Partial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomials

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dc.authoridKucukoglu, Irem/0000-0001-9100-2252
dc.authoridSrivastava, Hari M./0000-0002-9277-8092
dc.authoridSIMSEK, YILMAZ/0000-0002-0611-7141
dc.authorwosidKucukoglu, Irem/L-9198-2018
dc.authorwosidSrivastava, Hari M./N-9532-2013
dc.authorwosidSIMSEK, YILMAZ/C-1654-2016
dc.contributor.authorSrivastava, Hari M.
dc.contributor.authorKüçükoğlu, İrem
dc.contributor.authorŞimşek, Yılmaz
dc.date.accessioned2024-08-20T20:29:20Z
dc.date.available2024-08-20T20:29:20Z
dc.date.issued2017
dc.departmentAntalya Belek Üniversitesien_US
dc.description.abstractThe main motivation of this paper is to investigate some derivative properties of the generating functions for the numbers Y-n (lambda) and the polynomials Y-n(x; lambda), which were recently introduced by Simsek [30]. We give functional equations and differential equations (PDEs) of these generating functions. By using these functional and differential equations, we derive not only recurrence relations, but also several other identities and relations for these numbers and polynomials. Our identities include the Apostol Bernoulli numbers, the Apostol Euler numbers, the Stirling numbers of the first kind, the Cauchy numbers and the Hurwitz-Lerch zeta functions. Moreover, we give hypergeometric function representation for an integral involving these numbers and polynomials. Finally, we give infinite series representations of the numbers Y-n (lambda), the Changhee numbers, the Daehee numbers, the Lucas numbers and the Humbert polynomials. (C) 2017 Elsevier Inc. All rights reserved.en_US
dc.identifier.doi10.1016/j.jnt.2017.05.008
dc.identifier.endpage146en_US
dc.identifier.issn0022-314X
dc.identifier.issn1096-1658
dc.identifier.scopus2-s2.0-85026254557en_US
dc.identifier.scopusqualityQ2en_US
dc.identifier.startpage117en_US
dc.identifier.urihttps://doi.org/10.1016/j.jnt.2017.05.008
dc.identifier.urihttps://hdl.handle.net/20.500.14591/104
dc.identifier.volume181en_US
dc.identifier.wosWOS:000410021600007en_US
dc.identifier.wosqualityQ2en_US
dc.indekslendigikaynakWeb of Scienceen_US
dc.indekslendigikaynakScopusen_US
dc.language.isoenen_US
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCEen_US
dc.relation.ispartofJournal Of Number Theoryen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectGenerating functionsen_US
dc.subjectFunctional equationsen_US
dc.subjectPartial differential equationsen_US
dc.subjectHypergeometric functionsen_US
dc.subjectHurwitz Lerch zeta functionsen_US
dc.subjectApostol-Bernoulli numbers anden_US
dc.subjectApostol-Bernoulli polynomialsen_US
dc.subjectApostol-Euler numbers anden_US
dc.subjectApostol-Bernoulli polynomialsen_US
dc.subjectDaehee and Changhee numbersen_US
dc.subjectStirling numbers of the first kinden_US
dc.subjectCauchy numbersen_US
dc.subjectHumbert polynomialsen_US
dc.subjectLucas numbersen_US
dc.subjectBinomial coefficientsen_US
dc.titlePartial differential equations for a new family of numbers and polynomials unifying the Apostol-type numbers and the Apostol-type polynomialsen_US
dc.typeArticleen_US

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