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arXiv · 2305.12754

$q$-difference equations satisfied by the universal mock theta functions

Satoshi Tsuchimi
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Abstract

In this paper, we give fundamental solutions of some $q$-difference equations satisfied by the universal mock theta functions and the higher level Appell functions. As an application, we provide an alternative proof of the representation formulas of the universal mock theta functions and the higher level Appell functions using Zwegers' $\mu$-function.

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Satoshi Tsuchimi. 2023-05-22. $q$-difference equations satisfied by the universal mock theta functions. https://arxiv.org/abs/2305.12754

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