Startseite Extension of Pochhammer symbol, generalized hypergeometric function and τ-Gauss hypergeometric function
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Extension of Pochhammer symbol, generalized hypergeometric function and τ-Gauss hypergeometric function

  • Komal Singh Yadav , Bhagwat Sharan und Ashish Verma ORCID logo EMAIL logo
Veröffentlicht/Copyright: 2. Oktober 2024
Analysis
Aus der Zeitschrift Analysis Band 45 Heft 1

Abstract

We introduce new extension of the extended Pochhammer symbol and gamma function by using the extended Mittag-Leffler function. We also present extension of the generalized hypergeometric function as well as some of their special cases by using this extended Pochhammer symbol. Further, we define the extension of the τ-Gauss hypergeometric function. Integral and derivative formulas involving the Mellin transform and fractional calculus techniques associated with this extended τ-Gauss hypergeometric function are also given. Also, new extended τ-Gauss hypergeometric function also provides a few more interesting and well-known results. This enriches the theory of special functions. The obtained results are believed to be newly presented.

Acknowledgements

The first author would like to express their gratitude to the University Grants Commission of India for financial assistance in the form of a Senior Research Fellowship.

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Received: 2023-11-28
Revised: 2024-05-03
Accepted: 2024-09-02
Published Online: 2024-10-02
Published in Print: 2025-02-01

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