$q$-Middle Convolution and $q$-Painlevé Equation

Abstract

A $q$-deformation of the middle convolution was introduced by Sakai and Yamaguchi. We apply it to a linear $q$-difference equation associated with the $q$-Painlevé VI equation. Then we obtain integral transformations. We investigate the $q$-middle convolution in terms of the affine Weyl group symmetry of the $q$-Painlevé VI equation. We deduce an integral transformation on the $q$-Heun equation.

References in corpus (3)

• Middle Convolution and Heun's Equation
• q-Heun equation and initial-value space of q-Painlevé equation
• On $q$-Middle Convolution and $q$-Hypergeometric Equations

Cited by in corpus (1)

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