{"title":"Lie algebra representation and hybrid families related to Hermite polynomials","authors":"Subuhi Khan, Mahammad Lal Mia, Mahvish Ali","doi":"10.1016/S0034-4877(24)00083-1","DOIUrl":null,"url":null,"abstract":"<div><div>In this article, the Bessel and Tricomi functions are combined with Appell polynomials to introduce the families of Appell–Bessel and Appell–Tricomi functions. The 2-variable 2-parameter Hermite–Bessel and Hermite–Tricomi functions are considered as members of these families, and framed within the representation of the Lie algebra T3. Consequently, the implicit summation formulae for these functions are derived. Certain examples are also considered. The article concludes with the derivation of a relation involving the 2-variable 2-parameter Hermite–Tricomi functions by following the Weisner's approach.</div></div>","PeriodicalId":49630,"journal":{"name":"Reports on Mathematical Physics","volume":"94 3","pages":"Pages 335-352"},"PeriodicalIF":1.2000,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports on Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0034487724000831","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, the Bessel and Tricomi functions are combined with Appell polynomials to introduce the families of Appell–Bessel and Appell–Tricomi functions. The 2-variable 2-parameter Hermite–Bessel and Hermite–Tricomi functions are considered as members of these families, and framed within the representation of the Lie algebra T3. Consequently, the implicit summation formulae for these functions are derived. Certain examples are also considered. The article concludes with the derivation of a relation involving the 2-variable 2-parameter Hermite–Tricomi functions by following the Weisner's approach.
期刊介绍：
Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.
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