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
收藏
页码：37 / 50
页数：14
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