Two Parameter Gamma Function and its Properties

Kuldeep Singh Gehlot

paper

Two Parameter Gamma Function and its Properties

arXiv:1701.01052

Abstract

In this paper we introduce the Two Parameter Gamma Function, Beta Function and Pochhammer Symbol. We named them, as p - k Gamma Function, p - k Beta Function and p - k Pochhammer Symbol and denoted as $_{p} Γ_{k} (x),$ $_{p} B_{k} (x, y)$ and $_{p} (x)_{n, k}$ respectively. We prove the several identities for $_{p} Γ_{k} (x),$ $_{p} B_{k} (x, y)$ and $_{p} (x)_{n, k}$ those satisfied by the classical Gamma, Beta and Pochhammer Symbol. Also we provide the integral representation for the $_{p} Γ_{k} (x)$ and $_{p} B_{k} (x, y)$ .