On hypergeometric functions and Pochhammer $k$-symbol

Abstract

We introduce the $k$-generalized gamma function ${\Gamma }_k$, beta function $B_k$, and Pochhammer $k$-symbol $(x{)}_{n,k}$. We prove several identities generalizing those satisfied by the classical gamma function, beta function and Pochhammer symbol. We provided integral representation for the ${\Gamma }_k$ and $B_k$ functions.

12 pages, 3 figures

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