Identities and derivative formulas for the combinatorial and apostol-euler type numbers by their generating functions
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Tarih
2018
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Univ Nis, Fac Sci Math
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
The first aim of this paper is to give identities and relations for a new family of the combinatorial numbers and the Apostol-Euler type numbers of the second kind, the Stirling numbers, the Apostol-Bernoulli type numbers, the Bell numbers and the numbers of the Lyndon words by using some techniques including generating functions, functional equations and inversion formulas. The second aim is to derive some derivative formulas and combinatorial sums by applying derivative operators including the Caputo fractional derivative operators. Moreover, we give a recurrence relation for the Apostol-Euler type numbers of the second kind. By using this recurrence relation, we construct a computation algorithm for these numbers. In addition, we derive some novel formulas including the Stirling numbers and other special numbers. Finally, we also some remarks, comments and observations related to our results.
Açıklama
International Conference on Approximation and Computation - Theory and Applications (ACTA) -- NOV 30-DEC 02, 2017 -- Belgrade, SERBIA
KUCUKOGLU, IREM/0000-0001-9100-2252
KUCUKOGLU, IREM/0000-0001-9100-2252
Anahtar Kelimeler
Generating functions, Functional equations, Partial differential equations, Stirling numbers of the second kind, Euler numbers of the second kind, Apostol-Euler type polynomials of the second kind, lambda-Bernoulli numbers, Bell numbers, Combinatorial sums, Binomial coefficients, Arithmetical functions
Kaynak
Filomat
WoS Q Değeri
N/A
Scopus Q Değeri
Q3
Cilt
32
Sayı
20
