Euler-type transformations for the generalized hypergeometric function r+2 F r+1(x)

被引：14

作者：

Miller, A. R. ^{[1
]}

Paris, R. B. ^{[1
]}

机构：

[1] Univ Abertay Dundee, Div Complex Syst, Dundee DD1 1HG, Scotland

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2011年 / 62卷 / 01期

关键词：

Generalized hypergeometric function; Euler transformation; Kummer transformation; KUMMER-TYPE TRANSFORMATION; SUMMATION; FORMULA; SERIES; F-2(2);

D O I：

10.1007/s00033-010-0085-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide generalizations of two of Euler's classical transformation formulas for the Gauss hypergeometric function extended to the case of the generalized hypergeometric function (r+2) F (r+1)(x) when there are additional numeratorial and denominatorial parameters differing by unity. The method employed to deduce the latter is also implemented to obtain a Kummer-type transformation formula for (r+1) F (r+1) (x) that was recently derived in a different way.

引用

页码：31 / 45

页数：15

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