Formulae bringing to light from certain classes of numbers and polynomials

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dc.authoridSIMSEK, YILMAZ/0000-0002-0611-7141
dc.authoridKILAR, NESLIHAN/0000-0001-5797-6301
dc.contributor.authorKilar, Neslihan
dc.contributor.authorKim, Daeyeoul
dc.contributor.authorSimsek, Yilmaz
dc.date.accessioned2024-11-07T13:34:27Z
dc.date.available2024-11-07T13:34:27Z
dc.date.issued2023
dc.departmentNiğde Ömer Halisdemir Üniversitesi
dc.description.abstractWith aid of generating functions and their functional equation methods and special functions involving trigonometric functions, the motivation of this paper is to study by blending certain families polynomials associated with the Bernoulli numbers and polynomials, the Euler numbers and polynomials, the Hermite type polynomials, the Stirling numbers, the telephone numbers, the Chebyshev polynomials. Therefore, the purpose of this paper is to examine certain families of numbers and functions related to generalized Hermite-Kampe de Feriet polynomials and trigonometric functions. By using functional equations of generating functions, we derive numerous new formulae and relations involving parametric Hermite type polynomials, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the generalized Hermite-Kampe de Feriet polynomials and the telephone numbers. Moreover, applying derivative operator to these generating functions, we give many recurrence relations and computational formulae, and certain finite sums. Finally, some special cases of these results are reduced to not only the well-known Chebyshev polynomials, which have applications in a wide variety of different areas, but also special trigonometric functions and finite sums.
dc.description.sponsorshipNational Research Foundation [2021R1F1A1051093]
dc.description.sponsorshipThis article was funded by National Research Foundation (Grant no. 2021R1F1A1051093)
dc.identifier.doi10.1007/s13398-022-01370-x
dc.identifier.issn1578-7303
dc.identifier.issn1579-1505
dc.identifier.issue1
dc.identifier.scopus2-s2.0-85142662073
dc.identifier.scopusqualityQ1
dc.identifier.urihttps://doi.org/10.1007/s13398-022-01370-x
dc.identifier.urihttps://hdl.handle.net/11480/15990
dc.identifier.volume117
dc.identifier.wosWOS:000889066900004
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherSpringer-Verlag Italia Srl
dc.relation.ispartofRevista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-Matematicas
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_20241106
dc.subjectBernoulli numbers
dc.subjectEuler numbers
dc.subjectHermite type polynomials
dc.subjectStirling numbers
dc.subjectTelephone numbers
dc.subjectChebyshev polynomials
dc.subjectGenerating functions
dc.subjectTrigonometric functions
dc.titleFormulae bringing to light from certain classes of numbers and polynomials
dc.typeArticle

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