New generalized apostol-frobenius-euler polynomials and their matrix approach

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.

• Autores: Ortega, María José; Ramírez, William; Urieles, Alejandro
• Tipo de recurso: Article of journal
• Fecha de publicación: 2021
• Institución: Corporación Universidad de la Costa
• Repositorio: REDICUC - Repositorio CUC
• Idioma: eng
• OAI Identifier: oai:repositorio.cuc.edu.co:11323/8632
• Acceso en línea: https://hdl.handle.net/11323/8632; https://doi.org/10.46793/KGJMAT2103.393O; https://repositorio.cuc.edu.co/
• Palabra clave: Generalized Apostol-type polynomial; Apostol-Frobennius-Euler polynomials; Apostol-Bernoulli polynomials of higher order; Apostol-Genocchi polynomials of higher order; Stirling numbers of second kind; generalized Pascal matrix
• Rights: openAccess
• License: Attribution-NonCommercial-NoDerivatives 4.0 International