Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials

The main purpose of this paper is to investigate the Fourier series representation of the generalized Apostol-type Frobenius–Euler polynomials, and using the above-mentioned series we find its integral representation. At the same time applying the Fourier series representation of the Apostol Frobeni...

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Detalhes bibliográficos
Autor: Urieles, Alejandro
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:Colombia
Recursos:Universidad del Atlántico
Repositorio:Repositorio Uniatlantico
Idioma:inglés
OAI Identifier:oai:repositorio.uniatlantico.edu.co:20.500.12834/894
Acesso em linha:https://hdl.handle.net/20.500.12834/894
Access Level:acceso abierto
Palavra-chave:Generalized Apostol Frobenius–Euler polynomials; Hurwitz zeta function; Fourier expansion; Generalized Apostol Frobennius–Euler numbers
Descrição
Resumo:The main purpose of this paper is to investigate the Fourier series representation of the generalized Apostol-type Frobenius–Euler polynomials, and using the above-mentioned series we find its integral representation. At the same time applying the Fourier series representation of the Apostol Frobenius–Genocchi and Apostol Genocchi polynomials, we obtain its integral representation. Furthermore, using the Hurwitz–Lerch zeta function we introduce the formula in rational arguments of the generalized Apostol-type Frobenius–Euler polynomials in terms of the Hurwitz zeta function. Finally, we show the representation of rational arguments of the Apostol Frobenius Euler polynomials and the Apostol Frobenius–Genocchi polynomials.

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