Generalization of Q-apostol-type eulerian numbers and polynomials, and their interpolation functions

Abstract

In a recent paper [16], generating functions in terms of non-negative real parameters, q-Eulerian type polynomials and numbers (or q-Apostol type Frobenius-Euler numbers and polynomials) have been constructed by Y. Simsek. Additionally, some identities for these polynomials and numbers based on the generating functions and functional equations have been derived. Finally, a multiplication formula for the generalized Apostol type Frobenius-Euler polynomials has been given. In this paper, as a continuing study of [16], we will essentially present generalizations of the above material and, differently from aforementioned paper, we will express the interpolation functions related to these numbers and polynomials.