### New Generalized Apostol-Frobenius-Euler polynomials and their Matrix Approach

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**Authors:**M. J. ORTEGA, W. RAMíREZ AND A. URIELES

**DOI:**10.46793/KgJMat2103.393O

**Abstract:**

In this paper, we introduce a new extension of the generalized Apostol-Frobenius-Euler polynomials ℋ

_{n}

^{[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.

**Keywords:**

Generalized Apostol-type polynomials, Apostol-Frobennius-Euler polynomials, Apostol-Bernoulli polynomials of higher order, Apostol-Genocchi polynomials of higher order, Stirling numbers of second kind, generalized Pascal matrix.

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