On \(q\)-Middle Convolution and \(q\)-Hypergeometric Equations

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 repr...

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Bibliographic Details
Published in:arXiv.org 2023-06
Main Authors: Arai, Yumi, Takemura, Kouichi
Format: Article
Language:English
Subjects:
Convolution
Hypergeometric functions
Integral transforms
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2209.02227