulting in a very low percentage of misrounded results.

rawabstract:
This talk will describe Itanium's floating point architecture and how it has been used to produce a high performance, highly accurate quad precision elementary function library.\par Itanium's floating-point features will first be described, from the point of view of a computer architect. Many conflicting requirements vie for consideration during the design of a new computer architecture. These include instruction word size, number of registers, the set of operations, arithmetic precisions supported, and memory access. Some of the trade-offs during the design phase will be discussed.\par One of the objectives of the original Itanium design was to accelerate quad precision arithmetic. The talk will describe how the Itanium elementary function library was constructed, with attention to performance and accuracy. Because a pair of double-extended floating point words are used for internal operations involving quad precision numbers, intermediate results, holding 128 bits, provide 15 guard bits during intermediate calculations, resulting in a very low percentage of misrounded results.

entry:
@InProceedings{Markstein:2003:FQP,
  author =       "Peter Markstein",
  title =        "A fast quad precision elementary function library for
                 {Itanium}",
  crossref =     "Anonymous:2003:CRN",
  pages =        "5--12",
  year =         "2003",
  bibdate =      "Fri Jun 24 20:14:39 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "This talk will describe Itanium's floating point
                 architecture and how it has been used to produce a high
                 performance, highly accurate quad precision elementary
                 function library.\par

                 Itanium's floating-point features will first be
                 described, from the point of view of a computer
                 architect. Many conflicting requirements vie for
                 consideration during the design of a new computer
                 architecture. These include instruction word size,
                 number of registers, the set of operations, arithmetic
                 precisions supported, and memory access. Some of the
                 trade-offs during the design phase will be
                 discussed.\par

                 One of the objectives of the original Itanium design
                 was to accelerate quad precision arithmetic. The talk
                 will describe how the Itanium elementary function
                 library was constructed, with attention to performance
                 and accuracy. Because a pair of double-extended
                 floating point words are used for internal operations
                 involving quad precision numbers, intermediate results,
                 holding 128 bits, provide 15 guard bits during
                 intermediate calculations, resulting in a very low
                 percentage of misrounded results.",
  acknowledgement = ack-nhfb,
}


bibtype: book
filename: elefunt.bib
label: Mason:2003:CP
author: J. C. Mason and D. C. Handscomb
title: Chebyshev Polynomials
publisher: pub-CHAPMAN-HALL-CRC
address: pub-CHAPMAN-HALL-CRC:adr
pages: xiii + 341
year: 2003
ISBN: 0-8493-0355-9 OR 0849303559
ISBN13: 978-0-8493-0355-5 OR 9780849303555
LCCN: QA404.5 .M37 2003
bibdate: Fri Apr 17 09:45:35 MDT 2009
bibtimestamp: 2009.04.17 09:45:35 MDT
subject: Chebyshev polynomials
acknowledgement: ack-nhfb
rawauthor: J. C. Mason and D. C. Handscomb
rawtitle: {Chebyshev} Polynomials
TOC:
1 Definitions / 1 1.1 Preliminary remarks / 1 1.2 Trigonometric definitions and recurrences / 1 1.2.1 The first-kind polynomial $T_n$ / 2 1.2.2 The second-kind polynomial $U_n$ / 3 1.2.3 The third- and fourth-kind polynomials $V_n$ and $W_n$ (the airfoil polynomials) / 5 1.2.4 Connections between the four kinds of polynomial / 7 1.3 Shifted Chebyshev polynomials / 9 1.3.1 The shifted polynomials $T_n^*$, $U_n^*$, $V_n^*$, $W_n^*$ / 9 1.3.2 Chebyshev polynomials for the general range $[a, b]$ / 11 1.4 Chebyshev polynomials of a complex variable / 11 1.4.1 Conformal mapping of a circle to and from an ellipse / 12 1.4.2 Chebyshev polynomials in $z$ / 14 1.4.3 Shabat polynomials / 17 1.5 Problems for Chapter 1 / 17 2 Basic Properties and Formulae / 19 2.1 Introduction / 19 2.2 Chebyshev polynomial zeros and extrema / 19 2.3 Relations between Chebyshev polynomials and powers of x / 22 2.3.1 Powers of $x$ in terms of $T_n(x)$ / 22 2.3.2 $T_n(x)$ in terms of powers of $x$ / 23 2.3.3 Ratios of coefficients in $T_n(x)$ / 25 2.4 Evaluation of Chebyshev sums, products, integrals and derivatives / 25 2.4.1 Evaluation of a Chebyshev sum / 25 2.4.2 Stability of the evaluation of a Chebyshev sum / 29 2.4.3 Evaluation of a product / 31 2.4.4 Evaluation of an integral / 32 2.4.5 Evaluation of a derivative / 34 6.3.1 Aliasing / 152 6.3.2 Second-kind interpolation / 155 6.3.3 Third- and fourth-kind interpolation / 156 6.3.4 Conditioning / 158 6.4 Best $mathcal L_1$ approximation by Chebyshev interpolation / 158 6.5 Near-minimax approximation by Chebyshev interpolation / 160 6.6 Problems for Chapter 6 / 162 7 Near-Best $mathcal L_infty $, $mathcal L_1$ and $mathcal L_p$ Approximations / 165 7.1 Near-best $mathcal L_infty $ (near-minimax) approximations / 165 7.1.1 Second-kind expansions in $mathcal L_infty $ / 165 7.1.2 Third-kind expansions in $mathcal L_infty $ / 167 7.2 Near-best $mathcal L_1$ approximations / 169 7.3 Best and near-best $mathcal L_p$ approximations / 170 7.3.1 Complex variable results for elliptic-type regions / 172 7.4 Problems for Chapter 7 / 173 8 Integration Using Chebyshev Polynomials / 177 8.1 Indefinite integration with Chebyshev series / 177 8.2 Gauss--Chebyshev quadrature / 180 8.3 Quadrature methods of Clenshaw--Curtis type / 186 8.3.1 Introduction / 186 8.3.2 First-kind formulae / 187 8.3.3 Second-kind formulae / 189 8.3.4 Third-kind formulae / 191 8.3.5 General remark on methods of Clenshaw--Curtis type / 192 8.4 Error estimation for Clenshaw--Curtis methods / 192 8.4.1 First-kind polynomials / 193 8.4.2 Fitting an exponential curve / 195 8.4.3 Other abscissae and polynomials / 196 8.5 Some other work on Clenshaw--Curtis methods / 200 8.6 Problems for Chapter 8 / 201 9 Solution of Integral Equations / 203 9.1 Introduction / 203 9.2 Fredholm equations of the second kind / 204 9.3 Fredholm equations of the third kind / 206 9.4 Fredholm equations of the first kind / 207 9.5 Singular kernels / 209 9.5.1 Hilbert-type kernels and related kernels / 209 9.5.2 Symm's integral equation / 212 9.6 Regularisation of integral equations / 214 9.6.1 Discrete data with second derivative regularisation / 214 9.6.2 Details of a smoothing algorithm (second derivative regularisation) / 215 9.6.3 A smoothing algorithm with weighted function regularisation / 217 9.6.4 Evaluation of $V(lambda )$ / 220 9.6.5 Other basis functions / 221 9.7 Partial differential equations and boundary integral equation methods / 222 9.7.1 A hypersingular integral equation derived from a mixed boundary value problem for Laplace's equation / 222 9.8 Problems for Chapter 9 / 227 10 Solution of Ordinary Differential Equations / 231 10.1 Introduction / 231 10.2 A simple example / 232 10.2.1 Collocation methods / 234 10.2.2 Error of the collocation method / 237 10.2.3 Projection (tau) methods / 239 10.2.4 Error of the preceding projection method / 241 10.3 The original Lanczos tau ($tau $) method / 242 10.4 A more general linear equation / 244 10.4.1 Collocation method / 244 10.4.2 Projection method / 245 10.5 Pseudospectral methods --- another form of collocation / 245 10.5.1 Differentiation matrices / 246 10.5.2 Differentiation matrix for Chebyshev points / 247 10.5.3 Collocation using differentiation matrices / 249 10.6 Nonlinear equations / 251 10.7 Eigenvalue problems / 252 10.7.1 Collocation methods / 252 10.7.2 Collocation using the differentiation matrix / 254 10.8 Differential equations in one space and one time dimension / 256 10.8.1 Collocation methods / 257 10.8.2 Collocation using the differentiation matrix / 258 10.9 Problems for Chapter 10 / 259 11 Chebyshev and Spectral Methods for Partial Differential Equations / 261 11.1 Introduction / 261 11.2 Interior, boundary and mixed methods / 262 11.2.1 Interior methods / 262 11.2.2 Boundary methods / 263 11.2.3 Mixed methods / 265 11.3 Differentiation matrices and nodal representation / 265 11.4 Method of weighted residuals / 265 11.4.1 Continuous MWR / 265 11.4.2 Discrete MWR --- a new nomenclature / 266 11.5 Chebyshev series and Galerkin methods / 267 11.6 Collocation/interpolation and related methods / 269 11.7 PDE methods / 271 11.7.1 Error analysis / 272 11.8 Some PDE problems and various methods / 272 11.8.1 Power basis: collocation for Poisson problem / 273 11.8.2 Power basis: interior collocation for the L-membrane / 275 11.8.3 Chebyshev basis and discrete orthogonalisation / 278 11.8.4 Differentiation matrix approach: Poisson problem / 281 11.8.5 Explicit collocation for the quasilinear Dirichlet problem: Chebyshev basis / 283 11.9 Computational fluid dynamics / 295 11.10 Particular issues in spectral methods / 296 11.11 More advanced problems / 297 11.12 Problems for Chapter 11 / 298 12 Conclusion / 303 Bibliography / 305 Appendices: A Biographical Note / 321 B Summary of Notations, Definitions and Important Properties / 323 B.I Miscellaneous notations / 323 B.2 The four kinds of Chebyshev polynomial / 325 C Tables of Coefficients / 329 Index / 335

rawTOC:
1 Definitions / 1 \\ 1.1 Preliminary remarks / 1 \\ 1.2 Trigonometric definitions and recurrences / 1 \\ 1.2.1 The first-kind polynomial $T_n$ / 2 \\ 1.2.2 The second-kind polynomial $U_n$ / 3 \\ 1.2.3 The third- and fourth-kind polynomials $V_n$ and $W_n$ (the airfoil polynomials) / 5 \\ 1.2.4 Connections between the four kinds of polynomial / 7 \\ 1.3 Shifted Chebyshev polynomials / 9 \\ 1.3.1 The shifted polynomials $T_n^*$, $U_n^*$, $V_n^*$, $W_n^*$ / 9 \\ 1.3.2 Chebyshev polynomials for the general range $[a, b]$ / 11 \\ 1.4 Chebyshev polynomials of a complex variable / 11 \\ 1.4.1 Conformal mapping of a circle to and from an ellipse / 12 \\ 1.4.2 Chebyshev polynomials in $z$ / 14 \\ 1.4.3 Shabat polynomials / 17 \\ 1.5 Problems for Chapter 1 / 17 \\ 2 Basic Properties and Formulae / 19 \\ 2.1 Introduction / 19 \\ 2.2 Chebyshev polynomial zeros and extrema / 19 \\ 2.3 Relations between Chebyshev polynomials and powers of x / 22 \\ 2.3.1 Powers of $x$ in terms of $\{T_n(x)\}$ / 22 \\ 2.3.2 $T_n(x)$ in terms of powers of $x$ / 23 \\ 2.3.3 Ratios of coefficients in $T_n(x)$ / 25 \\ 2.4 Evaluation of Chebyshev sums, products, integrals and derivatives / 25 \\ 2.4.1 Evaluation of a Chebyshev sum / 25 \\ 2.4.2 Stability of the evaluation of a Chebyshev sum / 29 \\ 2.4.3 Evaluation of a product / 31 \\ 2.4.4 Evaluation of an integral / 32 \\ 2.4.5 Evaluation of a derivative / 34 \\ 6.3.1 Aliasing / 152 \\ 6.3.2 Second-kind interpolation / 155 \\ 6.3.3 Third- and fourth-kind interpolation / 156 \\ 6.3.4 Conditioning / 158 \\ 6.4 Best $\mathcal{L}_1$ approximation by Chebyshev interpolation / 158 \\ 6.5 Near-minimax approximation by Chebyshev interpolation / 160 \\ 6.6 Problems for Chapter 6 / 162 \\ 7 Near-Best $\mathcal{L}_\infty$, $\mathcal{L}_1$ and $\mathcal{L}_p$ Approximations / 165 \\ 7.1 Near-best $\mathcal{L}_\infty$ (near-minimax) approximations / 165 \\ 7.1.1 Second-kind expansions in $\mathcal{L}_\infty$ / 165 \\ 7.1.2 Third-kind expansions in $\mathcal{L}_\infty$ / 167 \\ 7.2 Near-best $\mathcal{L}_1$ approximations / 169 \\ 7.3 Best and near-best $\mathcal{L}_p$ approximations / 170 \\ 7.3.1 Complex variable results for elliptic-type regions / 172 \\ 7.4 Problems for Chapter 7 / 173 \\ 8 Integration Using Chebyshev Polynomials / 177 \\ 8.1 Indefinite integration with Chebyshev series / 177 \\ 8.2 Gauss--Chebyshev quadrature / 180 \\ 8.3 Quadrature methods of Clenshaw--Curtis type / 186 \\ 8.3.1 Introduction / 186 \\ 8.3.2 First-kind formulae / 187 \\ 8.3.3 Second-kind formulae / 189 \\ 8.3.4 Third-kind formulae / 191 \\ 8.3.5 General remark on methods of Clenshaw--Curtis type / 192 \\ 8.4 Error estimation for Clenshaw--Curtis methods / 192 \\ 8.4.1 First-kind polynomials / 193 \\ 8.4.2 Fitting an exponential curve / 195 \\ 8.4.3 Other abscissae and polynomials / 196 \\ 8.5 Some other work on Clenshaw--Curtis methods / 200 \\ 8.6 Problems for Chapter 8 / 201 \\ 9 Solution of Integral Equations / 203 \\ 9.1 Introduction / 203 \\ 9.2 Fredholm equations of the second kind / 204 \\ 9.3 Fredholm equations of the third kind / 206 \\ 9.4 Fredholm equations of the first kind / 207 \\ 9.5 Singular kernels / 209 \\ 9.5.1 Hilbert-type kernels and related kernels / 209 \\ 9.5.2 Symm's integral equation / 212 \\ 9.6 Regularisation of integral equations / 214 \\ 9.6.1 Discrete data with second derivative regularisation / 214 \\ 9.6.2 Details of a smoothing algorithm (second derivative regularisation) / 215 \\ 9.6.3 A smoothing algorithm with weighted function regularisation / 217 \\ 9.6.4 Evaluation of $V(\lambda)$ / 220 \\ 9.6.5 Other basis functions / 221 \\ 9.7 Partial differential equations and boundary integral equation methods / 222 \\ 9.7.1 A hypersingular integral equation derived from a mixed boundary value problem for Laplace's equation / 222 \\ 9.8 Problems for Chapter 9 / 227 \\ 10 Solution of Ordinary Differential Equations / 231 \\ 10.1 Introduction / 231 \\ 10.2 A simple example / 232 \\ 10.2.1 Collocation methods / 234 \\ 10.2.2 Error of the collocation method / 237 \\ 10.2.3 Projection (tau) methods / 239 \\ 10.2.4 Error of the preceding projection method / 241 \\ 10.3 The original Lanczos tau ($\tau$) method / 242 \\ 10.4 A more general linear equation / 244 \\ 10.4.1 Collocation method / 244 \\ 10.4.2 Projection method / 245 \\ 10.5 Pseudospectral methods --- another form of collocation / 245 \\ 10.5.1 Differentiation matrices / 246 \\ 10.5.2 Differentiation matrix for Chebyshev points / 247 \\ 10.5.3 Collocation using differentiation matrices / 249 \\ 10.6 Nonlinear equations / 251 \\ 10.7 Eigenvalue problems / 252 \\ 10.7.1 Collocation methods / 252 \\ 10.7.2 Collocation using the differentiation matrix / 254 \\ 10.8 Differential equations in one space and one time dimension / 256 \\ 10.8.1 Collocation methods / 257 \\ 10.8.2 Collocation using the differentiation matrix / 258 \\ 10.9 Problems for Chapter 10 / 259 \\ 11 Chebyshev and Spectral Methods for Partial Differential Equations / 261 \\ 11.1 Introduction / 261 \\ 11.2 Interior, boundary and mixed methods / 262 \\ 11.2.1 Interior methods / 262 \\ 11.2.2 Boundary methods / 263 \\ 11.2.3 Mixed methods / 265 \\ 11.3 Differentiation matrices and nodal representation / 265 \\ 11.4 Method of weighted residuals / 265 \\ 11.4.1 Continuous MWR / 265 \\ 11.4.2 Discrete MWR --- a new nomenclature / 266 \\ 11.5 Chebyshev series and Galerkin methods / 267 \\ 11.6 Collocation/interpolation and related methods / 269 \\ 11.7 PDE methods / 271 \\ 11.7.1 Error analysis / 272 \\ 11.8 Some PDE problems and various methods / 272 \\ 11.8.1 Power basis: collocation for Poisson problem / 273 \\ 11.8.2 Power basis: interior collocation for the L-membrane / 275 \\ 11.8.3 Chebyshev basis and discrete orthogonalisation / 278 \\ 11.8.4 Differentiation matrix approach: Poisson problem / 281 \\ 11.8.5 Explicit collocation for the quasilinear Dirichlet problem: Chebyshev basis / 283 \\ 11.9 Computational fluid dynamics / 295 \\ 11.10 Particular issues in spectral methods / 296 \\ 11.11 More advanced problems / 297 \\ 11.12 Problems for Chapter 11 / 298 \\ 12 Conclusion / 303 \\ Bibliography / 305 \\ Appendices: \\ A Biographical Note / 321 \\ B Summary of Notations, Definitions and Important Properties / 323 \\ B.I Miscellaneous notations / 323 \\ B.2 The four kinds of Chebyshev polynomial / 325 \\ C Tables of Coefficients / 329 \\ Index / 335

entry:
@Book{Mason:2003:CP,
  author =       "J. C. Mason and D. C. Handscomb",
  title =        "{Chebyshev} Polynomials",
  publisher =    pub-CHAPMAN-HALL-CRC,
  address =      pub-CHAPMAN-HALL-CRC:adr,
  pages =        "xiii + 341",
  year =         "2003",
  ISBN =         "0-8493-0355-9",
  ISBN-13 =      "978-0-8493-0355-5",
  LCCN =         "QA404.5 .M37 2003",
  bibdate =      "Fri Apr 17 09:45:35 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",
  acknowledgement = ack-nhfb,
  subject =      "Chebyshev polynomials",
  tableofcontents = "1 Definitions / 1 \\
                 1.1 Preliminary remarks / 1 \\
                 1.2 Trigonometric definitions and recurrences / 1 \\
                 1.2.1 The first-kind polynomial $T_n$ / 2 \\
                 1.2.2 The second-kind polynomial $U_n$ / 3 \\
                 1.2.3 The third- and fourth-kind polynomials $V_n$ and
                 $W_n$ (the airfoil polynomials) / 5 \\
                 1.2.4 Connections between the four kinds of polynomial
                 / 7 \\
                 1.3 Shifted Chebyshev polynomials / 9 \\
                 1.3.1 The shifted polynomials $T_n^*$, $U_n^*$,
                 $V_n^*$, $W_n^*$ / 9 \\
                 1.3.2 Chebyshev polynomials for the general range $[a,
                 b]$ / 11 \\
                 1.4 Chebyshev polynomials of a complex variable / 11
                 \\
                 1.4.1 Conformal mapping of a circle to and from an
                 ellipse / 12 \\
                 1.4.2 Chebyshev polynomials in $z$ / 14 \\
                 1.4.3 Shabat polynomials / 17 \\
                 1.5 Problems for Chapter 1 / 17 \\
                 2 Basic Properties and Formulae / 19 \\
                 2.1 Introduction / 19 \\
                 2.2 Chebyshev polynomial zeros and extrema / 19 \\
                 2.3 Relations between Chebyshev polynomials and powers
                 of x / 22 \\
                 2.3.1 Powers of $x$ in terms of $\{T_n(x)\}$ / 22 \\
                 2.3.2 $T_n(x)$ in terms of powers of $x$ / 23 \\
                 2.3.3 Ratios of coefficients in $T_n(x)$ / 25 \\
                 2.4 Evaluation of Chebyshev sums, products, integrals
                 and derivatives / 25 \\
                 2.4.1 Evaluation of a Chebyshev sum / 25 \\
                 2.4.2 Stability of the evaluation of a Chebyshev sum /
                 29 \\
                 2.4.3 Evaluation of a product / 31 \\
                 2.4.4 Evaluation of an integral / 32 \\
                 2.4.5 Evaluation of a derivative / 34 \\
                 6.3.1 Aliasing / 152 \\
                 6.3.2 Second-kind interpolation / 155 \\
                 6.3.3 Third- and fourth-kind interpolation / 156 \\
                 6.3.4 Conditioning / 158 \\
                 6.4 Best $\mathcal{L}_1$ approximation by Chebyshev
                 interpolation / 158 \\
                 6.5 Near-minimax approximation by Chebyshev
                 interpolation / 160 \\
                 6.6 Problems for Chapter 6 / 162 \\
                 7 Near-Best $\mathcal{L}_\infty$, $\mathcal{L}_1$ and
                 $\mathcal{L}_p$ Approximations / 165 \\
                 7.1 Near-best $\mathcal{L}_\infty$ (near-minimax)
                 approximations / 165 \\
                 7.1.1 Second-kind expansions in $\mathcal{L}_\infty$ /
                 165 \\
                 7.1.2 Third-kind expansions in $\mathcal{L}_\infty$ /
                 167 \\
                 7.2 Near-best $\mathcal{L}_1$ approximations / 169 \\
                 7.3 Best and near-best $\mathcal{L}_p$ approximations /
                 170 \\
                 7.3.1 Complex variable results for elliptic-type
                 regions / 172 \\
                 7.4 Problems for Chapter 7 / 173 \\
                 8 Integration Using Chebyshev Polynomials / 177 \\
                 8.1 Indefinite integration with Chebyshev series / 177
                 \\
                 8.2 Gauss--Chebyshev quadrature / 180 \\
                 8.3 Quadrature methods of Clenshaw--Curtis type / 186
                 \\
                 8.3.1 Introduction / 186 \\
                 8.3.2 First-kind formulae / 187 \\
                 8.3.3 Second-kind formulae / 189 \\
                 8.3.4 Third-kind formulae / 191 \\
                 8.3.5 General remark on methods of Clenshaw--Curtis
                 type / 192 \\
                 8.4 Error estimation for Clenshaw--Curtis methods / 192
                 \\
                 8.4.1 First-kind polynomials / 193 \\
                 8.4.2 Fitting an exponential curve / 195 \\
                 8.4.3 Other abscissae and polynomials / 196 \\
                 8.5 Some other work on Clenshaw--Curtis methods / 200
                 \\
                 8.6 Problems for Chapter 8 / 201 \\
                 9 Solution of Integral Equations / 203 \\
                 9.1 Introduction / 203 \\
                 9.2 Fredholm equations of the second kind / 204 \\
                 9.3 Fredholm equations of the third kind / 206 \\
                 9.4 Fredholm equations of the first kind / 207 \\
                 9.5 Singular kernels / 209 \\
                 9.5.1 Hilbert-type kernels and related kernels / 209
                 \\
                 9.5.2 Symm's integral equation / 212 \\
                 9.6 Regularisation of integral equations / 214 \\
                 9.6.1 Discrete data with second derivative
                 regularisation / 214 \\
                 9.6.2 Details of a smoothing algorithm (second
                 derivative regularisation) / 215 \\
                 9.6.3 A smoothing algorithm with weighted function
                 regularisation / 217 \\
                 9.6.4 Evaluation of $V(\lambda)$ / 220 \\
                 9.6.5 Other basis functions / 221 \\
                 9.7 Partial differential equations and boundary
                 integral equation methods / 222 \\
                 9.7.1 A hypersingular integral equation derived from a
                 mixed boundary value problem for Laplace's equation /
                 222 \\
                 9.8 Problems for Chapter 9 / 227 \\
                 10 Solution of Ordinary Differential Equations / 231
                 \\
                 10.1 Introduction / 231 \\
                 10.2 A simple example / 232 \\
                 10.2.1 Collocation methods / 234 \\
                 10.2.2 Error of the collocation method / 237 \\
                 10.2.3 Projection (tau) methods / 239 \\
                 10.2.4 Error of the preceding projection method / 241
                 \\
                 10.3 The original Lanczos tau ($\tau$) method / 242 \\
                 10.4 A more general linear equation / 244 \\
                 10.4.1 Collocation method / 244 \\
                 10.4.2 Projection method / 245 \\
                 10.5 Pseudospectral methods --- another form of
                 collocation / 245 \\
                 10.5.1 Differentiation matrices / 246 \\
                 10.5.2 Differentiation matrix for Chebyshev points /
                 247 \\
                 10.5.3 Collocation using differentiation matrices / 249
                 \\
                 10.6 Nonlinear equations / 251 \\
                 10.7 Eigenvalue problems / 252 \\
                 10.7.1 Collocation methods / 252 \\
                 10.7.2 Collocation using the differentiation matrix /
                 254 \\
                 10.8 Differential equations in one space and one time
                 dimension / 256 \\
                 10.8.1 Collocation methods / 257 \\
                 10.8.2 Collocation using the differentiation matrix /
                 258 \\
                 10.9 Problems for Chapter 10 / 259 \\
                 11 Chebyshev and Spectral Methods for Partial
                 Differential Equations / 261 \\
                 11.1 Introduction / 261 \\
                 11.2 Interior, boundary and mixed methods / 262 \\
                 11.2.1 Interior methods / 262 \\
                 11.2.2 Boundary methods / 263 \\
                 11.2.3 Mixed methods / 265 \\
                 11.3 Differentiation matrices and nodal representation
                 / 265 \\
                 11.4 Method of weighted residuals / 265 \\
                 11.4.1 Continuous MWR / 265 \\
                 11.4.2 Discrete MWR --- a new nomenclature / 266 \\
                 11.5 Chebyshev series and Galerkin methods / 267 \\
                 11.6 Collocation/interpolation and related methods /
                 269 \\
                 11.7 PDE methods / 271 \\
                 11.7.1 Error analysis / 272 \\
                 11.8 Some PDE problems and various methods / 272 \\
                 11.8.1 Power basis: collocation for Poisson problem /
                 273 \\
                 11.8.2 Power basis: interior collocation for the
                 L-membrane / 275 \\
                 11.8.3 Chebyshev basis and discrete orthogonalisation /
                 278 \\
                 11.8.4 Differentiation matrix approach: Poisson problem
                 / 281 \\
                 11.8.5 Explicit collocation for the quasilinear
                 Dirichlet problem: Chebyshev basis / 283 \\
                 11.9 Computational fluid dynamics / 295 \\
                 11.10 Particular issues in spectral methods / 296 \\
                 11.11 More advanced problems / 297 \\
                 11.12 Problems for Chapter 11 / 298 \\
                 12 Conclusion / 303 \\
                 Bibliography / 305 \\
                 Appendices: \\
                 A Biographical Note / 321 \\
                 B Summary of Notations, Definitions and Important
                 Properties / 323 \\
                 B.I Miscellaneous notations / 323 \\
                 B.2 The four kinds of Chebyshev polynomial / 325 \\
                 C Tables of Coefficients / 329 \\
                 Index / 335",
  xxauthor =     "J. C. Mason and D. C. (David Christopher) Handscomb",
  xxURL =        "http://www.loc.gov/catdir/enhancements/fy0646/2002073578-d.html",
}


bibtype: inproceedings
filename: elefunt.bib
label: Meunier:2003:EAG
author: Ludovic Meunier and Bruno Salvy
editor: Hoon Hong
title: ESF: an automatically generated encyclopedia of special functions
publisher: pub-ACM
address: pub-ACM:adr
pages: xiii + 341
month: aug
monthnumber: 8
year: 2003
DOI: https://doi.org/10.1145/860854.860898
ISBN: 1-58113-641-2 (paperback) OR 1581136412 (paperback)
ISBN13: 978-1-58113-641-8 (paperback) OR 9781581136418 (paperback)
LCCN: QA76.5 S98 2003; QA76.95.I59 2003
bibdate: Sat Nov 11 06:21:45 2023
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2023.11.11 06:21:45 ???
acknowledgement: ack-nhfb
bookDOI: https://doi.org/10.1145/860854
bookURL: https://dl.acm.org/doi/proceedings/10.1145/860854
rawauthor: Ludovic Meunier and Bruno Salvy
raweditor: Hoon Hong
rawtitle: {ESF}: an automatically generated encyclopedia of special functions
booktitle:
Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation: Philadelphia, PA, USA, August 3--6, 2003

abstract:
We present our on-going work on the automatic generation of an encyclopedia of special functions on the web, called The Encyclopedia of Special Functions (ESF) (url http://algo.inria.fr/esf). All mathematical formulae in the ESF are computed, typeset and displayed without any human intervention. This is achieved by exploiting a collection of computer algebra algorithms in a systematic way, on top of a specially designed data structure for a class of special functions.

rawabstract:
We present our on-going work on the automatic generation of an encyclopedia of special functions on the web, called The Encyclopedia of Special Functions (ESF) (\url{http://algo.inria.fr/esf}). All mathematical formulae in the ESF are computed, typeset and displayed without any human intervention. This is achieved by exploiting a collection of computer algebra algorithms in a systematic way, on top of a specially designed data structure for a class of special functions.

rawbooktitle:
Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation: {Philadelphia, PA, USA, August 3--6, 2003}

entry:
@InProceedings{Meunier:2003:EAG,
  author =       "Ludovic Meunier and Bruno Salvy",
  editor =       "Hoon Hong",
  booktitle =    "Proceedings of the 2003 International Symposium on
                 Symbolic and Algebraic Computation: {Philadelphia, PA,
                 USA, August 3--6, 2003}",
  title =        "{ESF}: an automatically generated encyclopedia of
                 special functions",
  publisher =    pub-ACM,
  address =      pub-ACM:adr,
  month =        aug,
  year =         "2003",
  DOI =          "https://doi.org/10.1145/860854.860898",
  ISBN =         "1-58113-641-2 (paperback)",
  ISBN-13 =      "978-1-58113-641-8 (paperback)",
  LCCN =         "QA76.5 S98 2003; QA76.95.I59 2003",
  bibdate =      "Sat Nov 11 06:21:45 2023",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  abstract =     "We present our on-going work on the automatic
                 generation of an encyclopedia of special functions on
                 the web, called The Encyclopedia of Special Functions
                 (ESF) (\url{http://algo.inria.fr/esf}). All
                 mathematical formulae in the ESF are computed, typeset
                 and displayed without any human intervention. This is
                 achieved by exploiting a collection of computer algebra
                 algorithms in a systematic way, on top of a specially
                 designed data structure for a class of special
                 functions.",
  acknowledgement = ack-nhfb,
  book-DOI =     "https://doi.org/10.1145/860854",
  book-URL =     "https://dl.acm.org/doi/proceedings/10.1145/860854",
}


bibtype: article
filename: elefunt.bib
label: Ovtchinnikov:2003:CEGb
author: E. Ovtchinnikov
journal: j-SIAM-J-NUMER-ANAL
volume: 41
number: 1
pages: 272--286
month: feb
monthnumber: 2
year: 2003
CODEN: SJNAAM
DOI: https://doi.org/10.1137/S0036142902411768
ISSN: 0036-1429 (print), 1095-7170 (electronic) OR 00361429 (print), 10957170 (electronic)
ISSNL: 0036-1429 OR 00361429
bibdate: Fri Aug 15 05:57:09 MDT 2003
bibsource: http://epubs.siam.org/sam-bin/dbq/toc/SINUM/41/1; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2003.08.15 05:57:09 MDT
URL: http://epubs.siam.org/sam-bin/dbq/article/41176
fjournal: SIAM Journal on Numerical Analysis
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://epubs.siam.org/sinum
rawauthor: E. Ovtchinnikov
title:
Convergence Estimates for the Generalized Davidson Method for Symmetric Eigenvalue Problems II: The Subspace Acceleration

rawtitle:
Convergence Estimates for the Generalized {Davidson} Method for Symmetric Eigenvalue Problems {II}: The Subspace Acceleration

entry:
@Article{Ovtchinnikov:2003:CEGb,
  author =       "E. Ovtchinnikov",
  title =        "Convergence Estimates for the Generalized {Davidson}
                 Method for Symmetric Eigenvalue Problems {II}: The
                 Subspace Acceleration",
  journal =      j-SIAM-J-NUMER-ANAL,
  volume =       "41",
  number =       "1",
  pages =        "272--286",
  month =        feb,
  year =         "2003",
  CODEN =        "SJNAAM",
  DOI =          "https://doi.org/10.1137/S0036142902411768",
  ISSN =         "0036-1429 (print), 1095-7170 (electronic)",
  ISSN-L =       "0036-1429",
  bibdate =      "Fri Aug 15 05:57:09 MDT 2003",
  bibsource =    "http://epubs.siam.org/sam-bin/dbq/toc/SINUM/41/1;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://epubs.siam.org/sam-bin/dbq/article/41176",
  acknowledgement = ack-nhfb,
  fjournal =     "SIAM Journal on Numerical Analysis",
  journal-URL =  "http://epubs.siam.org/sinum",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Paris:2003:AEG
author: R. B. Paris
title: The asymptotic expansion of a generalised incomplete gamma function
journal: j-J-COMPUT-APPL-MATH
volume: 151
number: 2
pages: 297--306
day: 15
month: feb
monthnumber: 2
year: 2003
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:33 MST 2017
bibtimestamp: 2017.02.25 12:52:33 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042702008099
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: R. B. Paris
rawtitle: The asymptotic expansion of a generalised incomplete gamma function
entry:
@Article{Paris:2003:AEG,
  author =       "R. B. Paris",
  title =        "The asymptotic expansion of a generalised incomplete
                 gamma function",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "151",
  number =       "2",
  pages =        "297--306",
  day =          "15",
  month =        feb,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:33 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702008099",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Paszkowski:2003:CAS
author: Stefan Paszkowski
title: Convergence Acceleration of Some Continued Fractions
journal: j-NUMER-ALGORITHMS
volume: 32
number: 2--4
pages: 193--247
month: apr
monthnumber: 4
year: 2003
CODEN: NUALEG
ISSN: 1017-1398 (print), 1572-9265 (electronic) OR 10171398 (print), 15729265 (electronic)
ISSNL: 1017-1398 OR 10171398
bibdate: Mon Sep 29 08:37:11 MDT 2003
bibsource: http://www.kluweronline.com/issn/1017-1398; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2003.09.29 08:37:11 MDT
fjournal: Numerical Algorithms
keywords: convergence acceleration
acknowledgement: ack-nhfb
journalURL: http://link.springer.com/journal/11075
rawauthor: Stefan Paszkowski
rawtitle: Convergence Acceleration of Some Continued Fractions
URL:
http://ipsapp007.kluweronline.com/content/getfile/5058/45/5/abstract.htm; http://ipsapp007.kluweronline.com/content/getfile/5058/45/5/fulltext.pdf

entry:
@Article{Paszkowski:2003:CAS,
  author =       "Stefan Paszkowski",
  title =        "Convergence Acceleration of Some Continued Fractions",
  journal =      j-NUMER-ALGORITHMS,
  volume =       "32",
  number =       "2--4",
  pages =        "193--247",
  month =        apr,
  year =         "2003",
  CODEN =        "NUALEG",
  ISSN =         "1017-1398 (print), 1572-9265 (electronic)",
  ISSN-L =       "1017-1398",
  bibdate =      "Mon Sep 29 08:37:11 MDT 2003",
  bibsource =    "http://www.kluweronline.com/issn/1017-1398;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://ipsapp007.kluweronline.com/content/getfile/5058/45/5/abstract.htm;
                 http://ipsapp007.kluweronline.com/content/getfile/5058/45/5/fulltext.pdf",
  acknowledgement = ack-nhfb,
  fjournal =     "Numerical Algorithms",
  journal-URL =  "http://link.springer.com/journal/11075",
  keywords =     "convergence acceleration",
}


bibtype: article
filename: elefunt.bib
label: Pedersen:2003:DGF
author: Henrik L. Pedersen
title: The double gamma function and related Pick functions
journal: j-J-COMPUT-APPL-MATH
volume: 153
number: 1--2
pages: 361--369
day: 1
month: apr
monthnumber: 4
year: 2003
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:34 MST 2017
bibtimestamp: 2017.02.25 12:52:34 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042702006040
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Henrik L. Pedersen
rawtitle: The double gamma function and related {Pick} functions
entry:
@Article{Pedersen:2003:DGF,
  author =       "Henrik L. Pedersen",
  title =        "The double gamma function and related {Pick}
                 functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "153",
  number =       "1--2",
  pages =        "361--369",
  day =          "1",
  month =        apr,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:34 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702006040",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: article
filename: elefunt.bib
label: Petropoulou:2003:CZB
author: Eugenia N. Petropoulou and Panayiotis D. Siafarikas and Ioannis D. Stabolas
title: On the common zeros of Bessel functions
journal: j-J-COMPUT-APPL-MATH
volume: 153
number: 1--2
pages: 387--393
day: 1
month: apr
monthnumber: 4
year: 2003
CODEN: JCAMDI
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Sat Feb 25 12:52:34 MST 2017
bibtimestamp: 2017.02.25 12:52:34 MST
URL: http://www.sciencedirect.com/science/article/pii/S0377042702006416
fjournal: Journal of Computational and Applied Mathematics
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Eugenia N. Petropoulou and Panayiotis D. Siafarikas and Ioannis D. Stabolas
rawtitle: On the common zeros of {Bessel} functions
entry:
@Article{Petropoulou:2003:CZB,
  author =       "Eugenia N. Petropoulou and Panayiotis D. Siafarikas
                 and Ioannis D. Stabolas",
  title =        "On the common zeros of {Bessel} functions",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "153",
  number =       "1--2",
  pages =        "387--393",
  day =          "1",
  month =        apr,
  year =         "2003",
  CODEN =        "JCAMDI",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Sat Feb 25 12:52:34 MST 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042702006416",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
}


bibtype: inproceedings
filename: elefunt.bib
label: Pineiro:2003:LHR
author: J.-A. Pineiro and J. D. Bruguera and M. D. Ercegovac
booktitle: ISCAS '03. Proceedings of the 2003 International Symposium on Circuits and Systems. 25--28 May 2003
title: On-line high-radix exponential with selection by rounding
volume: 4
publisher: pub-IEEE
address: pub-IEEE:adr
pages: IV-121--IV-124
year: 2003
bibdate: Sat Jul 16 11:25:05 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 11:25:05 MDT
acknowledgement: ack-nhfb
rawauthor: J.-A. Pineiro and J. D. Bruguera and M. D. Ercegovac
rawtitle: On-line high-radix exponential with selection by rounding
rawbooktitle:
{ISCAS '03. Proceedings of the 2003 International Symposium on Circuits and Systems. 25--28 May 2003}

entry:
@InProceedings{Pineiro:2003:LHR,
  author =       "J.-A. Pineiro and J. D. Bruguera and M. D. Ercegovac",
  booktitle =    "{ISCAS '03. Proceedings of the 2003 International
                 Symposium on Circuits and Systems. 25--28 May 2003}",
  title =        "On-line high-radix exponential with selection by
                 rounding",
  volume =       "4",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "IV-121--IV-124",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 11:25:05 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "An on-line high-radix algorithm for computing the
                 exponential function (e/sup x/) with arbitrary
                 precision n is presented. Selection by rounding and a
                 redundant digit-set for the digits e/sub j/ are used,
                 with selection by table in the first \ldots{}",
}


bibtype: book
filename: elefunt.bib
label: Sidi:2003:PEM
author: Avram Sidi
title: Practical Extrapolation Methods: Theory and Applications
volume: 10
publisher: pub-CAMBRIDGE
address: pub-CAMBRIDGE:adr
pages: xxii + 519
year: 2003
DOI: https://doi.org/10.1017/CBO9780511546815
LCCN: QA281 .S555 2003
bibdate: Mon Jul 5 16:49:09 MDT 2010
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib; z3950.loc.gov:7090/Voyager
bibtimestamp: 2010.07.05 16:49:09 MDT
series: Cambridge monographs on applied and computational mathematics
subject: extrapolation
acknowledgement: ack-nhfb
rawauthor: Avram Sidi
rawtitle: Practical Extrapolation Methods: Theory and Applications
ISBN:
0-521-66159-5 (hardcover), 0-511-54681-5 (e-book), 0-511-06018-1 (Adobe Reader), 0-511-06649-X (e-book) OR 0521661595 (hardcover), 0511546815 (ebook), 0511060181 (Adobe Reader), 051106649X (ebook)

ISBN13:
978-0-521-66159-1 (hardcover), 978-0-511-54681-5 (e-book), 978-0-511-06018-2 (Adobe Reader), 978-0-511-06649-8 (e-book) OR 9780521661591 (hardcover), 9780511546815 (ebook), 9780511060182 (Adobe Reader), 9780511066498 (ebook)

TOC:
Preface / xix--xxii Introduction / 1--18 I: The Richardson Extrapolation Process and Its Generalizations / 19--20 1: The Richardson Extrapolation Process / 21--41 2: Additional Topics in Richardson Extrapolation / 42--56 3: First Generalization of the Richardson Extrapolation Process / 57--80 4: GREP: Further Generalization of the Richardson Extrapolation Process / 81--94 5: The $D$-Transformation: A GREP for Infinite-Range Integrals / 95--120 6: The $d$-Transformation: A GREP for Infinite Series and Sequences / 121--157 7: Recursive Algorithms for GREP / 158--175 8: Analytic Study of GREP(1): Slowly Varying $A(y) in F^(1)$ / 176--202 9: Analytic Study of GREP(1): Quickly Varying $A(y) in F^(1)$ / 203--211 10: Efficient Use of GREP(1): Applications to the $D(1)$-, $d(1)$-, and $d(m)$-Transformations / 212--217 11: Reduction of the $D$-Transformation for Oscillatory Infinite-Range Integrals: The $bar D$-, $D'$-, $W$-, and $mW$-Transformations / 218--237 12: Acceleration of Convergence of Power Series by the $d$-Transformation: Rational $d$-Approximants / 238--252 13: Acceleration of Convergence of Fourier and Generalized Fourier Series by the $d$-Transformation: The Complex Series Approach with APS / 253--262 14: Special Topics in Richardson Extrapolation / 263--276 II: Sequence Transformations / 277--278 15: The Euler Transformation, Aitken 2-Process, and Lubkin W-Transformation / 279--296 16: The Shanks Transformation / 297--322 17: The Pade Table / 323--347 18: Generalizations of Pade Approximants / 348--362 19: The Levin- and Sidi $S$-Transformations / 363--374 20: The Wynn- and Brezinski-Algorithms / 375--383 21: The $G$-Transformation and Its Generalizations / 384--389 22: The Transformations of Overholt and Wimp / 390--395 23: Confluent Transformations / 396--406 24: Formal Theory of Sequence Transformations / 407--412 III: Further Applications / 413--414 25: Further Applications of Extrapolation Methods and Sequence Transformations / 415--456 IV: Appendices / 457--458 A: Review of Basic Asymptotics / 459--462 B: The Laplace Transform and Watson's Lemma / 463--464 C: The Gamma Function / 465--466 D: Bernoulli Numbers and Polynomials and the Euler Maclaurin Formula / 467--476 E: The Riemann Zeta Function and the Generalized Zeta Function / 477--479 F: Some Highlights of Polynomial Approximation Theory / 480--482 G: A Compendium of Sequence Transformations / 483--487 H: Efficient Application of Sequence Transformations: Summary / 488--492 I: FORTRAN 77 Program for the $d(m)$-Transformation / 493--500 Bibliography / 501--514 Index / 515--519

rawTOC:
Preface / xix--xxii \\ Introduction / 1--18 \\ I: The Richardson Extrapolation Process and Its Generalizations / 19--20 \\ 1: The Richardson Extrapolation Process / 21--41 \\ 2: Additional Topics in Richardson Extrapolation / 42--56 \\ 3: First Generalization of the Richardson Extrapolation Process / 57--80 \\ 4: GREP: Further Generalization of the Richardson Extrapolation Process / 81--94 \\ 5: The $D$-Transformation: A GREP for Infinite-Range Integrals / 95--120 \\ 6: The $d$-Transformation: A GREP for Infinite Series and Sequences / 121--157 \\ 7: Recursive Algorithms for GREP / 158--175 \\ 8: Analytic Study of GREP(1): Slowly Varying $A(y) \in F^{(1)}$ / 176--202 \\ 9: Analytic Study of GREP(1): Quickly Varying $A(y) \in F^{(1)}$ / 203--211 \\ 10: Efficient Use of GREP(1): Applications to the $D(1)$-, $d(1)$-, and $d(m)$-Transformations / 212--217 \\ 11: Reduction of the $D$-Transformation for Oscillatory Infinite-Range Integrals: The $\bar{D}$-, $D'$-, $W$-, and $mW$-Transformations / 218--237 \\ 12: Acceleration of Convergence of Power Series by the $d$-Transformation: Rational $d$-Approximants / 238--252 \\ 13: Acceleration of Convergence of Fourier and Generalized Fourier Series by the $d$-Transformation: The Complex Series Approach with APS / 253--262 \\ 14: Special Topics in Richardson Extrapolation / 263--276 \\ II: Sequence Transformations / 277--278 \\ 15: The Euler Transformation, Aitken 2-Process, and Lubkin W-Transformation / 279--296 \\ 16: The Shanks Transformation / 297--322 \\ 17: The Pad{\'e} Table / 323--347 \\ 18: Generalizations of Pad{\'e} Approximants / 348--362 \\ 19: The Levin- and Sidi $S$-Transformations / 363--374 \\ 20: The Wynn- and Brezinski-Algorithms / 375--383 \\ 21: The $G$-Transformation and Its Generalizations / 384--389 \\ 22: The Transformations of Overholt and Wimp / 390--395 \\ 23: Confluent Transformations / 396--406 \\ 24: Formal Theory of Sequence Transformations / 407--412 \\ III: Further Applications / 413--414 \\ 25: Further Applications of Extrapolation Methods and Sequence Transformations / 415--456 \\ IV: Appendices / 457--458 \\ A: Review of Basic Asymptotics / 459--462 \\ B: The Laplace Transform and Watson's Lemma / 463--464 \\ C: The Gamma Function / 465--466 \\ D: Bernoulli Numbers and Polynomials and the Euler Maclaurin Formula / 467--476 \\ E: The Riemann Zeta Function and the Generalized Zeta Function / 477--479 \\ F: Some Highlights of Polynomial Approximation Theory / 480--482 \\ G: A Compendium of Sequence Transformations / 483--487 \\ H: Efficient Application of Sequence Transformations: Summary / 488--492 \\ I: FORTRAN 77 Program for the $d(m)$-Transformation / 493--500 \\ Bibliography / 501--514 \\ Index / 515--519

entry:
@Book{Sidi:2003:PEM,
  author =       "Avram Sidi",
  title =        "Practical Extrapolation Methods: Theory and
                 Applications",
  volume =       "10",
  publisher =    pub-CAMBRIDGE,
  address =      pub-CAMBRIDGE:adr,
  pages =        "xxii + 519",
  year =         "2003",
  DOI =          "https://doi.org/10.1017/CBO9780511546815",
  ISBN =         "0-521-66159-5 (hardcover), 0-511-54681-5 (e-book),
                 0-511-06018-1 (Adobe Reader), 0-511-06649-X (e-book)",
  ISBN-13 =      "978-0-521-66159-1 (hardcover), 978-0-511-54681-5
                 (e-book), 978-0-511-06018-2 (Adobe Reader),
                 978-0-511-06649-8 (e-book)",
  LCCN =         "QA281 .S555 2003",
  bibdate =      "Mon Jul 5 16:49:09 MDT 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 z3950.loc.gov:7090/Voyager",
  series =       "Cambridge monographs on applied and computational
                 mathematics",
  acknowledgement = ack-nhfb,
  subject =      "extrapolation",
  tableofcontents = "Preface / xix--xxii \\
                 Introduction / 1--18 \\
                 I: The Richardson Extrapolation Process and Its
                 Generalizations / 19--20 \\
                 1: The Richardson Extrapolation Process / 21--41 \\
                 2: Additional Topics in Richardson Extrapolation /
                 42--56 \\
                 3: First Generalization of the Richardson Extrapolation
                 Process / 57--80 \\
                 4: GREP: Further Generalization of the Richardson
                 Extrapolation Process / 81--94 \\
                 5: The $D$-Transformation: A GREP for Infinite-Range
                 Integrals / 95--120 \\
                 6: The $d$-Transformation: A GREP for Infinite Series
                 and Sequences / 121--157 \\
                 7: Recursive Algorithms for GREP / 158--175 \\
                 8: Analytic Study of GREP(1): Slowly Varying $A(y) \in
                 F^{(1)}$ / 176--202 \\
                 9: Analytic Study of GREP(1): Quickly Varying $A(y) \in
                 F^{(1)}$ / 203--211 \\
                 10: Efficient Use of GREP(1): Applications to the
                 $D(1)$-, $d(1)$-, and $d(m)$-Transformations / 212--217
                 \\
                 11: Reduction of the $D$-Transformation for Oscillatory
                 Infinite-Range Integrals: The $\bar{D}$-, $D'$-, $W$-,
                 and $mW$-Transformations / 218--237 \\
                 12: Acceleration of Convergence of Power Series by the
                 $d$-Transformation: Rational $d$-Approximants /
                 238--252 \\
                 13: Acceleration of Convergence of Fourier and
                 Generalized Fourier Series by the $d$-Transformation:
                 The Complex Series Approach with APS / 253--262 \\
                 14: Special Topics in Richardson Extrapolation /
                 263--276 \\
                 II: Sequence Transformations / 277--278 \\
                 15: The Euler Transformation, Aitken 2-Process, and
                 Lubkin W-Transformation / 279--296 \\
                 16: The Shanks Transformation / 297--322 \\
                 17: The Pad{\'e} Table / 323--347 \\
                 18: Generalizations of Pad{\'e} Approximants / 348--362
                 \\
                 19: The Levin- and Sidi $S$-Transformations / 363--374
                 \\
                 20: The Wynn- and Brezinski-Algorithms / 375--383 \\
                 21: The $G$-Transformation and Its Generalizations /
                 384--389 \\
                 22: The Transformations of Overholt and Wimp / 390--395
                 \\
                 23: Confluent Transformations / 396--406 \\
                 24: Formal Theory of Sequence Transformations /
                 407--412 \\
                 III: Further Applications / 413--414 \\
                 25: Further Applications of Extrapolation Methods and
                 Sequence Transformations / 415--456 \\
                 IV: Appendices / 457--458 \\
                 A: Review of Basic Asymptotics / 459--462 \\
                 B: The Laplace Transform and Watson's Lemma / 463--464
                 \\
                 C: The Gamma Function / 465--466 \\
                 D: Bernoulli Numbers and Polynomials and the Euler
                 Maclaurin Formula / 467--476 \\
                 E: The Riemann Zeta Function and the Generalized Zeta
                 Function / 477--479 \\
                 F: Some Highlights of Polynomial Approximation Theory /
                 480--482 \\
                 G: A Compendium of Sequence Transformations / 483--487
                 \\
                 H: Efficient Application of Sequence Transformations:
                 Summary / 488--492 \\
                 I: FORTRAN 77 Program for the $d(m)$-Transformation /
                 493--500 \\
                 Bibliography / 501--514 \\
                 Index / 515--519",
  xxURL =        "http://www.loc.gov/catdir/samples/cam033/2002024669.html;
                 http://www.loc.gov/catdir/description/cam022/2002024669.html;
                 http://www.loc.gov/catdir/toc/cam024/2002024669.html",
}


bibtype: misc
filename: elefunt.bib
label: Tkachev:2003:EFI
author: Vladimir G. Tkachev
title: Elliptic functions: Introduction course
pages: xxii + 519
day: 25
month: nov
monthnumber: 11
year: 2003
bibdate: Wed Mar 15 08:43:21 2017
bibsource: https://www.math.utah.edu/pub/tex/bib/agm.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2017.03.15 08:43:21 ???
URL: http://users.mai.liu.se/vlatk48/teaching/lect2-agm.pdf
acknowledgement: ack-nhfb
howpublished: Web lecture notes.
rawauthor: Vladimir G. Tkachev
rawtitle: Elliptic functions: Introduction course
TOC:
Chapter 1. Elliptic integrals and Jacobi's theta functions / 5 1.1. Elliptic integrals and the AGM: real case / 5 1.1.3. The arithmetic-geometric mean iteration / 7 1.2. Lemniscates and elastic curves / 11 1.3. Euler's addition theorem / 18 1.4. Theta functions: preliminaries 5 / 24 Chapter 2. General theory of doubly periodic functions / 31 2.1. Preliminaries / 31 2.2. Periods of analytic functions / 33 2.3. Existence of doubly periodic functions / 36 2.4. Liouville's theorems / 38 2.5. The Weierstrass function $wp (z)$ / 43 2.6. Modular forms / 51 Bibliography / 61

rawTOC:
Chapter 1. Elliptic integrals and Jacobi's theta functions / 5 \\ 1.1. Elliptic integrals and the AGM: real case / 5 \\ 1.1.3. The arithmetic-geometric mean iteration / 7 \\ 1.2. Lemniscates and elastic curves / 11 \\ 1.3. Euler's addition theorem / 18 \\ 1.4. Theta functions: preliminaries 5 / 24 \\ Chapter 2. General theory of doubly periodic functions / 31 \\ 2.1. Preliminaries / 31 \\ 2.2. Periods of analytic functions / 33 \\ 2.3. Existence of doubly periodic functions / 36 \\ 2.4. Liouville's theorems / 38 \\ 2.5. The Weierstrass function $\wp(z)$ / 43 \\ 2.6. Modular forms / 51 \\ Bibliography / 61

entry:
@Misc{Tkachev:2003:EFI,
  author =       "Vladimir G. Tkachev",
  title =        "Elliptic functions: Introduction course",
  howpublished = "Web lecture notes.",
  day =          "25",
  month =        nov,
  year =         "2003",
  bibdate =      "Wed Mar 15 08:43:21 2017",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/agm.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  URL =          "http://users.mai.liu.se/vlatk48/teaching/lect2-agm.pdf",
  acknowledgement = ack-nhfb,
  tableofcontents = "Chapter 1. Elliptic integrals and Jacobi's theta
                 functions / 5 \\
                 1.1. Elliptic integrals and the AGM: real case / 5 \\
                 1.1.3. The arithmetic-geometric mean iteration / 7 \\
                 1.2. Lemniscates and elastic curves / 11 \\
                 1.3. Euler's addition theorem / 18 \\
                 1.4. Theta functions: preliminaries 5 / 24 \\
                 Chapter 2. General theory of doubly periodic functions
                 / 31 \\
                 2.1. Preliminaries / 31 \\
                 2.2. Periods of analytic functions / 33 \\
                 2.3. Existence of doubly periodic functions / 36 \\
                 2.4. Liouville's theorems / 38 \\
                 2.5. The Weierstrass function $\wp(z)$ / 43 \\
                 2.6. Modular forms / 51 \\
                 Bibliography / 61",
}


bibtype: inproceedings
filename: elefunt.bib
label: Wang:2003:TDF
author: Xiaojun Wang and B. E. Nelson
title: Tradeoffs of designing floating-point division and square root on Virtex FPGAs
publisher: pub-IEEE
address: pub-IEEE:adr
pages: 195--203
year: 2003
bibdate: Sat Jul 16 15:28:14 MDT 2005
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2005.07.16 15:28:14 MDT
acknowledgement: ack-nhfb
rawauthor: Xiaojun Wang and B. E. Nelson
rawtitle: Tradeoffs of designing floating-point division and square root on {Virtex FPGAs}
booktitle:
FCCM 2003: 11th Annual IEEE Symposium on Field-Programmable Custom Computing Machines, 9--11 April 2003

rawbooktitle:
{FCCM 2003}: 11th Annual {IEEE} Symposium on Field-Programmable Custom Computing Machines, 9--11 April 2003

entry:
@InProceedings{Wang:2003:TDF,
  author =       "Xiaojun Wang and B. E. Nelson",
  booktitle =    "{FCCM 2003}: 11th Annual {IEEE} Symposium on
                 Field-Programmable Custom Computing Machines, 9--11
                 April 2003",
  title =        "Tradeoffs of designing floating-point division and
                 square root on {Virtex FPGAs}",
  publisher =    pub-IEEE,
  address =      pub-IEEE:adr,
  pages =        "195--203",
  year =         "2003",
  CODEN =        "????",
  ISSN =         "????",
  bibdate =      "Sat Jul 16 15:28:14 MDT 2005",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  acknowledgement = ack-nhfb,
  summary =      "Low latency, high throughput and small area are three
                 major design considerations of an FPGA (field
                 programmable gate array) design. In this paper, we
                 present a high radix SRT division algorithm and a
                 binary restoring square root algorithm. We \ldots{}",
}


bibtype: article
filename: elefunt.bib
label: Yousif:2003:CBF
author: Hashim A. Yousif and Richard Melka
title: Computing Bessel functions of the second kind in extreme parameter regimes
journal: j-COMP-PHYS-COMM
volume: 151
number: 1
pages: 25--34
day: 1
month: mar
monthnumber: 3
year: 2003
CODEN: CPHCBZ
DOI: https://doi.org/10.1016/S0010-4655(02)00697-5
ISSN: 0010-4655 (print), 1879-2944 (electronic) OR 00104655 (print), 18792944 (electronic)
ISSNL: 0010-4655 OR 00104655
bibdate: Mon Feb 13 23:41:27 MST 2012
bibtimestamp: 2012.02.13 23:41:27 MST
URL: http://www.sciencedirect.com/science/article/pii/S0010465502006975
fjournal: Computer Physics Communications
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/00104655
rawauthor: Hashim A. Yousif and Richard Melka
rawtitle: Computing {Bessel} functions of the second kind in extreme parameter regimes
bibsource:
https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib; https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathematica.bib

abstract:
A useful method of computing the integral order Bessel functions of the second kind $ Y_n(x + i y) $ when either, the absolute value of the real part, or the imaginary part of the argument $ z = x + i y $ is small, is described. This method is based on computing the Bessel functions for extreme parameter regimes when $ x sim 0 $ (or $ y sim 0 $ ) and is useful because a number existing algorithms and methods fail to give correct results for small $x$ or small $y$. The approximating equations are derived by expanding the Bessel function in Taylor series, are tested and discussed. The present work is a continuation of the previous one conducted in regard to the Bessel function of the first kind. The results of our formalism are compared to the available existing numerical methods used in Mathematica, IMSL, MATLAB, and the Amos library. Our numerical method is easy to implement, efficient, and produces reliable results. In addition, this method reduces the computation of the Bessel functions of the second complex argument to that of real argument which simplify the computation considerably.

rawabstract:
A useful method of computing the integral order Bessel functions of the second kind $ Y_n(x + i y) $ when either, the absolute value of the real part, or the imaginary part of the argument $ z = x + i y $ is small, is described. This method is based on computing the Bessel functions for extreme parameter regimes when $ x \sim 0 $ (or $ y \sim 0 $ ) and is useful because a number existing algorithms and methods fail to give correct results for small $x$ or small $y$. The approximating equations are derived by expanding the Bessel function in Taylor series, are tested and discussed. The present work is a continuation of the previous one conducted in regard to the Bessel function of the first kind. The results of our formalism are compared to the available existing numerical methods used in Mathematica, IMSL, MATLAB, and the Amos library. Our numerical method is easy to implement, efficient, and produces reliable results. In addition, this method reduces the computation of the Bessel functions of the second complex argument to that of real argument which simplify the computation considerably.

entry:
@Article{Yousif:2003:CBF,
  author =       "Hashim A. Yousif and Richard Melka",
  title =        "Computing {Bessel} functions of the second kind in
                 extreme parameter regimes",
  journal =      j-COMP-PHYS-COMM,
  volume =       "151",
  number =       "1",
  pages =        "25--34",
  day =          "1",
  month =        mar,
  year =         "2003",
  CODEN =        "CPHCBZ",
  DOI =          "https://doi.org/10.1016/S0010-4655(02)00697-5",
  ISSN =         "0010-4655 (print), 1879-2944 (electronic)",
  ISSN-L =       "0010-4655",
  bibdate =      "Mon Feb 13 23:41:27 MST 2012",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/compphyscomm2000.bib;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathematica.bib",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0010465502006975",
  abstract =     "A useful method of computing the integral order Bessel
                 functions of the second kind $ Y_n(x + i y) $ when
                 either, the absolute value of the real part, or the
                 imaginary part of the argument $ z = x + i y $ is
                 small, is described. This method is based on computing
                 the Bessel functions for extreme parameter regimes when
                 $ x \sim 0 $ (or $ y \sim 0 $ ) and is useful because a
                 number existing algorithms and methods fail to give
                 correct results for small $x$ or small $y$. The
                 approximating equations are derived by expanding the
                 Bessel function in Taylor series, are tested and
                 discussed. The present work is a continuation of the
                 previous one conducted in regard to the Bessel function
                 of the first kind. The results of our formalism are
                 compared to the available existing numerical methods
                 used in Mathematica, IMSL, MATLAB, and the Amos
                 library. Our numerical method is easy to implement,
                 efficient, and produces reliable results. In addition,
                 this method reduces the computation of the Bessel
                 functions of the second complex argument to that of
                 real argument which simplify the computation
                 considerably.",
  acknowledgement = ack-nhfb,
  fjournal =     "Computer Physics Communications",
  journal-URL =  "http://www.sciencedirect.com/science/journal/00104655",
}


bibtype: book
filename: elefunt.bib
label: Zwillinger:2003:CSM
editor: Daniel Zwillinger
title: CRC Standard Mathematical Tables and Formulae
publisher: pub-CHAPMAN-HALL-CRC
address: pub-CHAPMAN-HALL-CRC:adr
edition: 31st
pages: xiv + 910
year: 2003
ISBN: 1-58488-291-3 (hardcover), 1-4200-3534-7 (e-book) OR 1584882913 (hardcover), 1420035347 (ebook)
LCCN: QA47 .M315 2003
bibdate: Thu Nov 25 11:07:20 MST 2010
bibtimestamp: 2010.11.25 11:07:20 MST
subject: mathematics; tables
acknowledgement: ack-nhfb
raweditor: Daniel Zwillinger
rawtitle: {CRC} Standard Mathematical Tables and Formulae
ISBN13:
978-1-58488-291-6 (hardcover), 978-1-4200-3534-6 (e-book) OR 9781584882916 (hardcover), 9781420035346 (ebook)

bibsource:
https://www.math.utah.edu/pub/tex/bib/elefunt.bib; https://www.math.utah.edu/pub/tex/bib/mathcw.bib; prodorbis.library.yale.edu:7090/voyager

TOC:
Preface Contributors Table of Contents 1 Analysis 2 Algebra 3 Discrete Mathematics 4 Geometry 5 Continuous Mathematics 6 Special Functions 7 Probability and Statistics 8 Scientific Computing 9 Financial Analysis 10 Miscellaneous List of References List of Figures List of Notation Index

rawTOC:
Preface \\ Contributors \\ Table of Contents \\ 1 Analysis \\ 2 Algebra \\ 3 Discrete Mathematics \\ 4 Geometry \\ 5 Continuous Mathematics \\ 6 Special Functions \\ 7 Probability and Statistics \\ 8 Scientific Computing \\ 9 Financial Analysis \\ 10 Miscellaneous \\ List of References \\ List of Figures \\ List of Notation \\ Index

entry:
@Book{Zwillinger:2003:CSM,
  editor =       "Daniel Zwillinger",
  title =        "{CRC} Standard Mathematical Tables and Formulae",
  publisher =    pub-CHAPMAN-HALL-CRC,
  address =      pub-CHAPMAN-HALL-CRC:adr,
  edition =      "31st",
  pages =        "xiv + 910",
  year =         "2003",
  ISBN =         "1-58488-291-3 (hardcover), 1-4200-3534-7 (e-book)",
  ISBN-13 =      "978-1-58488-291-6 (hardcover), 978-1-4200-3534-6
                 (e-book)",
  LCCN =         "QA47 .M315 2003",
  bibdate =      "Thu Nov 25 11:07:20 MST 2010",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
                 https://www.math.utah.edu/pub/tex/bib/mathcw.bib;
                 prodorbis.library.yale.edu:7090/voyager",
  acknowledgement = ack-nhfb,
  subject =      "mathematics; tables",
  tableofcontents = "Preface \\
                 Contributors \\
                 Table of Contents \\
                 1 Analysis \\
                 2 Algebra \\
                 3 Discrete Mathematics \\
                 4 Geometry \\
                 5 Continuous Mathematics \\
                 6 Special Functions \\
                 7 Probability and Statistics \\
                 8 Scientific Computing \\
                 9 Financial Analysis \\
                 10 Miscellaneous \\
                 List of References \\
                 List of Figures \\
                 List of Notation \\
                 Index",
}


bibtype: book
filename: elefunt.bib
label: Bell:2004:SFS
author: W. W. (William Wallace) Bell
title: Special Functions for Scientists and Engineers
publisher: pub-DOVER
address: pub-DOVER:adr
pages: xiv + 247
year: 2004
ISBN: 0-486-43521-0 OR 0486435210
ISBN13: 978-0-486-43521-3 OR 9780486435213
LCCN: QA351 .B4 2004
bibdate: Sat Oct 30 16:30:44 MDT 2010
bibsource: fsz3950.oclc.org:210/WorldCat; https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2010.10.30 16:30:44 MDT
series: Dover books on mathematics
remark: Reprinting of cite Bell:1968:SFS.
subject: Functions, Special
acknowledgement: ack-nhfb
rawauthor: W. W. (William Wallace) Bell
rawtitle: Special Functions for Scientists and Engineers
TOC:
Preface / v List of Symbols / ix Series Solution of Differential Equations Method of Frobenius / 1 Examples / 8 Problems / 21 Gamma and Beta Functions Definitions / 23 Properties of the beta and gamma functions / 24 Definition of the gamma function for negative values of the argument / 30 Examples / 37 Problems / 40 Legendre Polynomials and Functions Legendre's equation and its solution / 42 Generating function for the Legendre polynomials / 46 Further expressions for the Legendre polynomials / 48 Explicit expressions for and special values of the Legendre polynomials / 50 Orthogonality properties of the Legendre polynomials / 52 Legendre series / 55 Relations between the Legendre polynomials and their derivatives; / 58 recurrence relations Associated Legendre functions / 62 Properties of the associated Legendre functions / 65 Legendre functions of the second kind / 70 Spherical harmonics / 78 Graphs of the Legendre functions / 82 Examples / 85 Problems / 90 Bessel Functions Bessel's equation and its solutions; Bessel functions of the first and second kind / 92 Generating function for the Bessel functions / 99 Integral representations for Bessel functions / 101 Recurrence relations / 104 Hankel functions / 107 Equations reducible to Bessel's equation / 108 Modified Bessel functions / 110 Recurrence relations for the modified Bessel functions / 113 Integral representations for the modified Bessel functions / 116 Kelvin's functions / 120 Spherical Bessel functions / 121 Behaviour of the Bessel functions for large and small values of the argument / 127 Graphs of the Bessel functions / 133 Orthonormality of the Bessel functions; Bessel series / 137 Integrals involving Bessel functions / 141 Examples / 148 Problems / 154 Hermite Polynomials Hermite's equation and its solution / 156 Generating function / 157 Other expressions for the Hermite polynomials / 158 Explicit expressions for, and special values of, the Hermite polynomials / 160 Orthogonality properties of the Hermite polynomials / 161 Relations between Hermite polynomials and their derivatives; recurrence relations / 162 Weber--Hermite functions / 163 Examples / 164 Problems / 166 Laguerre Polynomials Laguerre's equation and its solution / 168 Generating function / 169 Alternative expression for the Laguerre polynomials / 170 Explicit expressions for, and special values of, the Laguerre polynomials / 171 Orthogonality properties of the Laguerre polynomials / 172 Relations between Laguerre polynomials and their derivatives; recurrence relations / 173 Associated Laguerre polynomials / 176 Properties of the associated Laguerre polynomials / 177 Notation / 182 Examples / 182 Problems / 185 Chebyshev Polynomials Definition of Chebyshev polynomials; Chebyshev's equation / 187 Generating function / 190 Orthogonality properties / 192 Recurrence relations / 193 Examples / 194 Problems / 196 Gegenbauer and Jacobi Polynomials Gegenbauer polynomials / 197 Jacobi polynomials / 198 Examples / 200 Problems / 201 Hypergeometric Functions Definition of hypergeometric functions / 203 Properties of the hypergeometric function / 207 Properties of the confluent hypergeometric function / 210 Examples / 212 Problem / 216 Other Special Functions Incomplete gamma functions / 218 Exponential integral and related functions / 218 The error function and related functions / 221 Riemann's zeta function / 223 Debye functions / 224 Elliptic integrals / 224 Examples / 225 Problems / 228 Appendices Convergence of Legendre series / 230 Euler's constant / 231 Differential equations / 233 Orthogonality relations / 234 Generating functions / 236 Hints and Solutions to Problems / 237 Bibliography / 243 Index / 245

rawTOC:
Preface / v List of Symbols / ix Series Solution of Differential Equations Method of Frobenius / 1 \\ Examples / 8 \\ Problems / 21 \\ Gamma and Beta Functions Definitions / 23 \\ Properties of the beta and gamma functions / 24 \\ Definition of the gamma function for negative values of the argument / 30 \\ Examples / 37 \\ Problems / 40 \\ Legendre Polynomials and Functions Legendre's equation and its solution / 42 \\ Generating function for the Legendre polynomials / 46 \\ Further expressions for the Legendre polynomials / 48 \\ Explicit expressions for and special values of the Legendre polynomials / 50 \\ Orthogonality properties of the Legendre polynomials / 52 \\ Legendre series / 55 \\ Relations between the Legendre polynomials and their derivatives; / 58 \\ recurrence relations Associated Legendre functions / 62 \\ Properties of the associated Legendre functions / 65 \\ Legendre functions of the second kind / 70 \\ Spherical harmonics / 78 \\ Graphs of the Legendre functions / 82 \\ Examples / 85 \\ Problems / 90 \\ Bessel Functions Bessel's equation and its solutions; Bessel functions of the first and second kind / 92 \\ Generating function for the Bessel functions / 99 \\ Integral representations for Bessel functions / 101 \\ Recurrence relations / 104 \\ Hankel functions / 107 \\ Equations reducible to Bessel's equation / 108 \\ Modified Bessel functions / 110 \\ Recurrence relations for the modified Bessel functions / 113 \\ Integral representations for the modified Bessel functions / 116 \\ Kelvin's functions / 120 \\ Spherical Bessel functions / 121 \\ Behaviour of the Bessel functions for large and small values of the argument / 127 \\ Graphs of the Bessel functions / 133 \\ Orthonormality of the Bessel functions; Bessel series / 137 \\ Integrals involving Bessel functions / 141 \\ Examples / 148 \\ Problems / 154 \\ Hermite Polynomials Hermite's equation and its solution / 156 \\ Generating function / 157 \\ Other expressions for the Hermite polynomials / 158 \\ Explicit expressions for, and special values of, the Hermite polynomials / 160 \\ Orthogonality properties of the Hermite polynomials / 161 \\ Relations between Hermite polynomials and their derivatives; recurrence relations / 162 \\ Weber--Hermite functions / 163 \\ Examples / 164 \\ Problems / 166 \\ Laguerre Polynomials Laguerre's equation and its solution / 168 \\ Generating function / 169 \\ Alternative expression for the Laguerre polynomials / 170 \\ Explicit expressions for, and special values of, the Laguerre polynomials / 171 \\ Orthogonality properties of the Laguerre polynomials / 172 \\ Relations between Laguerre polynomials and their derivatives; recurrence relations / 173 \\ Associated Laguerre polynomials / 176 \\ Properties of the associated Laguerre polynomials / 177 \\ Notation / 182 \\ Examples / 182 \\ Problems / 185 \\ Chebyshev Polynomials Definition of Chebyshev polynomials; Chebyshev's equation / 187 \\ Generating function / 190 \\ Orthogonality properties / 192 \\ Recurrence relations / 193 \\ Examples / 194 \\ Problems / 196 \\ Gegenbauer and Jacobi Polynomials Gegenbauer polynomials / 197 \\ Jacobi polynomials / 198 \\ Examples / 200 \\ Problems / 201 \\ Hypergeometric Functions Definition of hypergeometric functions / 203 \\ Properties of the hypergeometric function / 207 \\ Properties of the confluent hypergeometric function / 210 \\ Examples / 212 \\ Problem / 216 \\ Other Special Functions Incomplete gamma functions / 218 \\ Exponential integral and related functions / 218 \\ The error function and related functions / 221 \\ Riemann's zeta function / 223 \\ Debye functions / 224 \\ Elliptic integrals / 224 \\ Examples / 225 \\ Problems / 228 \\ Appendices Convergence of Legendre series / 230 \\ Euler's constant / 231 \\ Differential equations / 233 \\ Orthogonality relations / 234 \\ Generating functions / 236 \\ Hints and Solutions to Problems / 237 \\ Bibliography / 243 \\ Index / 245

entry:
@Book{Bell:2004:SFS,
  author =       "W. W. (William Wallace) Bell",
  title =        "Special Functions for Scientists and Engineers",
  publisher =    pub-DOVER,
  address =      pub-DOVER:adr,
  pages =        "xiv + 247",
  year =         "2004",
  ISBN =         "0-486-43521-0",
  ISBN-13 =      "978-0-486-43521-3",
  LCCN =         "QA351 .B4 2004",
  bibdate =      "Sat Oct 30 16:30:44 MDT 2010",
  bibsource =    "fsz3950.oclc.org:210/WorldCat;
                 https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  series =       "Dover books on mathematics",
  acknowledgement = ack-nhfb,
  remark =       "Reprinting of \cite{Bell:1968:SFS}.",
  subject =      "Functions, Special",
  tableofcontents = "Preface / v List of Symbols / ix Series Solution of
                 Differential Equations Method of Frobenius / 1 \\
                 Examples / 8 \\
                 Problems / 21 \\
                 Gamma and Beta Functions Definitions / 23 \\
                 Properties of the beta and gamma functions / 24 \\
                 Definition of the gamma function for negative values of
                 the argument / 30 \\
                 Examples / 37 \\
                 Problems / 40 \\
                 Legendre Polynomials and Functions Legendre's equation
                 and its solution / 42 \\
                 Generating function for the Legendre polynomials / 46
                 \\
                 Further expressions for the Legendre polynomials / 48
                 \\
                 Explicit expressions for and special values of the
                 Legendre polynomials / 50 \\
                 Orthogonality properties of the Legendre polynomials /
                 52 \\
                 Legendre series / 55 \\
                 Relations between the Legendre polynomials and their
                 derivatives; / 58 \\
                 recurrence relations Associated Legendre functions / 62
                 \\
                 Properties of the associated Legendre functions / 65
                 \\
                 Legendre functions of the second kind / 70 \\
                 Spherical harmonics / 78 \\
                 Graphs of the Legendre functions / 82 \\
                 Examples / 85 \\
                 Problems / 90 \\
                 Bessel Functions Bessel's equation and its solutions;
                 Bessel functions of the first and second kind / 92 \\
                 Generating function for the Bessel functions / 99 \\
                 Integral representations for Bessel functions / 101 \\
                 Recurrence relations / 104 \\
                 Hankel functions / 107 \\
                 Equations reducible to Bessel's equation / 108 \\
                 Modified Bessel functions / 110 \\
                 Recurrence relations for the modified Bessel functions
                 / 113 \\
                 Integral representations for the modified Bessel
                 functions / 116 \\
                 Kelvin's functions / 120 \\
                 Spherical Bessel functions / 121 \\
                 Behaviour of the Bessel functions for large and small
                 values of the argument / 127 \\
                 Graphs of the Bessel functions / 133 \\
                 Orthonormality of the Bessel functions; Bessel series /
                 137 \\
                 Integrals involving Bessel functions / 141 \\
                 Examples / 148 \\
                 Problems / 154 \\
                 Hermite Polynomials Hermite's equation and its solution
                 / 156 \\
                 Generating function / 157 \\
                 Other expressions for the Hermite polynomials / 158 \\
                 Explicit expressions for, and special values of, the
                 Hermite polynomials / 160 \\
                 Orthogonality properties of the Hermite polynomials /
                 161 \\
                 Relations between Hermite polynomials and their
                 derivatives; recurrence relations / 162 \\
                 Weber--Hermite functions / 163 \\
                 Examples / 164 \\
                 Problems / 166 \\
                 Laguerre Polynomials Laguerre's equation and its
                 solution / 168 \\
                 Generating function / 169 \\
                 Alternative expression for the Laguerre polynomials /
                 170 \\
                 Explicit expressions for, and special values of, the
                 Laguerre polynomials / 171 \\
                 Orthogonality properties of the Laguerre polynomials /
                 172 \\
                 Relations between Laguerre polynomials and their
                 derivatives; recurrence relations / 173 \\
                 Associated Laguerre polynomials / 176 \\
                 Properties of the associated Laguerre polynomials / 177
                 \\
                 Notation / 182 \\
                 Examples / 182 \\
                 Problems / 185 \\
                 Chebyshev Polynomials Definition of Chebyshev
                 polynomials; Chebyshev's equation / 187 \\
                 Generating function / 190 \\
                 Orthogonality properties / 192 \\
                 Recurrence relations / 193 \\
                 Examples / 194 \\
                 Problems / 196 \\
                 Gegenbauer and Jacobi Polynomials Gegenbauer
                 polynomials / 197 \\
                 Jacobi polynomials / 198 \\
                 Examples / 200 \\
                 Problems / 201 \\
                 Hypergeometric Functions Definition of hypergeometric
                 functions / 203 \\
                 Properties of the hypergeometric function / 207 \\
                 Properties of the confluent hypergeometric function /
                 210 \\
                 Examples / 212 \\
                 Problem / 216 \\
                 Other Special Functions Incomplete gamma functions /
                 218 \\
                 Exponential integral and related functions / 218 \\
                 The error function and related functions / 221 \\
                 Riemann's zeta function / 223 \\
                 Debye functions / 224 \\
                 Elliptic integrals / 224 \\
                 Examples / 225 \\
                 Problems / 228 \\
                 Appendices Convergence of Legendre series / 230 \\
                 Euler's constant / 231 \\
                 Differential equations / 233 \\
                 Orthogonality relations / 234 \\
                 Generating functions / 236 \\
                 Hints and Solutions to Problems / 237 \\
                 Bibliography / 243 \\
                 Index / 245",
}


bibtype: article
filename: elefunt.bib
label: Berrut:2004:APS
author: Jean-Paul Berrut and Hans D. Mittelmann
title: Adaptive Point Shifts in Rational Approximation with Optimized Denominator
journal: j-J-COMPUT-APPL-MATH
volume: 164--165
pages: 81--92
day: 1
month: mar
monthnumber: 3
year: 2004
CODEN: JCAMDI
DOI: https://doi.org/10.1016/S0377-0427(03)00485-0
ISSN: 0377-0427 (print), 1879-1778 (electronic) OR 03770427 (print), 18791778 (electronic)
ISSNL: 0377-0427 OR 03770427
bibdate: Tue Mar 24 21:10:48 2009
bibsource: https://www.math.utah.edu/pub/tex/bib/elefunt.bib
bibtimestamp: 2009.03.24 21:10:48 ???
fjournal: Journal of Computational and Applied Mathematics
keywords: interpolation; optimal interpolation; point shifts; rational approximation
acknowledgement: ack-nhfb
journalURL: http://www.sciencedirect.com/science/journal/03770427
rawauthor: Jean-Paul Berrut and Hans D. Mittelmann
rawtitle: Adaptive Point Shifts in Rational Approximation with Optimized Denominator
note:
Proceedings of the 10th International Congress on Computational and Applied Mathematics University of Leuven, Belgium, 22--26 July 2002. Edited by M. J. Goovaerts, S. Vandewalle, and L. Wuytack.

abstract:
Classical rational interpolation is known to suffer from several drawbacks, such as unattainable points and randomly located poles for a small number of nodes, as well as an erratic behavior of the error as this number grows larger. In a former article, we have suggested to obtain rational interpolants by a procedure that attaches optimally placed poles to the interpolating polynomial, using the barycentric representation of the interpolants. In order to improve upon the condition of the derivatives in the solution of differential equations, we have then experimented with a conformal point shift suggested by Kosloff and Tal-Ezer. As it turned out, such shifts can achieve a spectacular improvement in the quality of the approximation itself for functions with a large gradient in the center of the interval. This leads us to the present work which combines the pole attachment method with shifts optimally adjusted to the interpolated function. Such shifts are also constructed for functions with several shocks away from the extremities of the interval.

rawabstract:
Classical rational interpolation is known to suffer from several drawbacks, such as unattainable points and randomly located poles for a small number of nodes, as well as an erratic behavior of the error as this number grows larger. In a former article, we have suggested to obtain rational interpolants by a procedure that attaches optimally placed poles to the interpolating polynomial, using the barycentric representation of the interpolants. In order to improve upon the condition of the derivatives in the solution of differential equations, we have then experimented with a conformal point shift suggested by Kosloff and Tal-Ezer. As it turned out, such shifts can achieve a spectacular improvement in the quality of the approximation itself for functions with a large gradient in the center of the interval. This leads us to the present work which combines the pole attachment method with shifts optimally adjusted to the interpolated function. Such shifts are also constructed for functions with several shocks away from the extremities of the interval.

rawnote:
Proceedings of the 10th International Congress on Computational and Applied Mathematics University of Leuven, Belgium, 22--26 July 2002. Edited by M. J. Goovaerts, S. Vandewalle, and L. Wuytack.

entry:
@Article{Berrut:2004:APS,
  author =       "Jean-Paul Berrut and Hans D. Mittelmann",
  title =        "Adaptive Point Shifts in Rational Approximation with
                 Optimized Denominator",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "164--165",
  number =       "??",
  pages =        "81--92",
  day =          "1",
  month =        mar,
  year =         "2004",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/S0377-0427(03)00485-0",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  bibdate =      "Tue Mar 24 21:10:48 2009",
  bibsource =    "https://www.math.utah.edu/pub/tex/bib/elefunt.bib",
  note =         "Proceedings of the 10th International Congress on
                 Computational and Applied Mathematics University of
                 Leuven, Belgium, 22--26 July 2002. Edited by M. J.
                 Goovaerts, S. Vandewalle, and L. Wuytack.",
  abstract =     "Classical rational interpolation is known to suffer
                 from several drawbacks, such as unattainable points and
                 randomly located poles for a small number of nodes, as
                 well as an erratic behavior of the error as this number
                 grows larger. In a former article, we have suggested to
                 obtain rational interpolants by a procedure that
                 attaches optimally placed poles to the interpolating
                 polynomial, using the barycentric representation of the
                 interpolants. In order to improve upon the condition of
                 the derivatives in the solution of differential
                 equations, we have then experimented with a conformal
                 point shift suggested by Kosloff and Tal-Ezer. As it
                 turned out, such shifts can achieve a spectacular
                 improvement in the quality of the approximation itself
                 for functions with a large gradient in the center of
                 the interval. This leads us to the present work which
                 combines the pole attachment method with shifts
                 optimally adjusted to the interpolated function. Such
                 shifts are also constructed for functions with several
                 shocks away from the extremities of the interval.",
  acknowledgement = ack-nhfb,
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "interpolation; optimal interpolation; point shifts;
                 rational approximation",
}


