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arXiv · 2209.02227

On $q$-Middle Convolution and $q$-Hypergeometric Equations

Yumi Arai·Kouichi Takemura
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Abstract

The $q$-middle convolution was introduced by Sakai and Yamaguchi. In this paper, we reformulate $q$-integral transformations associated with the $q$-middle convolution. In particular, we discuss convergence of the $q$-integral transformations. As an application, we obtain $q$-integral representations of solutions to the variants of the $q$-hypergeometric equation by applying the $q$-middle convolution.

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BibTeXRIS

Yumi Arai, Kouichi Takemura. 2022-09-06. On $q$-Middle Convolution and $q$-Hypergeometric Equations. https://doi.org/10.3842/sigma.2023.037

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