On 𝑞-Middle Convolution and 𝑞-Hypergeometric Equations

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 the 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.