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On a system of $q$-partial differential equations with applications to $q$-series (1709.06784v1)
Published 20 Sep 2017 in math.CV
Abstract: Using the theory of functions of several variables and $q$-calculus, we prove an expansion theorem for the analytic function in several variables which satisfies a system of $q$-partial differential equations. Some curious applications of this expansion theorem to $q$-series are discussed. In particular, an extension of Andrews' transformation formula for the $q$-Lauricella function is given.