Integral representations and formulas for the unified and modified presentation of Fubini numbers and polynomials

Abstract

The aim of this paper is to give some different type integral representations for the unified and modified presentation of Fubini numbers and polynomials. By applying both the p-adic integrals including the Volkenborn integral and the fermionic p-adic integral, and the Riemann integral to the generating functions of the unified and modified presentation of Fubini numbers and polynomials, we give some integral representations including these numbers and polynomials, as well as the Daehee numbers, the Bernoulli numbers and polynomials, the Euler numbers and polynomials, and some special numbers. Using the generating function methods, we also give some formulas for these numbers and polynomials.