Construction and computation of unified Stirling-type numbers emerging from p-adic integrals and symmetric polynomials

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dc.authorid0000-0001-9100-2252
dc.authorid0000-0002-0611-7141
dc.contributor.authorKucukoglu, Irem
dc.contributor.authorSimsek, Yilmaz
dc.date.accessioned2026-01-24T12:31:02Z
dc.date.available2026-01-24T12:31:02Z
dc.date.issued2021
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractThe aim of this paper is to give construction and computation methods for generalized and unified representations of Stirling-type numbers and Bernoulli-type numbers and polynomials. Firstly, we define generalized and unified representations of the falling factorials. By using these new representations as components of the generating functions, we also construct generalized and unified representations of Stirling-type numbers. By making use of the symmetric polynomials, we give computational formulas and algorithm for these numbers. Applying Riemann integral to the unified falling factorials, we introduce new families of Bernoulli-type numbers and polynomials of the second kind by their computation formulas and plots drawn by the Wolfram programming language in Mathematica. Applying p-adic integrals to the unified falling factorials, we construct two new sequences that involve some well-known special numbers such as the Stirling numbers, the Bernoulli numbers and the Euler numbers. Finally, we give not only further remarks and observations, but also some open questions regarding the potential applications and relations of our results.
dc.identifier.doi10.1007/s13398-021-01107-2
dc.identifier.issn1578-7303
dc.identifier.issn1579-1505
dc.identifier.issue4
dc.identifier.scopus2-s2.0-85112260073
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1007/s13398-021-01107-2
dc.identifier.urihttps://hdl.handle.net/20.500.12868/5607
dc.identifier.volume115
dc.identifier.wosWOS:000683728600002
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer-Verlag Italia Srl
dc.relation.ispartofRevista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WoS_20260121
dc.subjectFactorial polynomials
dc.subjectBernoulli and Euler numbers
dc.subjectStirling numbers
dc.subjectSymmetric polynomials
dc.subjectCatalan numbers
dc.subjectCentral factorial numbers
dc.subjectComputational formulas
dc.subjectComputational algorithms
dc.subjectp-adic integrals
dc.titleConstruction and computation of unified Stirling-type numbers emerging from p-adic integrals and symmetric polynomials
dc.typeArticle

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