Generating functions for new families of combinatorial numbers and polynomials: Approach to poisson-charlier polynomials and probability distribution function

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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.issued2019
dc.departmentALKÜ
dc.descriptionSimsek, Burcin/0000-0003-2857-6629; SIMSEK, YILMAZ/0000-0002-0611-7141; KUCUKOGLU, IREM/0000-0001-9100-2252
dc.description.abstractThe aim of this paper is to construct generating functions for new families of combinatorial numbers and polynomials. By using these generating functions with their functional and differential equations, we not only investigate properties of these new families, but also derive many new identities, relations, derivative formulas, and combinatorial sums with the inclusion of binomials coefficients, falling factorial, the Stirling numbers, the Bell polynomials (i.e., exponential polynomials), the Poisson-Charlier polynomials, combinatorial numbers and polynomials, the Bersntein basis functions, and the probability distribution functions. Furthermore, by applying the p-adic integrals and Riemann integral, we obtain some combinatorial sums including the binomial coefficients, falling factorial, the Bernoulli numbers, the Euler numbers, the Stirling numbers, the Bell polynomials (i.e., exponential polynomials), and the Cauchy numbers (or the Bernoulli numbers of the second kind). Finally, we give some remarks and observations on our results related to some probability distributions such as the binomial distribution and the Poisson distribution.
dc.description.sponsorshipScientific Research Project Administration of Akdeniz UniversityAkdeniz University
dc.description.sponsorshipThis paper is dedicated to Hari Mohan Srivastava on the occasion of his 80th Birthday. Yilmaz Simsek was supported by the Scientific Research Project Administration of Akdeniz University.
dc.identifier.doi10.3390/axioms8040112
dc.identifier.issn2075-1680
dc.identifier.issue4en_US
dc.identifier.scopusqualityN/A
dc.identifier.urihttps://doi.org/10.3390/axioms8040112
dc.identifier.urihttps://hdl.handle.net/20.500.12868/507
dc.identifier.volume8en_US
dc.identifier.wosWOS:000505589700029
dc.identifier.wosqualityN/A
dc.indekslendigikaynakWeb of Science
dc.indekslendigikaynakScopus
dc.institutionauthor0-belirlenecek
dc.language.isoen
dc.publisherMdpi
dc.relation.ispartofAxioms
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanı
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectgenerating functions
dc.subjectfunctional equations
dc.subjectpartial differential equations
dc.subjectspecial numbers and polynomials
dc.subjectBernoulli numbers
dc.subjectEuler numbers
dc.subjectStirling numbers
dc.subjectBell polynomials
dc.subjectCauchy numbers
dc.subjectPoisson-Charlier polynomials
dc.subjectBernstein basis functions
dc.subjectDaehee numbers and polynomials
dc.subjectcombinatorial sums
dc.subjectbinomial coefficients
dc.subjectp-adic integral
dc.subjectprobability distribution
dc.titleGenerating functions for new families of combinatorial numbers and polynomials: Approach to poisson-charlier polynomials and probability distribution function
dc.typeArticle

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