Kernel Function, $q$-Integral Transformation and $q$-Heun Equations
Kouichi Takemura
TL;DR
This paper introduces kernel functions for the $q$-Heun equation, enabling $q$-integral transformations of solutions and providing insights into special solutions from this perspective.
Contribution
It presents new kernel functions for the $q$-Heun equation and applies them to derive $q$-integral transformations of solutions, advancing understanding of these equations.
Findings
Kernel functions for the $q$-Heun equation are constructed.
$q$-integral transformations of solutions are established.
Special solutions are analyzed via the $q$-integral transformation.
Abstract
We find kernel functions of the -Heun equation and its variants. We apply them to obtain -integral transformations of solutions to the -Heun equation and its variants. We discuss special solutions of the -Heun equation from the perspective of the -integral transformation.
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Taxonomy
TopicsNonlinear Waves and Solitons · Quantum Mechanics and Non-Hermitian Physics · Molecular spectroscopy and chirality