NEW BIPARAMETRIC FAMILIES OF APOSTOL-FROBENIUS-EULER POLYNOMIALS OF LEVEL m

Abstract

We introduce two biparametric families of Apostol-Frobenius-Euler polynomials of level m. We give some algebraic properties, as well as some other identities which connect these polynomial class with the generalized λ-Stirling type numbers of the second kind, the generalized Apostol–Bernoulli polynomials, the generalized Apostol–Genocchi polynomials, the generalized Apostol–Euler polynomials and Jacobi polynomials. Finally, we will show the differential properties of this new family of polynomials.