FORMULAS AND COMBINATORIAL IDENTITIES FOR CATALAN-TYPE NUMBERS AND POLYNOMIALS: THEIR ANALYSIS WITH COMPUTATIONAL ALGORITHMS

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dc.authorid0000-0002-0611-7141
dc.authorid0000-0001-9100-2252
dc.contributor.authorKucukoglu, I
dc.contributor.authorSimsek, Y.
dc.date.accessioned2026-01-24T12:29:26Z
dc.date.available2026-01-24T12:29:26Z
dc.date.issued2022
dc.departmentAlanya Alaaddin Keykubat Üniversitesi
dc.description.abstractIn this paper, we aim to provide generating functions for a higher-order expansion of a certain class of Catalan-type numbers and polynomials, and to give some computational algorithms for evaluating these numbers and polynomials. With the implementation of these computational algorithms in Mathematica by Wolfram programming language, we provide some plots drawn depending on varying special cases of the Catalan-type polynomials of higher-order. By using generating functions, we also derive some formulas and combinatorial identities. By applying not only the Riemann integral, but also the p-adic integrals to these formulas, we get some integral formulas involving the Catalan-type numbers and polynomials, the factorial polynomials, the Stirling numbers, the Bernoulli numbers of the second kind, the Daehee and Changhee numbers and polynomials. By using these integral formulas, we derive other combinatorial sums including the Catalan-type numbers. In addition, we provide some finite and infinite series representations which arise from the Catalan-type numbers.
dc.description.sponsorshipScientific Research Project Administration of Akdeniz University
dc.description.sponsorshipSecond author of the present paper was supported by the Scientific Research Project Administration of Akdeniz University
dc.identifier.doi10.30546/1683-6154.21.2.2022.158
dc.identifier.endpage177
dc.identifier.issn1683-3511
dc.identifier.issn1683-6154
dc.identifier.issue2
dc.identifier.scopus2-s2.0-85151919739
dc.identifier.scopusqualityQ1
dc.identifier.startpage158
dc.identifier.urihttps://doi.org/10.30546/1683-6154.21.2.2022.158
dc.identifier.urihttps://hdl.handle.net/20.500.12868/5343
dc.identifier.volume21
dc.identifier.wosWOS:000823360200004
dc.identifier.wosqualityQ1
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.language.isoen
dc.publisherMinistry Communications & High Technologies Republic Azerbaijan
dc.relation.ispartofApplied and Computational Mathematics
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.snmzKA_WoS_20260121
dc.subjectGenerating Functions
dc.subjectp-adic Integrals
dc.subjectComputational Algorithms
dc.subjectSpecial Numbers and Polynomials
dc.subjectBinomial Coefficients
dc.subjectFactorial Polynomials
dc.subjectHarmonic Numbers
dc.subjectCatalan Numbers
dc.subjectBernoulli Numbers
dc.subjectEuler Numbers
dc.subjectStirling Numbers
dc.subjectDaehee Numbers and Polynomials
dc.subjectChanghee Numbers and Polynomials
dc.subjectComplete Bell Polynomials
dc.subjectFinite Sums
dc.titleFORMULAS AND COMBINATORIAL IDENTITIES FOR CATALAN-TYPE NUMBERS AND POLYNOMIALS: THEIR ANALYSIS WITH COMPUTATIONAL ALGORITHMS
dc.typeArticle

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