$q$-Middle Convolution and $q$-Painlev\'e Equation
Classical Analysis and ODEs
2022-07-21 v2 Mathematical Physics
math.MP
Abstract
A -deformation of the middle convolution was introduced by Sakai and Yamaguchi. We apply it to a linear -difference equation associated with the -Painlev\'e VI equation. Then we obtain integral transformations. We investigate the -middle convolution in terms of the affine Weyl group symmetry of the -Painlev\'e VI equation. We deduce an integral transformation on the -Heun equation.
Cite
@article{arxiv.2201.03960,
title = {$q$-Middle Convolution and $q$-Painlev\'e Equation},
author = {Shoko Sasaki and Shun Takagi and Kouichi Takemura},
journal= {arXiv preprint arXiv:2201.03960},
year = {2022}
}