• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1605-1621
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• 2017

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.

• Journal of the Korean Mathematical Society
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• v.55 no.4
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• pp.975-986
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• 2018

Some new family of Fubini type numbers and polynomials associated with Apostol-Bernoulli numbers and polynomilas were introduced recently by Kilar and Simsek ([5]) and we study the two variable Fubini polynomials as Appell polynomials whose coefficients are the Fubini polynomials. In this paper, we would like to utilize umbral calculus in order to study two variable higher-order Fubini polynomials. We derive some of their properties, explicit expressions and recurrence relations. In addition, we express the two variable higher-order Fubini polynomials in terms of some families of special polynomials and vice versa.