Special functions
 Responsibility
 George E. Andrews, Richard Askey, Ranjan Roy.
 Language
 English.
 Edition
 1st pbk. ed.
 Imprint
 Cambridge, U.K. ; New York : Cambridge University Press, 2000.
 Physical description
 xvi, 664 p. : ill ; 24 cm.
 Series
 Encyclopedia of mathematics and its applications ; v. 71.
Access
Creators/Contributors
 Author/Creator
 Andrews, George E., 1938
 Contributor
 Roy, Ranjan, 1948
 Askey, Richard.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 641653) and indexes.
 Contents

 1. The Gamma and Beta functions 2. The hypergeometric functions 3. Hypergeometric transformations and identities 4. Bessel functions and confluent hypergeometric functions 5. Orthogonal polynomials 6. Special orthogonal transformations 7. Topics in orthogonal polynomials 8. The Selberg integral and its applications 9. Spherical harmonics 10. Introduction to qseries 11. Partitions 12. Bailey chains Appendix 1. Infinite products Appendix 2. Summability and fractional integration Appendix 3. Asymptotic expansions Appendix 4. EulerMaclaurin summation formula Appendix 5. Lagrange inversion formula Appendix 6. Series solutions of differential equations.
 (source: Nielsen Book Data)
 Publisher's Summary
 Special functions, natural generalizations of the elementary functions, have been studied for centuries. The greatest mathematicians, among them Euler, Gauss, Legendre, Eisenstein, Riemann, and Ramanujan, have laid the foundations for this beautiful and useful area of mathematics. 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, using the basic building block of the gamma function. In addition to relatively new work on gamma and beta functions, such as Selberg's multidimensional integrals, many important but relatively unknown nineteenth century results are included. Other topics include qextensions of beta integrals and of hypergeometric series, Bailey chains, spherical harmonics, and applications to combinatorial problems. The authors provide organizing ideas, motivation, and historical background for the study and application of some important special functions. This clearly expressed and readable 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.
(source: Nielsen Book Data)  Supplemental links

Publisher description
Table of contents
Subjects
Bibliographic information
 Reprint/reissue date
 2000
 Original date
 1999
 Series
 Encyclopedia of mathematics and its applications ; v. 71
 Note
 Originally published: 1999.
 ISBN
 0521789885 (pbk.)
 9780521789882 (pbk.)
 0521623219
 9780521623216
 0521623219