q,k-generalized gamma and beta functions

Abstract

We introduce the q,k-generalized Pochhammer symbol. We construct $Γ_{q,k}$ and $B_{q,k}$, the q,k-generalized gamma and beta fuctions, and show that they satisfy properties that generalize those satisfied by the classical gamma and beta functions. Moreover, we provide integral representations for $Γ_{q,k}$ and $B_{q,k}.$