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

Author

Listed:
  • Hari Mohan Srivastava

    (Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan)

  • 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)

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.

Suggested Citation

  • Hari Mohan Srivastava & Asifa Tassaddiq & Gauhar Rahman & Kottakkaran Sooppy Nisar & Ilyas Khan, 2019. "A New Extension of the τ -Gauss Hypergeometric Function and Its Associated Properties," Mathematics, MDPI, vol. 7(10), pages 1-9, October.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:10:p:996-:d:278488
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