APPELL'S FUNCTION F-1 AND EXTON'S TRIPLE HYPERGEOMETRIC FUNCTION X-9

被引：0

作者：

Choi, Junesang ^{[1
]}

Rathie, Arjun K. ^{[2
]}

机构：

[1] Dongguk Univ, Dept Math, Gyeongju 780714, South Korea

[2] Cent Univ Kerala, Sch Math & Phys Sci, Dept Math, Kasaragod 671328, India

来源：

JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS | 2013年 / 20卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

hypergeometric functions of several variables; multiple Gaussian hyper-geometric series; Appell's function F-1; Exton's triple hypergeometric function X-9; Gauss's hyper-geometric functions; generalizations of Kummer's second theorem;

D O I：

10.7468/jksmeb.2013.24.1.37

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the theory of hypergeometric functions of one or several variables, a remarkable amount of mathematicians's concern has been given to develop their transformation formulas and summation identities. Here we aim at presenting explicit expressions (in a single form) of the following weighted Appell's function F-1: (1 + 2x)(-alpha) (1 + 2z)(-b) F-1 (c, a, b; 2c + j; 4x/1+ 2x, 4z/1 + 2z) (j = 0, +/- 1...,+/- 5) in terms of Exton's triple hypergeometric X-9. The results are derived with the help of generalizations of Kummer's second theorem very recently provided by Kim et al. A large number of very interesting special cases including Exton's result are also given.

引用

页码：37 / 50

页数：14

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