Implementation of computation formulas for certain classes of Apostol-type polynomials and some properties associated with these polynomials

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dc.contributor.authorKucukoglu, Irem
dc.date.accessioned2026-01-24T12:01:03Z
dc.date.available2026-01-24T12:01:03Z
dc.date.issued2021
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractThe main purpose of this paper is to present various identities and computation formulas for certain classes of Apostol-type numbers and polynomials. The results of this paper contain not only the $\\lambda$-Apostol-Daehee numbers and polynomials, but also Simsek numbers and polynomials, the Stirling numbers of the first kind, the Daehee numbers, and the Chu-Vandermonde identity. Furthermore, we derive an infinite series representation for the $\\lambda$-Apostol-Daehee polynomials. By using functional equations containing the generating functions for the Cauchy numbers and the Riemann integrals of the generating functions for the $\\lambda$-Apostol-Daehee numbers and polynomials, we also derive some identities and formulas for these numbers and polynomials. Moreover, we give implementation of a computation formula for the $\\lambda$-Apostol-Daehee polynomials in Mathematica by Wolfram language. By this implementation, we also present some plots of these polynomials in order to investigate their behaviour some randomly selected special cases of their parameters. Finally, we conclude the paper with some comments and observations on our results.
dc.identifier.doi10.31801/cfsuasmas.831024
dc.identifier.endpage442
dc.identifier.issn1303-5991
dc.identifier.issn2618-6470
dc.identifier.issue1
dc.identifier.startpage426
dc.identifier.trdizinid439306
dc.identifier.urihttps://search.trdizin.gov.tr/tr/yayin/detay/439306
dc.identifier.urihttps://doi.org/10.31801/cfsuasmas.831024
dc.identifier.urihttps://hdl.handle.net/20.500.12868/3922
dc.identifier.volume70
dc.indekslendigikaynakTR-Dizin
dc.language.isoen
dc.relation.ispartofCommunications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
dc.relation.publicationcategoryMakale - Ulusal Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.snmzKA_TR-Dizin_20260121
dc.subjectGenerating functions
dc.subjectFunctional Equations
dc.subjectSpecial numbers and polynomials
dc.subjectStirling numbers of the first kind
dc.subjectApostol-type numbers and polynomials
dc.subjectSimsek numbers and polynomials
dc.subjectBernoulli numbers of the second kind
dc.subjectDaehee numbers and polynomials
dc.subjectIntegral formulas
dc.subjectChu-Vandermonde identity
dc.subjectBernstein basis functions
dc.subjectCombinatorial sums
dc.titleImplementation of computation formulas for certain classes of Apostol-type polynomials and some properties associated with these polynomials
dc.typeArticle

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