Identities and relations for Fubini type numbers and polynomials via generating functions and $p$-adic integral approach

Neslihan Kilar, Yilmaz Simsek

The Fubini type polynomials have many application not only especially in combinatorial analysis, but also other branches of mathematics, in engineering and related areas. Therefore, by using the $p$-adic integrals method and functional equation of the generating functions for Fubini type polynomials and numbers, we derive various different new identities, relations and formulas including well-known numbers and polynomials such as the Bernoulli numbers and polynomials, the Euler numbers and polynomials, the Stirling numbers of the second kind, the $\lambda$-array polynomials and the Lah numbers.