Some Generalized Special Functions and their Properties

Year 2022, Volume: 6 Issue: 1, 45 - 65, 31.03.2022

Shahid Mubeen , Syed Shah Gauhar Rahman , Kottakkaran Nisar , Thabet Abdeljawad

https://doi.org/10.31197/atnaa.768532

Abstract

In this present paper, first, we investigate a new generalized Pochhammer's symbol and its various properties in terms of a new symbol $(s; k)$, where $s; k > 0$. Then, we define a new generalization of gamma and beta functions and their various associated properties in the form of $(s; k)$. Also, we define a new generalization of hypergeometric functions and develop differential equations for generalized hypergeometric functions in the form of $(s; k)$. We present that generalized hypergeometric functions are the solution of the said differential equation. Furthermore, some useful results and properties and integral representation related to these generalized Pochhammer's symbol, gamma function, beta function, and hypergeometric functions are presented.

Keywords

Pochhammer symbol, beta function, Gamma function, generalized Pochhammer symbol, generalized hypergeometric function

Supporting Institution

None

Project Number

None

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