Some Generalized Special Functions and their Properties

Authors : Shahid MUBEEN, Syed SHAH, Gauhar RAHMAN, Kottakkaran NİSAR, Thabet ABDELJAWAD

Pages : 45-65

Doi:10.31197/atnaa.768532

View : 17 | Download : 17

Publication Date : 2022-03-31

Article Type : Research Paper

Abstract :In this present paper, first, we investigate a new generalized Pochhammer`s symbol and its various properties in terms of a new symbol $insert ignore into journalissuearticles values(s; k);$, where $s; k > 0$. Then, we define a new generalization of gamma and beta functions and their various associated properties in the form of $insert ignore into journalissuearticles values(s; k);$. Also, we define a new generalization of hypergeometric functions and develop differential equations for generalized hypergeometric functions in the form of $insert ignore into journalissuearticles values(s; k);$. 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