Special functions and orthogonal polynomials

By:

Beals, Richard

Contributor(s):

Wong, Roderick

Series: Cambridge studies in advanced mathematics ; 153Publication details: Cambridge University Press, 2016. Cambridge:Description: xiii, 473 pages : ill ; hb, 24 cmISBN:

9781107106987

Subject(s):

DDC classification:

515.55 BEA

Summary: 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'.

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Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	515.55 BEA (Browse shelf(Opens below))	1	Available		030166

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Previous	515.5 LEB Special functions and their applications	515.52 FAR Solved problems in analysis: as applied to gamma, beta, Legendre, and Bessel functions	515.53 LUK Integrals of Bessel functions	515.55 BEA Special functions and orthogonal polynomials	515.56 PAT Introduction to the theory of the Riemann zeta-function	515.63 LEP Lectures on vector bundles	515.64 GEL Calculus of variations :	Next

Includes bibliographical references (pages 443-462) and index.

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'.

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