Geodesic
New Generalized Apostol-Frobenius-Euler polynomials and their Matrix Approach
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 3, p. 393 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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In this paper, we introduce a new extension of the generalized Apostol-Frobenius-Euler polynomials $\mathcal{H}_n^{[m-1,\alpha]}(x;c,a;\lambda;u)$. 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 $\mathcal{U}^{[m-1,\alpha]}(x;c,a;\lambda;u)$ and the new generalized Apostol-Frobenius-Euler matrix $\mathcal{U}^{[m-1,\alpha]}(c,a;\lambda;u)$, we deduce a product formula for $\mathcal{U}^{[m-1,\alpha]}(x;c,a;\lambda;u)$ and provide some factorizations of the Apostol-Frobenius-Euler polynomial matrix $\mathcal{U}^{[m-1,\alpha]}(x;c,a;\lambda;u)$, which involving the generalized Pascalinebreak matrix.
Classification : 33E12 30H50
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 
@article{KJM_2021_45_3_a5,
     author = {Mar{\'\i}a Jos\'e Ortega and William Ram{\'\i}rez and Alejandro Urieles},
     title = {New {Generalized} {Apostol-Frobenius-Euler} polynomials and their {Matrix} {Approach}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {393 },
     year = {2021},
     volume = {45},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2021_45_3_a5/}
}
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María José Ortega; William Ramírez; Alejandro Urieles. New Generalized Apostol-Frobenius-Euler polynomials and their Matrix Approach. Kragujevac Journal of Mathematics, Tome 45 (2021) no. 3, p. 393 . http://geodesic.mathdoc.fr/item/KJM_2021_45_3_a5/