J. Korean Math. Soc. 2017; 54(5): 1605-1621
Online first article May 24, 2017 Printed September 1, 2017
https://doi.org/10.4134/JKMS.j160597
Copyright © The Korean Mathematical Society.
Neslihan Kilar and Yilmaz Simsek
University of Akdeniz, University of Akdeniz
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
MSC numbers: 11B37, 11B68, 11B73, 05A15, 05A19, 12D10, 26C05, 30C15
2019; 56(1): 265-284
2007; 44(2): 487-498
2018; 55(5): 1207-1220
2018; 55(5): 1179-1192
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd