Geodesic
New Generalized Apostol-Frobenius-Euler polynomials and their Matrix Approach
Kragujevac Journal of Mathematics, Tome 45 (2021) no. 3, p. 393

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 
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     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},
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     year = {2021},
     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/