On Defining the $q$-Beta Function for Negative Integers


Inci Ege




The $q$-beta function $B_q(t,s)$ is defined for $s,t>0$ and $0<q<1$. Its definition can be extended, by regularization, to negative non-integer values of $t$ and $s$. In this paper we define the $q$-beta function $B_q(t,s)$ for negative integer values of $t$ and $s$.