Special functions
Subtitle: a graduate text
By: Richard Beals, Roderick Wong
Contributors: Wong, R. (Roderick), 1944-
Series: Cambridge studies in advanced mathematics -- 126
Publisher: Cambridge University Press
Published: 2010
Place of publication: Cambridge; New York
Language: eng
Number of pages: 456
ISBN-13: 9780521197977
Subjects: Textbooks; Special Functions
Description: "The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations - the hypergeometric equation and the confluent hypergeometric equation - and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference"--
Notes: Includes bibliographical references and indexes.
Table of contents: title: Orientation; title: Gamma, beta, zeta; title: Second-order differential equations; title: Orthogonal polynomials; title: Discrete orthogonal polynomials; title: Confluent hypergeometric functions; title: Cylinder functions; title: Hypergeometric functions; title: Spherical functions; title: Asymptotics; title: Elliptic functions.