Generating functions for new families of combinatorial numbers and polynomials: Approach to poisson-charlier polynomials and probability distribution function
[ X ]
Tarih
2019
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Mdpi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
The 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.
Açıklama
Simsek, Burcin/0000-0003-2857-6629; SIMSEK, YILMAZ/0000-0002-0611-7141; KUCUKOGLU, IREM/0000-0001-9100-2252
Anahtar Kelimeler
generating functions, functional equations, partial differential equations, special numbers and polynomials, Bernoulli numbers, Euler numbers, Stirling numbers, Bell polynomials, Cauchy numbers, Poisson-Charlier polynomials, Bernstein basis functions, Daehee numbers and polynomials, combinatorial sums, binomial coefficients, p-adic integral, probability distribution
Kaynak
Axioms
WoS Q Değeri
N/A
Scopus Q Değeri
N/A
Cilt
8
Sayı
4
