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Encyclopedia of Special Functions: The Askey-Bateman Project最新文献

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Wilson and Related Polynomials Wilson和相关多项式
Encyclopedia of Special Functions: The Askey-Bateman Project Pub Date : 2020-09-30 DOI: 10.1017/9780511979156.006
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引用次数: 0
The Askey–Wilson Family of Polynomials Askey-Wilson多项式族
Encyclopedia of Special Functions: The Askey-Bateman Project Pub Date : 2020-09-30 DOI: 10.1017/9780511979156.009
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引用次数: 0
Some q-Orthogonal Polynomials 一些q-正交多项式
Encyclopedia of Special Functions: The Askey-Bateman Project Pub Date : 2020-09-30 DOI: 10.1017/CBO9781107325982.015
M. Ismail
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引用次数: 0
Jacobi and Related Polynomials 雅可比和相关多项式
Encyclopedia of Special Functions: The Askey-Bateman Project Pub Date : 2020-09-30 DOI: 10.1017/9780511979156.004
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引用次数: 0
Orthogonal Polynomials on the Unit Circle 单位圆上的正交多项式
Encyclopedia of Special Functions: The Askey-Bateman Project Pub Date : 2020-09-30 DOI: 10.1017/9780511979156.010
Manuel ALFAROa
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引用次数: 365
Index 指数
Encyclopedia of Special Functions: The Askey-Bateman Project Pub Date : 2020-09-30 DOI: 10.1017/9780511979156.015
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引用次数: 0
Hypergeometric and Basic Hypergeometric Series and Integrals Associated with Root Systems 与根系统相关的超几何和基本超几何级数和积分
Encyclopedia of Special Functions: The Askey-Bateman Project Pub Date : 2017-05-25 DOI: 10.1017/9780511777165.006
M. Schlosser
{"title":"Hypergeometric and Basic Hypergeometric Series and Integrals Associated with Root Systems","authors":"M. Schlosser","doi":"10.1017/9780511777165.006","DOIUrl":"https://doi.org/10.1017/9780511777165.006","url":null,"abstract":"We give an overview of some of the main results from the theories of hypergeometric and basic hypergeometric series and integrals associated with root systems. In particular, we list a number of summations, transformations and explicit evaluations for such multiple series and integrals. We concentrate on such results which do not directly extend to the elliptic level. This text is a provisional version of a chapter on hypergeometric and basic hypergeometric series and integrals associated with root systems for volume 2 of the new Askey--Bateman project which deals with \"Multivariable special functions\".","PeriodicalId":356498,"journal":{"name":"Encyclopedia of Special Functions: The Askey-Bateman Project","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114906869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Dunkl Operators and Related Special Functions Dunkl算子和相关的特殊函数
Encyclopedia of Special Functions: The Askey-Bateman Project Pub Date : 2012-10-10 DOI: 10.1017/9780511777165.008
C. Dunkl
{"title":"Dunkl Operators and Related Special Functions","authors":"C. Dunkl","doi":"10.1017/9780511777165.008","DOIUrl":"https://doi.org/10.1017/9780511777165.008","url":null,"abstract":"Functions like the exponential, Chebyshev polynomials, and monomial symmetric polynomials are preeminent among all special functions. They have simple definitions and can be expressed using easily specified integers like n!. Families of functions like Gegenbauer, Jacobi and Jack symmetric polynomials and Bessel functions are labeled by parameters. These could be unspecified transcendental numbers or drawn from large sets of real numbers, for example the complement of {-1/2, -3/2, -5/2,...}. One aim of this chapter is to provide a harmonic analysis setting in which parameters play a natural role. The basic objects are finite reflection (Coxeter) groups and algebras of operators on polynomials which generalize the algebra of partial differential operators. These algebras have as many parameters as the number of conjugacy classes of reflections in the associated groups.","PeriodicalId":356498,"journal":{"name":"Encyclopedia of Special Functions: The Askey-Bateman Project","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124975256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Macdonald–Koornwinder Polynomials
Encyclopedia of Special Functions: The Askey-Bateman Project Pub Date : 2011-11-25 DOI: 10.1017/9780511777165.010
J. Stokman
{"title":"Macdonald–Koornwinder Polynomials","authors":"J. Stokman","doi":"10.1017/9780511777165.010","DOIUrl":"https://doi.org/10.1017/9780511777165.010","url":null,"abstract":"An overview of the basic results on Macdonald(-Koornwinder) polynomials and double affine Hecke algebras is given. We develop the theory in such a way that it naturally encompasses all known cases. Among the basic properties of the Macdonald polynomials we treat are the quadratic norm formulas, duality and the evaluation formulas. This text is a provisional version of a chapter on Macdonald polynomials for volume 5 of the Askey-Bateman project, entitled \"Multivariable special functions\".","PeriodicalId":356498,"journal":{"name":"Encyclopedia of Special Functions: The Askey-Bateman Project","volume":"45 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123309290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The Moment Problem 时间问题
Encyclopedia of Special Functions: The Askey-Bateman Project Pub Date : 2002-04-01 DOI: 10.1017/9780511979156.012
A. Gut
{"title":"The Moment Problem","authors":"A. Gut","doi":"10.1017/9780511979156.012","DOIUrl":"https://doi.org/10.1017/9780511979156.012","url":null,"abstract":"The purpose of this paper is to provide some additional insight into the moment problem by connecting a condition by Lin, Bondesson's class of hyperbolically completely monotone densities, and the theory of regularly varying functions. In particular, two questions addressed in a recent paper by Stoyanov concerning powers of random variables and functions that (do not) preserve uniqueness will be investigated.","PeriodicalId":356498,"journal":{"name":"Encyclopedia of Special Functions: The Askey-Bateman Project","volume":"112 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2002-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124332011","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 197
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