Note on generalized hypergeometric function

作     者：Rao, Snehal B. Shukla, A. K. 

作者机构：Maharaja Sayajirao Univ Baroda Dept Appl Math Vadodara 390001 India SV Natl Inst Technol Dept Appl Math & Humanities Surat 395007 India 

出 版 物：《INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS》 (积分变换与特殊函数)

年 卷 期：2013年第24卷第11期

页      面：896-904页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：generalized hypergeometric function integral representation fractional integral and differential operators 33C20 33E20 26A33 

摘      要：Virchenko and Rumiantseva [On the generalized associated legendre functions. Fract Cal Appl Anal. 2008;11(2): 175- 185] gave another generalization F-2(1)tau,beta(a, b;c;z) of the hypergeometric function. In this paper, we give integral representations and differentiation formulae of F-2(1)tau,beta (a, b;c;z), alongwith relation of F-2(1)tau,beta (a, b;c;z) with the generalized Mittag-Leffler function E-alpha,beta(gamma,q)(z) [Shukla AK, Prajapati JC. On a generalization of Mittag-Leffler function and its properties. J Math Anal Appl. 2007;336(2): 797-811.]. Further properties of the generalized hypergeometric function R-2(1)(a, b;c;t;z) [Virchenko N, Kalla SL, Al-Zamel A. Some results on a generalized hypergeometric function. Integral Transforms Spec Funct. 2001;12(1): 89-100.], namely integral representation and differentiation formulae are also studied.