Unified presentations of the generating functions for a comprehensive class of numbers and polynomials

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dc.contributor.authorKucukoglu, Irem
dc.contributor.authorŞimşek, Yilmaz
dc.date.accessioned2026-01-24T12:20:58Z
dc.date.available2026-01-24T12:20:58Z
dc.date.issued2024
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractThe aim of this paper is to construct unified presentations of the ordinary and exponential generating functions for a comprehensive class of numbers and polynomials by p-adic analysis of a uniformly differentiable function. Moreover, we classify these generating functions according to which of the classes of “Appell sequences”, “Sheffer sequences” and accordingly other classes they belong to. In addition, we give some applications of the constructed unified presentations of the generating functions. In particular, we derive some identities and provide some differential equations satisfied by the constructed unified presentations of the generating functions. We also handle some special cases of these generating functions and provide several tables which summarize the special cases discussed throughout this paper. Over and above, by applying the p-adic integrals, we derive some further identities regarding the constructed unified presentations of the generating functions. Lastly, we raise some open questions and conclude our paper by providing final comments and observations on our results. © 2024, MTJPAM Turkey. All rights reserved.
dc.identifier.endpage63
dc.identifier.issue1
dc.identifier.scopus2-s2.0-85193705428
dc.identifier.scopusqualityQ1
dc.identifier.startpage40
dc.identifier.urihttps://hdl.handle.net/20.500.12868/4742
dc.identifier.volume6
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMTJPAM Turkey
dc.relation.ispartofMontes Taurus Journal of Pure and Applied Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_Scopus_20260121
dc.subjectAppell sequences
dc.subjectfunctional equations
dc.subjectGenerating functions
dc.subjectp-adic integration
dc.subjectpartial differential equations
dc.subjectSheffer sequences
dc.subjectspecial numbers and polynomials
dc.subjectuniformly differential functions
dc.titleUnified presentations of the generating functions for a comprehensive class of numbers and polynomials
dc.typeArticle

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