New Biparametric Families of Apostol-Frobenius-Euler Polynomials 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 $\lambda$-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.

Keywords

• generalized apostol-type polynomials
• apostol–frobennius–euler polynomials
• apostol-bernoulli polynomials of higher order
• apostol–genocchi polynomials of higher order
• generalized $\lambda$-stirling numbers of second kind