q-Middle Convolution and q-Painlevé Equation

@article{Sasaki2022qMiddleCA,
  title={q-Middle Convolution and q-Painlev{\'e} Equation},
  author={Shoko Sasaki and Shunsuke Takagi and Kouichi Takemura},
  journal={Symmetry, Integrability and Geometry: Methods and Applications},
  year={2022}
}
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. 

On q-middle convolution and q-hypergeometric equations

. We reformulate q -integral transformations associated with the q -middle convolution. We obtain q -integral representations of the variants of the q -hypergeometric equation by applying the q

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