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Special functions and orthogonal polynomials /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Special functions and orthogonal polynomials // Richard Beals, Roderick S.C. Wong.
其他題名:	Special Functions & Orthogonal Polynomials
作者:	Beals, Richard,
其他作者:	Wong, Roderick,
面頁冊數:	1 online resource (xiii, 473 pages) :digital, PDF file(s). :
附註:	Title from publisher's bibliographic system (viewed on 05 May 2016).
標題:	Mathematical analysis. -
電子資源:	https://doi.org/10.1017/CBO9781316227381
ISBN:	9781316227381 (ebook)

Special functions and orthogonal polynomials /
Beals, Richard,1938-

Special functions and orthogonal polynomials /Special Functions & Orthogonal PolynomialsRichard Beals, Roderick S.C. Wong. - 1 online resource (xiii, 473 pages) :digital, PDF file(s). - Cambridge studies in advanced mathematics ;153. - Cambridge studies in advanced mathematics ;134..

Title from publisher's bibliographic system (viewed on 05 May 2016).

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'.

ISBN: 9781316227381 (ebook)Subjects--Topical Terms:

527926
Mathematical analysis.

LC Class. No.: QA404.5 / .B3227 2016

Dewey Class. No.: 515/.55

Special functions and orthogonal polynomials /
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500 $a Title from publisher's bibliographic system (viewed on 05 May 2016).
520 $a 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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