On a system of $q$-partial differential equations with applications to $q$-series

Zhi-Guo Liu

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arXiv · 1709.06784

On a system of $q$-partial differential equations with applications to $q$-series

Zhi-Guo Liu

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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.

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Zhi-Guo Liu. 2017-09-20. On a system of $q$-partial differential equations with applications to $q$-series. https://arxiv.org/abs/1709.06784

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