The Resource Special functions, George E. Andrews, Richard Askey, Ranjan Roy, (electronic resource)

Special functions, George E. Andrews, Richard Askey, Ranjan Roy, (electronic resource)

Label
Special functions
Title
Special functions
Statement of responsibility
George E. Andrews, Richard Askey, Ranjan Roy
Creator
Contributor
Subject
Language
eng
Cataloging source
DLC
http://library.link/vocab/creatorDate
1938-
http://library.link/vocab/creatorName
Andrews, George E.
Dewey number
515/.5
Index
index present
LC call number
QA351
LC item number
.A74 1999
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1948-
http://library.link/vocab/relatedWorkOrContributorName
  • Askey, Richard
  • Roy, Ranjan
Series statement
Encyclopedia of mathematics and its applications
Series volume
v. 71
http://library.link/vocab/subjectName
Functions, Special
Label
Special functions, George E. Andrews, Richard Askey, Ranjan Roy, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 641-653) and indexes
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Cover; Half Title; Series Page; Title; Copyright; Dedication; Contents; Preface; 1 The Gamma and Beta Functions; 1.1 The Gamma and Beta Integrals and Functions; 1.2 The Euler Reflection Formula; 1.3 The Hurwitz and Riemann Zeta Functions; 1.4 Stirling's Asymptotic Formula; 1.5 Gauss's Multiplication Formula for Г(mx); 1.6 Integral Representations for Log Г(x) and Ψ(x); 1.7 Kummer's Fourier Expansion of Log Г(x); 1.8 Integrals of Dirichlet and Volumes of Ellipsoids; 1.9 The Bohr-Mollerup Theorem; 1.10 Gauss and Jacobi Sums; 1.11 A Probabilistic Evaluation of the Beta Function
  • 1.12 The p-adic Gamma FunctionExercises; 2 The Hypergeometric Functions; 2.1 The Hypergeometric Series; 2.2 Euler's Integral Representation; 2.3 The Hypergeometric Equation; 2.4 The Barnes Integral for the Hypergeometric Function; 2.5 Contiguous Relations; 2.6 Dilogarithms; 2.7 Binomial Sums; 2.8 Dougall's Bilateral Sum; 2.9 Fractional Integration by Parts and Hypergeometric Integrals; Exercises; 3 Hypergeometric Transformations and Identities; 3.1 Quadratic Transformations; 3.2 The Arithmetic-Geometric Mean and Elliptic Integrals; 3.3 Transformations of Balanced Series
  • 3.4 Whipple's Transformation3.5 Dougall's Formula and Hypergeometric Identities; 3.6 Integral Analogs of Hypergeometric Sums; 3.7 Contiguous Relations; 3.8 The Wilson Polynomials; 3.9 Quadratic Transformations - Riemann's View; 3.10 Indefinite Hypergeometric Summation; 3.11 The W-Z Method; 3.12 Contiguous Relations and Summation Methods; Exercises; 4 Bessel Functions and Confluent Hypergeometric Functions; 4.1 The Confluent Hypergeometric Equation; 4.2 Barnes's Integral for 1F1; 4.3 Whittaker Functions; 4.4 Examples of 1F1 and Whittaker Functions; 4.5 Bessel's Equation and Bessel Functions
  • 4.6 Recurrence Relations4.7 Integral Representations of Bessel Functions; 4.8 Asymptotic Expansions; 4.9 Fourier Transforms and Bessel Functions; 4.10 Addition Theorems; 4.11 Integrals of Bessel Functions; 4.12 The Modified Bessel Functions; 4.13 Nicholson's Integral; 4.14 Zeros of Bessel Functions; 4.15 Monotonicity Properties of Bessel Functions; 4.16 Zero-Free Regions for 1F1 Functions; Exercises; 5 Orthogonal Polynomials; 5.1 Chebyshev Polynomials; 5.2 Recurrence; 5.3 Gauss Quadrature; 5.4 Zeros of Orthogonal Polynomials; 5.5 Continued Fractions; 5.6 Kernel Polynomials
  • 5.7 Parseval's Formula5.8 The Moment-Generating Function; Exercises; 6 Special Orthogonal Polynomials; 6.1 Hermite Polynomials; 6.2 Laguerre Polynomials; 6.3 Jacobi Polynomials and Gram Determinants; 6.4 Generating Functions for Jacobi Polynomials; 6.5 Completeness of Orthogonal Polynomials; 6.6 Asymptotic Behavior of Pn(α,β)(x) for Large n; 6.7 Integral Representations of Jacobi Polynomials; 6.8 Linearization of Products of Orthogonal Polynomials; 6.9 Matching Polynomials; 6.10 The Hypergeometric Orthogonal Polynomials; 6.11 An Extension of the Ultraspherical Polynomials; Exercises
  • 7 Topics in Orthogonal Polynomials
Dimensions
unknown
Extent
1 online resource (682 p.)
Form of item
online
Isbn
9781107269941
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2670000000356577
  • (EBL)1218103
  • (SSID)ssj0000877432
  • (PQKBManifestationID)11435888
  • (PQKBTitleCode)TC0000877432
  • (PQKBWorkID)10907431
  • (PQKB)11621989
  • (UkCbUP)CR9781107325937
  • (MiAaPQ)EBC1218103
  • (EXLCZ)992670000000356577
Label
Special functions, George E. Andrews, Richard Askey, Ranjan Roy, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 641-653) and indexes
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Cover; Half Title; Series Page; Title; Copyright; Dedication; Contents; Preface; 1 The Gamma and Beta Functions; 1.1 The Gamma and Beta Integrals and Functions; 1.2 The Euler Reflection Formula; 1.3 The Hurwitz and Riemann Zeta Functions; 1.4 Stirling's Asymptotic Formula; 1.5 Gauss's Multiplication Formula for Г(mx); 1.6 Integral Representations for Log Г(x) and Ψ(x); 1.7 Kummer's Fourier Expansion of Log Г(x); 1.8 Integrals of Dirichlet and Volumes of Ellipsoids; 1.9 The Bohr-Mollerup Theorem; 1.10 Gauss and Jacobi Sums; 1.11 A Probabilistic Evaluation of the Beta Function
  • 1.12 The p-adic Gamma FunctionExercises; 2 The Hypergeometric Functions; 2.1 The Hypergeometric Series; 2.2 Euler's Integral Representation; 2.3 The Hypergeometric Equation; 2.4 The Barnes Integral for the Hypergeometric Function; 2.5 Contiguous Relations; 2.6 Dilogarithms; 2.7 Binomial Sums; 2.8 Dougall's Bilateral Sum; 2.9 Fractional Integration by Parts and Hypergeometric Integrals; Exercises; 3 Hypergeometric Transformations and Identities; 3.1 Quadratic Transformations; 3.2 The Arithmetic-Geometric Mean and Elliptic Integrals; 3.3 Transformations of Balanced Series
  • 3.4 Whipple's Transformation3.5 Dougall's Formula and Hypergeometric Identities; 3.6 Integral Analogs of Hypergeometric Sums; 3.7 Contiguous Relations; 3.8 The Wilson Polynomials; 3.9 Quadratic Transformations - Riemann's View; 3.10 Indefinite Hypergeometric Summation; 3.11 The W-Z Method; 3.12 Contiguous Relations and Summation Methods; Exercises; 4 Bessel Functions and Confluent Hypergeometric Functions; 4.1 The Confluent Hypergeometric Equation; 4.2 Barnes's Integral for 1F1; 4.3 Whittaker Functions; 4.4 Examples of 1F1 and Whittaker Functions; 4.5 Bessel's Equation and Bessel Functions
  • 4.6 Recurrence Relations4.7 Integral Representations of Bessel Functions; 4.8 Asymptotic Expansions; 4.9 Fourier Transforms and Bessel Functions; 4.10 Addition Theorems; 4.11 Integrals of Bessel Functions; 4.12 The Modified Bessel Functions; 4.13 Nicholson's Integral; 4.14 Zeros of Bessel Functions; 4.15 Monotonicity Properties of Bessel Functions; 4.16 Zero-Free Regions for 1F1 Functions; Exercises; 5 Orthogonal Polynomials; 5.1 Chebyshev Polynomials; 5.2 Recurrence; 5.3 Gauss Quadrature; 5.4 Zeros of Orthogonal Polynomials; 5.5 Continued Fractions; 5.6 Kernel Polynomials
  • 5.7 Parseval's Formula5.8 The Moment-Generating Function; Exercises; 6 Special Orthogonal Polynomials; 6.1 Hermite Polynomials; 6.2 Laguerre Polynomials; 6.3 Jacobi Polynomials and Gram Determinants; 6.4 Generating Functions for Jacobi Polynomials; 6.5 Completeness of Orthogonal Polynomials; 6.6 Asymptotic Behavior of Pn(α,β)(x) for Large n; 6.7 Integral Representations of Jacobi Polynomials; 6.8 Linearization of Products of Orthogonal Polynomials; 6.9 Matching Polynomials; 6.10 The Hypergeometric Orthogonal Polynomials; 6.11 An Extension of the Ultraspherical Polynomials; Exercises
  • 7 Topics in Orthogonal Polynomials
Dimensions
unknown
Extent
1 online resource (682 p.)
Form of item
online
Isbn
9781107269941
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2670000000356577
  • (EBL)1218103
  • (SSID)ssj0000877432
  • (PQKBManifestationID)11435888
  • (PQKBTitleCode)TC0000877432
  • (PQKBWorkID)10907431
  • (PQKB)11621989
  • (UkCbUP)CR9781107325937
  • (MiAaPQ)EBC1218103
  • (EXLCZ)992670000000356577

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