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Open AccessArticle

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

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Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
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Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
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Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
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College of Computer and Information Sciences, Majmaah University, Al Majmaah 11952, Saudi Arabia
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Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal 18000, Upper Dir, Pakistan
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Department of Mathematics, College of Arts and Science, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
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Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al Majmaah 11952, Saudi Arabia
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Author to whom correspondence should be addressed.
Mathematics 2019, 7(10), 996; https://doi.org/10.3390/math7100996
Received: 29 June 2019 / Revised: 15 September 2019 / Accepted: 16 October 2019 / Published: 20 October 2019
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2019)
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. View Full-Text
Keywords: gamma function and its extension; Pochhammer symbol and its extensions; hypergeometric function and its extensions; τ-Gauss hypergeometric function and its extensions; τ-Kummer hypergeometric function; Fox-Wright function gamma function and its extension; Pochhammer symbol and its extensions; hypergeometric function and its extensions; τ-Gauss hypergeometric function and its extensions; τ-Kummer hypergeometric function; Fox-Wright function
MDPI and ACS Style

Srivastava, H.M.; Tassaddiq, A.; Rahman, G.; Nisar, K.S.; Khan, I. A New Extension of the τ-Gauss Hypergeometric Function and Its Associated Properties. Mathematics 2019, 7, 996.

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