A New Extension of the τ-Gauss Hypergeometric Function and Its Associated Properties

被引：11

作者：

Srivastava, Hari Mohan ^{[1
,2
,3
]}

Tassaddiq, Asifa ^{[4
]}

Rahman, Gauhar ^{[5
]}

Nisar, Kottakkaran Sooppy ^{[6
]}

Khan, Ilyas ^{[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] Azerbaijan Univ, Dept Math & Informat, 71 Jeyhun Hajibeyli St, AZ-1007 Baku, Azerbaijan

[4] Majmaah Univ, Coll Comp & Informat Sci, Al Majmaah 11952, Saudi Arabia

[5] Shaheed Benazir Bhutto Univ, Dept Math, Sheringal 18000, Upper Dir, Pakistan

[6] Prince Sattam Bin Abdulaziz Univ, Coll Arts & Sci, Dept Math, Wadi Aldawaser 11991, Saudi Arabia

[7] Majmaah Univ, Coll Sci Al Zulfi, Dept Math, Al Majmaah 11952, Saudi Arabia

来源：

MATHEMATICS | 2019年 / 7卷 / 10期

关键词：

gamma function and its extension; Pochhammer symbol and its extensions; hypergeometric function and its extensions; tau-Gauss hypergeometric function and its extensions; tau-Kummer hypergeometric function; Fox-Wright function; POCHHAMMER SYMBOL; GAMMA;

D O I：

10.3390/math7100996

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we define an extended version of the Pochhammer symbol and then introduce the corresponding extension of the tau-Gauss hypergeometric function. The basic properties of the extended tau-Gauss hypergeometric function, including integral and derivative formulas involving the Mellin transform and the operators of fractional calculus, are derived. We also consider some new and known results as consequences of our proposed extension of the tau-Gauss hypergeometric function.

引用

页数：9

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