Computational identities for extensions of some families of special numbers and polynomials

Basit Öğe Kaydı
dc.authorid0000-0001-9100-2252
dc.authorid0000-0002-0611-7141
dc.contributor.authorKucukoglu, Irem
dc.contributor.authorSimsek, Yilmaz
dc.date.accessioned2026-01-24T12:26:38Z
dc.date.available2026-01-24T12:26:38Z
dc.date.issued2021
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractThe main purpose of this paper is to obtain computational identities and formulas for a certain class of combinatorial-type numbers and polynomials. By the aid of the generating function technique, we derive a recurrence relation and an infinite series involving the aforementioned class of combinatorial-type numbers. By applying the Riemann integral to the combinatorial-type polynomials with multivariables, we present some integral formulas for these polynomials, including the Bernoulli numbers of the second kind. By the implementation of the p-adic integral approach to the combinatorial-type polynomials with multivariables, we also obtain formulas for the Volkenborn integral and the fermionic p-adic integral of these polynomials. Furthermore, we provide an approximation for the combinatorial-type numbers with the aid of the Stirling's approximation for factorials. By coding some of our results in Mathematica using the Wolfram programming language, we also provide some numerical evaluations and illustrations on the combinatorial type numbers and their Stirling's approximation with table and figures. We also give some remarks and observations on the combinatorial-type numbers together with their relationships to other well-known special numbers and polynomials. As a result of these observations, we derive some computation formulas containing the Dirichlet series involving the Mobius function, the Bernoulli numbers, the Catalan numbers, the Stirling numbers, the Apostol-Bernoulli numbers, the Apostol-Euler numbers, the Apostol-Genocchi numbers and some kinds of combinatorial numbers. Besides, some inequalities for the combinatorial-type numbers are presented. Finally, we conclude this paper by briefly overviewing the results with their potential applications.
dc.description.sponsorshipScientific Research Project Administration of Akdeniz University
dc.description.sponsorshipSecond author of the present paper was supported by the Scientific Research Project Administration of Akdeniz University.
dc.identifier.doi10.3906/mat-2101-83
dc.identifier.endpage2365
dc.identifier.issn1300-0098
dc.identifier.issn1303-6149
dc.identifier.issue5
dc.identifier.scopus2-s2.0-85115808154
dc.identifier.scopusqualityQ2
dc.identifier.startpage2341
dc.identifier.trdizinid528658
dc.identifier.urihttps://doi.org/10.3906/mat-2101-83
dc.identifier.urihttps://search.trdizin.gov.tr/tr/yayin/detay/528658
dc.identifier.urihttps://hdl.handle.net/20.500.12868/4824
dc.identifier.volume45
dc.identifier.wosWOS:000696500900001
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.indekslendigikaynakTR-Dizin
dc.language.isoen
dc.publisherTubitak Scientific & Technological Research Council Turkey
dc.relation.ispartofTurkish Journal of Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_WoS_20260121
dc.subjectGenerating functions
dc.subjectp-adic integrals
dc.subjectCatalan numbers
dc.subjectspecial numbers and polynomials
dc.subjectCombinatorial numbers
dc.subjectStirling approximation
dc.titleComputational identities for extensions of some families of special numbers and polynomials
dc.typeArticle

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