Some Identities for the Two Variable Fubini Polynomials

Abstract

In this paper, we perform a further investigation for the Fubini polynomials. By making use of the generating function methods and Padé approximation techniques, we establish some new identities for the two variable Fubini polynomials. Some special cases as well as immediate consequences of the main results presented here are also considered.

Truncated Fubini Polynomials

“…We firstly remember the classical two-variable Fubini polynomials by the following generating function (cf. [2,3,5,6,10,13]):…”

“…see [1][2][3][4][5][6][7][8][9][10] for details about the aforesaid polynomials. The Bernoulli numbers B n and Euler numbers E n are obtained by the special cases of the corresponding polynomials at x = 0, namely: B n (0) := B n and E n (0) := E n .…”

“…The Stirling numbers of the second kind are given by the following exponential generating function: [2][3][4][5]7,8,10,13]…”

“…where the notation (x) µ called the falling factorial equals [2][3][4][5][7][8][9][10]13], and see also the references cited therein. The Apostol-type Stirling numbers of the second kind is defined by (cf.…”

A Parametric Kind of the Degenerate Fubini Numbers and Polynomials

“…In the last decade, many mathematicians, namely, Kargin [1], Duran and Acikgoz [2], Kim et al [3,4], Kilar and Simsek [5], Su and He [6] have been studied in the area of the Fubini polynomials and numbers, degenerate Fubini polynomials and numbers. The range of Appell polynomials sequences is one of the important classes of polynomial sequences.…”