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Symmetry, Integrability and Geometry: Methods and Applications, 2024, Volume 20, 083, 22 pp.
DOI: https://doi.org/10.3842/SIGMA.2024.083 (Mi sigma2085) 		 
Kernel Function, $q$-Integral Transformation and $q$-Heun Equations

Kouichi Takemura

Department of Mathematics, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan
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DOI: https://doi.org/10.3842/SIGMA.2024.083
URL: https://www.emis.de/journals/SIGMA/2024/083/
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.
Keywords: kernel function, Jackson integral, Heun equation, $q$-Heun equation, Ruijsenaars system.
Funding agency Grant number
Japan Society for the Promotion of Science JP22K03368
He is supported by JSPS KAKENHI Grant Number JP22K03368.
Received: February 14, 2024; in final form September 12, 2024; Published online September 19, 2024
Bibliographic databases:
Document Type: Article
MSC: 39A13, 44A20
Language: English
Citation: Kouichi Takemura, “Kernel Function, $q$-Integral Transformation and $q$-Heun Equations”, SIGMA, 20 (2024), 083, 22 pp.
Citation in format AMSBIB
\Bibitem{Tak24}
\by Kouichi~Takemura
\paper Kernel Function, $q$-Integral Transformation and $q$-Heun Equations
\jour SIGMA
\yr 2024
\vol 20
\papernumber 083
\totalpages 22
\mathnet{http://mi.mathnet.ru/sigma2085}
\crossref{https://doi.org/10.3842/SIGMA.2024.083}
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