Abstract
In this article, we define an extended version of the Pochhammer symbol and then introduce the corresponding extension of the τ-Gauss hypergeometric function. The basic properties of the extended τ-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 τ-Gauss hypergeometric function.
Highlights
Throughout this article, we denote the sets of positive integers, negative integers, and complex numbers by N, Z−, and C, respectively
Where ρ j ∈ C ( j = 1, · · ·, p). Another interesting extension of the Pochhammer symbol and the associated hypergeometric functions was recently given by Srivastava et al in [11]
The following are some of the special cases of τ-Gauss hypergeometric functions defined by (11)
Summary
Hari Mohan Srivastava 1,2,3 , Asifa Tassaddiq 4, * , Gauhar Rahman 5 , Kottakkaran Sooppy Nisar 6 and Ilyas Khan 7. College of Computer and Information Sciences, Majmaah University, Al Majmaah 11952, Saudi Arabia
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