Certain q-Polynomial Expansions for Functions of Several Variables

Three new expansion formulae in series of some general classes of q-polynomials are presented here for a function of several variables, which is defined by a multiple power series with essentially arbitrary terms. These general results are then applied to derive several new or known polynomial expansions (and multiplication theorems) for various q-hypergeometric functions of one and more variables. It is also shown how one of the applications considered yields a q-extension of a known hypergeometric generating function.