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

Hari Mohan Srivastava, Asifa Tassaddiq, Gauhar Rahman, Kottakkaran Sooppy Nisar and Ilyas Khan
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Hari Mohan Srivastava: Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Asifa Tassaddiq: College of Computer and Information Sciences, Majmaah University, Al Majmaah 11952, Saudi Arabia
Gauhar Rahman: Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal 18000, Upper Dir, Pakistan
Kottakkaran Sooppy Nisar: Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
Ilyas Khan: Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al Majmaah 11952, Saudi Arabia

Mathematics, 2019, vol. 7, issue 10, 1-9

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.

Keywords: gamma function and its extension; Pochhammer symbol and its extensions; hypergeometric function and its extensions; ? -Gauss hypergeometric function and its extensions; ? -Kummer hypergeometric function; Fox-Wright function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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