A q-extension of a partial differential equation and the Hahn polynomials

Using the theory of analytic functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of $$q$$q-partial differential equations, then, it can be expanded in terms of the product of the homogeneous Hahn polynomials. Some non-trivial applications of this expansion theorem to $$q$$q-series are discussed.