Identities and derivative formulas for the combinatorial and apostol-euler type numbers by their generating functions

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dc.contributor.authorKüçükoğlu, İrem
dc.contributor.authorŞimşek, Yılmaz
dc.date.accessioned2021-02-19T21:16:39Z
dc.date.available2021-02-19T21:16:39Z
dc.date.issued2018
dc.departmentALKÜ
dc.descriptionInternational Conference on Approximation and Computation - Theory and Applications (ACTA) -- NOV 30-DEC 02, 2017 -- Belgrade, SERBIA
dc.descriptionKUCUKOGLU, IREM/0000-0001-9100-2252
dc.description.abstractThe first aim of this paper is to give identities and relations for a new family of the combinatorial numbers and the Apostol-Euler type numbers of the second kind, the Stirling numbers, the Apostol-Bernoulli type numbers, the Bell numbers and the numbers of the Lyndon words by using some techniques including generating functions, functional equations and inversion formulas. The second aim is to derive some derivative formulas and combinatorial sums by applying derivative operators including the Caputo fractional derivative operators. Moreover, we give a recurrence relation for the Apostol-Euler type numbers of the second kind. By using this recurrence relation, we construct a computation algorithm for these numbers. In addition, we derive some novel formulas including the Stirling numbers and other special numbers. Finally, we also some remarks, comments and observations related to our results.
dc.description.sponsorshipSerbian Acad Sci & Arts, Math Inst, Univ Belgrade, Fac Mech Engn, Univ Belgrade, Fac Math, Univ Belgrade, Sch Elect Engn, Univ Nis, Univ Kragujevac, Fac Sci, Univ Novi Sad, Fac Sci
dc.description.sponsorshipScientific Research Project Administration of Akdeniz UniversityAkdeniz University [FBA-2018-3292]
dc.description.sponsorshipThe present paper was supported by Scientific Research Project Administration of Akdeniz University (with Project Number: FBA-2018-3292).
dc.identifier.doi10.2298/FIL1820879K
dc.identifier.endpage6891en_US
dc.identifier.issn0354-5180
dc.identifier.issue20en_US
dc.identifier.scopusqualityQ3
dc.identifier.startpage6879en_US
dc.identifier.urihttps://doi.org/10.2298/FIL1820879K
dc.identifier.urihttps://hdl.handle.net/20.500.12868/510
dc.identifier.volume32en_US
dc.identifier.wosWOS:000463447500004
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthor0-belirlenecek
dc.language.isoen
dc.publisherUniv Nis, Fac Sci Math
dc.relation.ispartofFilomat
dc.relation.publicationcategoryKonferans Öğesi - Uluslararası - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectGenerating functions
dc.subjectFunctional equations
dc.subjectPartial differential equations
dc.subjectStirling numbers of the second kind
dc.subjectEuler numbers of the second kind
dc.subjectApostol-Euler type polynomials of the second kind
dc.subjectlambda-Bernoulli numbers
dc.subjectBell numbers
dc.subjectCombinatorial sums
dc.subjectBinomial coefficients
dc.subjectArithmetical functions
dc.titleIdentities and derivative formulas for the combinatorial and apostol-euler type numbers by their generating functions
dc.typeConference Object

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