{"title":"On q -Middle Convolution and q -Hypergeometric Equations","authors":"Yumi Arai, K. Takemura","doi":"10.3842/SIGMA.2023.037","DOIUrl":null,"url":null,"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.","PeriodicalId":49453,"journal":{"name":"Symmetry Integrability and Geometry-Methods and Applications","volume":" ","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2022-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry Integrability and Geometry-Methods and Applications","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.3842/SIGMA.2023.037","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
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.
期刊介绍：
Scope
Geometrical methods in mathematical physics
Lie theory and differential equations
Classical and quantum integrable systems
Algebraic methods in dynamical systems and chaos
Exactly and quasi-exactly solvable models
Lie groups and algebras, representation theory
Orthogonal polynomials and special functions
Integrable probability and stochastic processes
Quantum algebras, quantum groups and their representations
Symplectic, Poisson and noncommutative geometry
Algebraic geometry and its applications
Quantum field theories and string/gauge theories
Statistical physics and condensed matter physics
Quantum gravity and cosmology.
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