New classes of Catalan-type numbers and polynomials with their applications related to p-adic integrals and computational algorithms
[ X ]
Tarih
2020
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Scientific Technical Research Council Turkey-Tubitak
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
The 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.
Açıklama
Simsek, Burcin/0000-0003-2857-6629; KUCUKOGLU, IREM/0000-0001-9100-2252
Anahtar Kelimeler
Generating function, Bernoulli polynomials, Stirling numbers, Catalan numbers, partial differential equations, computational algorithms, p-adic integral
Kaynak
Turkish Journal of Mathematics
WoS Q Değeri
Q3
Scopus Q Değeri
Cilt
44
Sayı
6
