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Symmetry, Integrability and Geometry: Methods and Applications, 2023, Volume 19, 037, 40 pp.
DOI: https://doi.org/10.3842/SIGMA.2023.037
(Mi sigma1932)
 

This article is cited in 1 scientific paper (total in 1 paper)

On $q$-Middle Convolution and $q$-Hypergeometric Equations

Yumi Arai, Kouichi Takemura

Department of Mathematics, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan
Full-text PDF (567 kB) Citations (1)
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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 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.
Keywords: hypergeometric function, $q$-hypergeometric equation, middle convolution, $q$-integral.
Funding agency Grant number
Japan Society for the Promotion of Science JP22K03368
The second author was supported by JSPS KAKENHI Grant Number JP22K03368.
Received: October 14, 2022; in final form May 19, 2023; Published online June 5, 2023
Document Type: Article
MSC: 33D15, 39A13
Language: English
Citation: Yumi Arai, Kouichi Takemura, “On $q$-Middle Convolution and $q$-Hypergeometric Equations”, SIGMA, 19 (2023), 037, 40 pp.
Citation in format AMSBIB
\Bibitem{AraTak23}
\by Yumi~Arai, Kouichi~Takemura
\paper On $q$-Middle Convolution and $q$-Hypergeometric Equations
\jour SIGMA
\yr 2023
\vol 19
\papernumber 037
\totalpages 40
\mathnet{http://mi.mathnet.ru/sigma1932}
\crossref{https://doi.org/10.3842/SIGMA.2023.037}
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