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

Advances in Difference Equations

Daniel Bedoya¹  María José Ortega²  William Ramírez²  Alejandro Urieles³ 

[1] Departamento de Ciencias Básicas, Universidad Metropolitana, Barranquilla, Colombia;Departamento de Ciencias Naturales y Exactas, Universidad de la Costa, Barranquilla, Colombia;Programa de Matemáticas, Universidad del Atlántico, Km 7 Vía Pto, Barranquilla, Colombia;

关键词: Generalized Apostol Frobenius–Euler polynomials;    Hurwitz zeta function;    Fourier expansion;    Generalized Apostol Frobennius–Euler numbers;   

DOI  :  10.1186/s13662-020-02988-0

来源: Springer

【 摘 要 】

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.

【 授权许可】

CC BY