$q$-Generating functions for one and two variables

Abstract

We use a multidimensional extension of Bailey's transform to derive two very general $q$-generating functions, which are $q$-analogues of a paper by Exton. These expressions are then specialized to give more practical formulae, which are $q$-analogues of generating relations for Karlssons generalized Kampé de Fériet function. A number of examples are given including $q$-Laguerre polynomials of two variables.