On hypergeometric functions and Pochhammer $k$-symbol

Rafael Diaz, Eddy Pariguan

Published 2004-05-31, updated 2005-04-19Version 2

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.