Geodesic
On $q$-Middle Convolution and $q$-Hypergeometric Equations
Symmetry, integrability and geometry: methods and applications, Tome 19 (2023) Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     author = {Yumi Arai and Kouichi Takemura},
     title = {On $q${-Middle} {Convolution} and $q${-Hypergeometric} {Equations}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2023},
     volume = {19},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a36/}
}
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Yumi Arai; Kouichi Takemura. On $q$-Middle Convolution and $q$-Hypergeometric Equations. Symmetry, integrability and geometry: methods and applications, Tome 19 (2023). http://geodesic.mathdoc.fr/item/SIGMA_2023_19_a36/

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