Computational and implementational analysis of generating functions for higher order combinatorial numbers and polynomials attached to Dirichlet characters
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Tarih
2022
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Wiley
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
The main purpose of this paper is to give computational and implementational analysis of generating functions for some extensions of combinatorial numbers and polynomials attached to Dirichlet characters. By using generating function methods and p-adic q-integral techniques, it is also aimed to derive some computational formulas for these numbers and polynomials. By implementing both the derived computational formulas and the constructed generating functions in Mathematica, we present some tables and plots for these numbers and polynomials, and their generating functions to illustrate the effects of their parameters for some special cases. Moreover, by making an observation on some results of this paper, we derive some novel computational formulas for the finite sums that contain the Dirichlet characters and falling factorials. We also assess some cases of these special finite sums. In the sequel, we pose some open problems regarding these special finite sums. Apart from these findings, we also give not only Fourier series expansion but also asymptotic estimates for the mentioned combinatorial numbers. In addition, we give some Raabe-type multiplication formulas for the mentioned combinatorial polynomials. Finally, we give an observation on decompositions of the generating functions attached to any group homomorphism.
Açıklama
Anahtar Kelimeler
Apostol-Bernoulli numbers and polynomials, combinatorial numbers, Dirichlet character, generating functions, group homomorphism, mathematica implementation, p-adic q-integral, Simsek numbers and polynomials, special finite character sums, Stirling numbers, Raabe-type multiplication formula
Kaynak
Mathematical Methods in The Applied Sciences
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
45
Sayı
9
