On the Triple Lauricella–Horn–Karlsson <i>q</i>-Hypergeometric Functions

Abstract

The Horn–Karlsson approach to find convergence regions is applied to find convergence regions for triple q-hypergeometric functions. It turns out that the convergence regions are significantly increased in the q-case; just as for q-Appell and q-Lauricella functions, additions are replaced by Ward q-additions. Mostly referring to Krishna Srivastava 1956, we give q-integral representations for these functions.

Keywords

• triple <i>q</i>-hypergeometric function
• convergence region
• Ward <i>q</i>-addition
• <i>q</i>-integral representation