Recurrence relations, associated formulas, and combinatorial sums for some parametrically generalized polynomials arising from an analysis of the Laplace transform and generating functions

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dc.authoridSIMSEK, YILMAZ/0000-0002-0611-7141
dc.authoridKILAR, NESLIHAN/0000-0001-5797-6301
dc.authoridSrivastava, Hari M./0000-0002-9277-8092
dc.contributor.authorKilar, Neslihan
dc.contributor.authorSimsek, Yilmaz
dc.contributor.authorSrivastava, H. M.
dc.date.accessioned2024-11-07T13:35:18Z
dc.date.available2024-11-07T13:35:18Z
dc.date.issued2023
dc.departmentNiğde Ömer Halisdemir Üniversitesi
dc.description.abstractThe aim of this paper is to obtain some interesting infinite series representations for the Apostol-type parametrically generalized polynomials with the aid of the Laplace transform and generating functions. In particular, by using the method of generating functions, we derive not only recurrence relations, but also several other formulas, identities, and relations as well as combinatorial sums for these parametrically generalized numbers and polynomials and for other known special numbers and polynomials. These identities, relations and combinatorial sums are related to the two-parameter types of the Apostol-Bernoulli polynomials of higher order, the two-parameter types of Apostol-Euler polynomials of higher order, the two-parameter types of Apostol-Genocchi polynomials of higher order, the Apostol-Bernoulli polynomials of higher order, the Apostol-Euler polynomials of higher order, the Apostol-Genocchi polynomials of higher order, the cosine- and sine-Bernoulli polynomials, the cosine- and sine-Euler polynomials, the lambda-array-type polynomials, the lambda-Stirling numbers, the polynomials C-n(x,y)Cn(x,y), and the polynomials S-n(x,y)Sn(x,y). Finally, we present several new recurrence relations for these special polynomials and numbers.
dc.description.sponsorshipScientific Research Project Administration of the University of Akdeniz
dc.description.sponsorshipThe author Y. Simsek was supported by the Scientific Research Project Administration of the University of Akdeniz
dc.identifier.doi10.1007/s11139-022-00679-w
dc.identifier.endpage756
dc.identifier.issn1382-4090
dc.identifier.issn1572-9303
dc.identifier.issue3
dc.identifier.scopus2-s2.0-85145042831
dc.identifier.scopusqualityQ2
dc.identifier.startpage731
dc.identifier.urihttps://doi.org/10.1007/s11139-022-00679-w
dc.identifier.urihttps://hdl.handle.net/11480/16444
dc.identifier.volume61
dc.identifier.wosWOS:000921992400001
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer
dc.relation.ispartofRamanujan Journal
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_20241106
dc.subjectApostol-Bernoulli numbers and polynomials
dc.subjectApostol-Euler numbers and polynomials
dc.subjectApostol-Genocchi numbers and polynomials
dc.subjectParametrically generalized numbers and polynomials
dc.subjectSpecial numbers and polynomials
dc.subjectLaplace transform
dc.subjectGenerating functions
dc.titleRecurrence relations, associated formulas, and combinatorial sums for some parametrically generalized polynomials arising from an analysis of the Laplace transform and generating functions
dc.typeArticle

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