Some Relations Between the Riemann Zeta Function and the Generalized Bernoulli Polynomials of Level $m$

Year 2019, Volume: 2 Issue: 4, 188 - 201, 26.12.2019

Yamilet Quintana , Héctor Torres-guzmán

https://doi.org/10.32323/ujma.602178

Cited By: 4

Abstract

The main purpose of this paper is to show some relations between the Riemann zeta function and the generalized Bernoulli polynomials of level $m$. Our approach is based on the use of Fourier expansions for the periodic generalized Bernoulli functions of level $m$, as well as  quadrature formulae of Euler-Maclaurin type. Some illustrative examples involving such relations are also given.

Keywords

Bernoulli polynomials, Euler-Maclaurin quadrature formulae, generalized Bernoulli polynomials of level $m$, quadrature formula, Riemann zeta function

Supporting Institution

Decanato de Investigación y Desarrollo, Universidad Simón Bolívar

Project Number

DID-USB (S1-IC-CB-004-17)

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