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

作者：Kilar Neslihan^*; Simsek Yilmaz

来源：Journal of the Korean Mathematical Society, 2017, 54(5): 1605-1621.

DOI：10.4134/JKMS.j160597

• Bernoulli numbers
• Apostol-Bernoulli numbers
• ApostolBernoulli polynomials
• Frobenius-Euler numbers
• Stirling numbers
• Fubini numbers
• generating functions
• functional equations
• binomial coefficients
• combinatorial sum

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.

• 出版日期2017