Some Families of Multilinear q-Generating Functions and Combinatorial q-Series Identities

A number of linear, bilinear, and multilinear generating functions are obtained here for various families of q-orthogonal polynomials. In particular, the bilinear and multilinear generating functions derived here for the q-laguerre polynomials would provide q-extensions of numerous results for the classical Laguerre polynomials, including (for example) the celebrated Hille-Hardy formula. Many combinatorial q-series identities are also proven by applying the theory of basic (or q-) hypergeometric functions.