On $q$-Middle Convolution and $q$-Hypergeometric Equations
Classical Analysis and ODEs
2023-06-06 v3
Abstract
The -middle convolution was introduced by Sakai and Yamaguchi. In this paper, we reformulate -integral transformations associated with the -middle convolution. In particular, we discuss convergence of the -integral transformations. As an application, we obtain -integral representations of solutions to the variants of the -hypergeometric equation by applying the -middle convolution.
Cite
@article{arxiv.2209.02227,
title = {On $q$-Middle Convolution and $q$-Hypergeometric Equations},
author = {Yumi Arai and Kouichi Takemura},
journal= {arXiv preprint arXiv:2209.02227},
year = {2023}
}