A parametric kind of the Fubini-type polynomials

Abstract

By introducing two specific generating functions, we define a kind of parametric Fubini-type polynomials. We investigate some fundamental properties of these parametric-kind Fubini-type polynomials. In particular, we derive the relations between the parametric-kind Fubini-type polynomials and other polynomials including (for example) the parametric-kind Apostol–Bernoulli, the Apostol–Euler and the Apostol–Genocchi polynomials of order $$\alpha $$. Finally, we derive several families of multilinear and multilateral generating functions for the parametric-kind Fubini-type polynomials as well as other polynomials which are considered in this paper.