Special functions /:
"This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials. The basic building block of the functions studied in this book is the gamma functio...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | , |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK ; New York, NY, USA :
Cambridge University Press,
1999.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
v. 71. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials. The basic building block of the functions studied in this book is the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, a number of important but relatively unknown nineteenth century results are included."--BOOK JACKET. "The authors provide organizing ideas, motivation, and historical background for the study and application of some important special functions. This work can serve as a learning tool and lasting reference for students and researchers in special functions, mathematical physics, differential equations, mathematical computing, number theory, and combinatorics."--Jacket |
| Beschreibung: | 1 online resource (xvi, 664 pages) |
| Bibliographie: | Includes bibliographical references (pages 641-653) and indexes. |
| ISBN: | 9781107266865 1107266866 9781107325937 1107325935 |
Internformat
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| 505 | 8 | |a 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 | |
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| author | Andrews, George E., 1938- |
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| contents | 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 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Andrews, George E., 1938- https://id.oclc.org/worldcat/entity/E39PBJm96RJCb3xFv6qP6tB9Dq http://id.loc.gov/authorities/names/n50022491 Special functions / George E. Andrews, Richard Askey, Ranjan Roy. Cambridge, UK ; New York, NY, USA : Cambridge University Press, 1999. 1 online resource (xvi, 664 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; v. 71 Includes bibliographical references (pages 641-653) and indexes. "This treatise presents an overview of special functions, focusing primarily on hypergeometric functions and the associated hypergeometric series, including Bessel functions and classical orthogonal polynomials. The basic building block of the functions studied in this book is the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, a number of important but relatively unknown nineteenth century results are included."--BOOK JACKET. "The authors provide organizing ideas, motivation, and historical background for the study and application of some important special functions. This work can serve as a learning tool and lasting reference for students and researchers in special functions, mathematical physics, differential equations, mathematical computing, number theory, and combinatorics."--Jacket Print version record. 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 Functions, Special. http://id.loc.gov/authorities/subjects/sh85052348 Fonctions spéciales. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Functions, Special fast Spezielle Funktion gnd http://d-nb.info/gnd/4182213-4 Speciale functies (wiskunde) gtt Fonctions spéciales. ram Electronic book. Askey, Richard. Roy, Ranjan, 1948- https://id.oclc.org/worldcat/entity/E39PCjDqJKXrRtrjpXfBBVPVJC http://id.loc.gov/authorities/names/n98047180 Print version: Andrews, George E., 1938- Special functions. Cambridge, UK ; New York, NY, USA : Cambridge University Press, 1999 0521623219 (DLC) 98025757 (OCoLC)39189987 Encyclopedia of mathematics and its applications ; v. 71. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=589166 Volltext |
| spellingShingle | Andrews, George E., 1938- Special functions / Encyclopedia of mathematics and its applications ; 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 Functions, Special. http://id.loc.gov/authorities/subjects/sh85052348 Fonctions spéciales. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Functions, Special fast Spezielle Funktion gnd http://d-nb.info/gnd/4182213-4 Speciale functies (wiskunde) gtt Fonctions spéciales. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85052348 http://d-nb.info/gnd/4182213-4 |
| title | Special functions / |
| title_auth | Special functions / |
| title_exact_search | Special functions / |
| title_full | Special functions / George E. Andrews, Richard Askey, Ranjan Roy. |
| title_fullStr | Special functions / George E. Andrews, Richard Askey, Ranjan Roy. |
| title_full_unstemmed | Special functions / George E. Andrews, Richard Askey, Ranjan Roy. |
| title_short | Special functions / |
| title_sort | special functions |
| topic | Functions, Special. http://id.loc.gov/authorities/subjects/sh85052348 Fonctions spéciales. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Functions, Special fast Spezielle Funktion gnd http://d-nb.info/gnd/4182213-4 Speciale functies (wiskunde) gtt Fonctions spéciales. ram |
| topic_facet | Functions, Special. Fonctions spéciales. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Functions, Special Spezielle Funktion Speciale functies (wiskunde) Electronic book. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=589166 |
| work_keys_str_mv | AT andrewsgeorgee specialfunctions AT askeyrichard specialfunctions AT royranjan specialfunctions |