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

Yamilet Quintana; Héctor Torres-guzmán

doi:10.32323/ujma.602178

EN

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

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)

References

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[17] G. M. Phillips, Interpolation and Approximation by Polynomials, Springer-Verlag, New York, 2003.
[18] Y. Quintana, W. Ramirez, A. Urieles, On an operational matrix method based on generalized Bernoulli polynomials of level m, Calcolo, 55(3) (2018), 29 pages.
[19] Y. Quintana, A. Urieles, Quadrature formulae of Euler-Maclaurin type based on generalized Euler polynomials of level m, Bull. Comput. Appl. Math., 6(2) (2018), 43-64.
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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Yamilet Quintana ^*
0000-0003-1053-0892
Venezuela

Héctor Torres-guzmán This is me
0000-0002-9101-7355
Venezuela

Publication Date

December 26, 2019

Submission Date

August 5, 2019

Acceptance Date

October 14, 2019

Published in Issue

Year 2019 Volume: 2 Number: 4

DOI

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

IZ

https://izlik.org/JA39RL59RK

APA

Quintana, Y., & Torres-guzmán, H. (2019). Some Relations Between the Riemann Zeta Function and the Generalized Bernoulli Polynomials of Level $m$. Universal Journal of Mathematics and Applications, 2(4), 188-201. https://doi.org/10.32323/ujma.602178

AMA

1.Quintana Y, Torres-guzmán H. Some Relations Between the Riemann Zeta Function and the Generalized Bernoulli Polynomials of Level $m$. Univ. J. Math. Appl. 2019;2(4):188-201. doi:10.32323/ujma.602178

Chicago

Quintana, Yamilet, and Héctor Torres-guzmán. 2019. “Some Relations Between the Riemann Zeta Function and the Generalized Bernoulli Polynomials of Level $m$”. Universal Journal of Mathematics and Applications 2 (4): 188-201. https://doi.org/10.32323/ujma.602178.

EndNote

Quintana Y, Torres-guzmán H (December 1, 2019) Some Relations Between the Riemann Zeta Function and the Generalized Bernoulli Polynomials of Level $m$. Universal Journal of Mathematics and Applications 2 4 188–201.

IEEE

[1]Y. Quintana and H. Torres-guzmán, “Some Relations Between the Riemann Zeta Function and the Generalized Bernoulli Polynomials of Level $m$”, Univ. J. Math. Appl., vol. 2, no. 4, pp. 188–201, Dec. 2019, doi: 10.32323/ujma.602178.

ISNAD

Quintana, Yamilet - Torres-guzmán, Héctor. “Some Relations Between the Riemann Zeta Function and the Generalized Bernoulli Polynomials of Level $m$”. Universal Journal of Mathematics and Applications 2/4 (December 1, 2019): 188-201. https://doi.org/10.32323/ujma.602178.

JAMA

1.Quintana Y, Torres-guzmán H. Some Relations Between the Riemann Zeta Function and the Generalized Bernoulli Polynomials of Level $m$. Univ. J. Math. Appl. 2019;2:188–201.

MLA

Quintana, Yamilet, and Héctor Torres-guzmán. “Some Relations Between the Riemann Zeta Function and the Generalized Bernoulli Polynomials of Level $m$”. Universal Journal of Mathematics and Applications, vol. 2, no. 4, Dec. 2019, pp. 188-01, doi:10.32323/ujma.602178.

Vancouver

1.Yamilet Quintana, Héctor Torres-guzmán. Some Relations Between the Riemann Zeta Function and the Generalized Bernoulli Polynomials of Level $m$. Univ. J. Math. Appl. 2019 Dec. 1;2(4):188-201. doi:10.32323/ujma.602178