Special Functions and Orthogonal Polynomials

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Richard Beals (Yale University, Connecticut) Roderick Wong (City University of Hong Kong)

Special Functions and Orthogonal Polynomials

Richard Beals (Yale University, Connecticut), Roderick Wong (City University of Hong Kong)

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English

Cambridge University Press
19 May 2016

Mathematics; Algebra; Real analysis, real variables; Complex analysis, complex variables

Series: Cambridge Studies in Advanced Mathematics

The subject of special functions is often presented as a collection of disparate results, rarely organized in a coherent way. This book emphasizes general principles that unify and demarcate the subjects of study. The authors' main goals are to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more. It shows how much of the subject can be traced back to two equations - the hypergeometric equation and confluent hypergeometric equation - and it details the ways in which these equations are canonical and special. There is extended coverage of orthogonal polynomials, including connections to approximation theory, continued fractions, and the moment problem, as well as an introduction to new asymptotic methods. There are also chapters on Meijer G-functions and elliptic functions. The final chapter introduces Painlevé transcendents, which have been termed the 'special functions of the twenty-first century'.

By: Richard Beals (Yale University Connecticut), Roderick Wong (City University of Hong Kong)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: 2nd Revised edition
Volume: 153
Dimensions: Height: 237mm, Width: 154mm, Spine: 32mm
Weight: 780g
ISBN: 9781107106987
ISBN 10: 1107106982
Series: Cambridge Studies in Advanced Mathematics
Pages: 488
Publication Date: 19 May 2016
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

Richard Beals is a former Professor of Mathematics at the University of Chicago and Yale University. He is the author or co-author of books on mathematical analysis, linear operators and inverse scattering theory, and has authored more than 100 research papers in areas including partial differential equations, mathematical economics and mathematical psychology. Roderick Wong is Chair Professor of Mathematics at the City University of Hong Kong. He is the author of books on asymptotic approximations of integrals and applied analysis. He has published over 140 research papers in areas such as asymptotic analysis, singular perturbation theory and special functions.