Some summation theorems and transformations for hypergeometric functions of Kampé de Fériet and Srivastava

被引：0

作者：

Srivastava, Hari M. ^{[1
,2
,3
,4
,5
,6
]}

Gupta, Bhawna ^{[7
]}

Qureshi, Mohammad Idris ^{[8
]}

Baboo, Mohd Shaid ^{[7
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

[2] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan

[3] Kyung Hee Univ, Ctr Converging Humanities, 26 Kyungheedae Ro, Seoul 02447, South Korea

[4] Azerbaijan Univ, Dept Math & Informat, 71 Jeyhun Hajibeyli St, AZ-1007 Baku, Azerbaijan

[5] Chung Yuan Christian Univ, Dept Appl Math, Taoyuan 320314, Taiwan

[6] Int Telemat Univ Uninettuno, Sect Math, I-00186 Rome, Italy

[7] Sharda Univ, Sch Basic Sci & Res, Dept Math, Greater Noida 201306, Uttar Pradesh, India

[8] Jamia Millia Islamia, Dept Appl Sci & Humanities, Fac Engn & Technol, New Delhi 110025, India

来源：

GEORGIAN MATHEMATICAL JOURNAL | 2024年 / 31卷 / 05期

关键词：

Catalan's constant; general multivariable hypergeometric functions; Riemann's zeta function; polylogarithm function; NEUMANN EXPANSIONS; SERIES; REDUCTION; FORMULAS; CONVERGENCE;

D O I：

10.1515/gmj-2023-2114

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Owing to the remarkable success of the hypergeometric functions of one variable, the authors present a study of some families of hypergeometric functions of two or more variables. These functions include (for example) the Kampe de Feriet-type hypergeometric functions in two variables and Srivastava's general hypergeometric function in three variables. The main aim of this paper is to provide several (presumably new) transformation and summation formulas for appropriately specified members of each of these families of hypergeometric functions in two and three variables. The methodology and techniques, which are used in this paper, are based upon the evaluation of some definite integrals involving logarithmic functions in terms of Riemann's zeta function, Catalan's constant, polylogarithm functions, and so on.

引用

页码：885 / 897

页数：13

共 49 条

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