登入選單
返回Google圖書搜尋
Special Functions and Orthogonal Polynomials
Richard BealsRoderick Wong
出版Cambridge University Press, 2016-05-17
主題Mathematics / GeneralMathematics / Algebra / GeneralMathematics / Mathematical AnalysisMathematics / Complex Analysis
ISBN11071069829781107106987
URLhttp://books.google.com.hk/books?id=RusIDAAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋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'.