Special Solutions of $q$-Heun Equation by $q$-Integral Transformations
Ayaka Murakami, Kouichi Takemura
TL;DR
This paper derives special solutions to the $q$-Heun equation expressed as finite sums of $q$-hypergeometric functions, using $q$-integral transformations of polynomial solutions.
Contribution
It introduces a novel method of obtaining special solutions of the $q$-Heun equation via $q$-integral transformations, expanding the solution space.
Findings
Solutions expressed as finite sums of $q$-hypergeometric functions
Use of $q$-integral transformations to derive solutions
Extension of polynomial solutions to special solutions
Abstract
We obtain special solutions of the -Heun equation which are expressed as finite summations of -hypergeometric functions. These solutions are obtained by considering the -integral transformations of the polynomial-type solutions.
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