New classes of Catalan-type numbers and polynomials with their applications related to p-adic integrals and computational algorithms

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dc.contributor.authorKüçükoğlu, İrem
dc.contributor.authorŞimşek, Burçin
dc.contributor.authorŞimşek, Yılmaz
dc.date.accessioned2021-02-19T21:16:39Z
dc.date.available2021-02-19T21:16:39Z
dc.date.issued2020
dc.departmentALKÜ
dc.descriptionSimsek, Burcin/0000-0003-2857-6629; KUCUKOGLU, IREM/0000-0001-9100-2252
dc.description.abstractThe aim of this paper is to construct generating functions for new classes of Catalan-type numbers and polynomials. Using these functions and their functional equations, we give various new identities and relations involving these numbers and polynomials, the Bernoulli numbers and polynomials, the Stirling numbers of the second kind, the Catalan numbers and other classes of special numbers, polynomials and functions. Some infinite series representations, including the Catalan-type numbers and combinatorial numbers, are investigated. Moreover, some recurrence relations and computational algorithms for these numbers and polynomials are provided. By implementing these algorithms in the Python programming language, we illustrate the Catalan-type numbers and polynomials with their plots under the special conditions. We also give some derivative formulas for these polynomials. Applying the Riemann integral, contour integral, Volkenborn (bosonic p-adic) integral and fermionic p-adic integral to these polynomials, we also derive some integral formulas. With the help of these integral formulas, we give some identities and relations associated with some classes of special numbers and also the Cauchy-type numbers.
dc.description.sponsorshipScientific Research Project Administration of Akdeniz UniversityAkdeniz University [FBA-2020-5299]
dc.description.sponsorshipThe third author of the present paper was supported by the Scientific Research Project Administration of Akdeniz University (with Project ID No: FBA-2020-5299).
dc.identifier.doi10.3906/mat-2008-24
dc.identifier.endpage2355en_US
dc.identifier.issn1300-0098
dc.identifier.issn1303-6149
dc.identifier.issue6en_US
dc.identifier.startpage2337en_US
dc.identifier.urihttps://doi.org/10.3906/mat-2008-24
dc.identifier.urihttps://hdl.handle.net/20.500.12868/506
dc.identifier.volume44en_US
dc.identifier.wosWOS:000590703900020
dc.identifier.wosqualityQ3
dc.indekslendigikaynakWeb of Science
dc.institutionauthor0-belirlenecek
dc.language.isoen
dc.publisherScientific Technical Research Council Turkey-Tubitak
dc.relation.ispartofTurkish Journal of Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectGenerating function
dc.subjectBernoulli polynomials
dc.subjectStirling numbers
dc.subjectCatalan numbers
dc.subjectpartial differential equations
dc.subjectcomputational algorithms
dc.subjectp-adic integral
dc.titleNew classes of Catalan-type numbers and polynomials with their applications related to p-adic integrals and computational algorithms
dc.typeArticle

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