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http://dx.doi.org/10.4134/JKMS.j160597

A NEW FAMILY OF FUBINI TYPE NUMBERS AND POLYNOMIALS ASSOCIATED WITH APOSTOL-BERNOULLI NUMBERS AND POLYNOMIALS  

Kilar, Neslihan (Department of Mathematics Faculty of Science University of Akdeniz)
Simsek, Yilmaz (Department of Mathematics Faculty of Science University of Akdeniz)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.5, 2017 , pp. 1605-1621 More about this Journal
Abstract
The purpose of this paper is to construct a new family of the special numbers which are related to the Fubini type numbers and the other well-known special numbers such as the Apostol-Bernoulli numbers, the Frobenius-Euler numbers and the Stirling numbers. We investigate some fundamental properties of these numbers and polynomials. By using generating functions and their functional equations, we derive various formulas and relations related to these numbers and polynomials. In order to compute the values of these numbers and polynomials, we give their recurrence relations. We give combinatorial sums including the Fubini type numbers and the others. Moreover, we give remarks and observation on these numbers and polynomials.
Keywords
Bernoulli numbers; Apostol-Bernoulli numbers; Apostol-Bernoulli polynomials; Frobenius-Euler numbers; Stirling numbers; Fubini numbers; generating functions; functional equations; binomial coefficients; combinatorial sum;
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Times Cited By KSCI : 1  (Citation Analysis)
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