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

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DOI: 10.46793/KgJMat2103.393O


In this paper, we introduce a new extension of the generalized Apostol-Frobenius-Euler polynomials n[m1](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 ????[m1](x; c,a; λ; u) and the new generalized Apostol-Frobenius-Euler matrix ????[m1](c,a; λ; u), we deduce a product formula for ????[m1](x; c,a; λ; u) and provide some factorizations of the Apostol-Frobenius-Euler polynomial matrix ????[m1](x; c,a; λ; u), which involving the generalized Pascal matrix.


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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