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
收藏
页码：31 / 45
页数：15
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