2023
DOI: 10.3842/sigma.2023.037
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On q -Middle Convolution and q -Hypergeometric Equations

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.

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