Geodesic
$q$-Middle Convolution and $q$-Painlevé Equation
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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A $q$-deformation of the middle convolution was introduced by Sakai and Yamaguchi. We apply it to a linear $q$-difference equation associated with the $q$-Painlevé VI equation. Then we obtain integral transformations. We investigate the $q$-middle convolution in terms of the affine Weyl group symmetry of the $q$-Painlevé VI equation. We deduce an integral transformation on the $q$-Heun equation.
Keywords: middle convolution, integral transformation.
Mots-clés : $q$-Painlevé equation, $q$-Heun equation 
@article{SIGMA_2022_18_a55,
     author = {Shoko Sasaki and Shun Takagi and Kouichi Takemura},
     title = {$q${-Middle} {Convolution} and $q${-Painlev\'e} {Equation}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2022},
     volume = {18},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a55/}
}
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Shoko Sasaki; Shun Takagi; Kouichi Takemura. $q$-Middle Convolution and $q$-Painlevé Equation. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a55/

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