Computational and implementational analysis of generating functions for higher order combinatorial numbers and polynomials attached to Dirichlet characters

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dc.authorid0000-0001-9100-2252
dc.contributor.authorKucukoglu, Irem
dc.date.accessioned2026-01-24T12:30:50Z
dc.date.available2026-01-24T12:30:50Z
dc.date.issued2022
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractThe main purpose of this paper is to give computational and implementational analysis of generating functions for some extensions of combinatorial numbers and polynomials attached to Dirichlet characters. By using generating function methods and p-adic q-integral techniques, it is also aimed to derive some computational formulas for these numbers and polynomials. By implementing both the derived computational formulas and the constructed generating functions in Mathematica, we present some tables and plots for these numbers and polynomials, and their generating functions to illustrate the effects of their parameters for some special cases. Moreover, by making an observation on some results of this paper, we derive some novel computational formulas for the finite sums that contain the Dirichlet characters and falling factorials. We also assess some cases of these special finite sums. In the sequel, we pose some open problems regarding these special finite sums. Apart from these findings, we also give not only Fourier series expansion but also asymptotic estimates for the mentioned combinatorial numbers. In addition, we give some Raabe-type multiplication formulas for the mentioned combinatorial polynomials. Finally, we give an observation on decompositions of the generating functions attached to any group homomorphism.
dc.identifier.doi10.1002/mma.8092
dc.identifier.endpage5066
dc.identifier.issn0170-4214
dc.identifier.issn1099-1476
dc.identifier.issue9
dc.identifier.scopus2-s2.0-85123584042
dc.identifier.scopusqualityQ1
dc.identifier.startpage5043
dc.identifier.urihttps://doi.org/10.1002/mma.8092
dc.identifier.urihttps://hdl.handle.net/20.500.12868/5469
dc.identifier.volume45
dc.identifier.wosWOS:000747862000001
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherWiley
dc.relation.ispartofMathematical Methods in The Applied Sciences
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WoS_20260121
dc.subjectApostol-Bernoulli numbers and polynomials
dc.subjectcombinatorial numbers
dc.subjectDirichlet character
dc.subjectgenerating functions
dc.subjectgroup homomorphism
dc.subjectmathematica implementation
dc.subjectp-adic q-integral
dc.subjectSimsek numbers and polynomials
dc.subjectspecial finite character sums
dc.subjectStirling numbers
dc.subjectRaabe-type multiplication formula
dc.titleComputational and implementational analysis of generating functions for higher order combinatorial numbers and polynomials attached to Dirichlet characters
dc.typeArticle

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