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A $q$-extension of a partial differential equation and the Hahn polynomials (1805.07292v1)
Published 17 May 2018 in math.CO, math.AP, math.CV, and math.NT
Abstract: Using the theory of analytic functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of $q$-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 $q$-series are discussed.