Kernel Function, 𝑞-Integral Transformation and 𝑞-Heun Equations

Abstract

We find kernel functions of the 𝑞-Heun equation and its variants. We apply them to obtain 𝑞-integral transformations of solutions to the 𝑞-Heun equation and its variants. We discuss special solutions of the 𝑞-Heun equation from the perspective of the 𝑞-integral transformation.