New generalized apostol-frobenius-euler polynomials and their matrix approach (2021)
In this paper, we introduce a new extension of the generalized Apostol-Frobenius-Euler polynomials ℋn[m−1,α](x; c,a; λ; u). We give some algebraic and diﬀerential properties, as well as, relationships between this polynomials class with other polynomials and numbers. We also, introduce the generalized Apostol-Frobenius-Euler polynomials matrix ????[m−1,α](x; c,a; λ; u) and the new generalized Apostol-Frobenius-Euler matrix ????[m−1,α](c,a; λ; u), we deduce a product formula for ????[m−1,α](x; c,a; λ; u) and provide some factorizations of the Apostol-Frobenius-Euler polynomial matrix ????[m−1,α](x; c,a; λ; u), which involving the generalized Pascal matrix.