Applications of Fourier Series and Zeta Functions to Genocchi Polynomials

Authors

Serkan Araci, Department of Economics, Faculty of Economics, Administrative and Social Science, Hasan Kalyoncu University, TR-27410 Gaziantep, TurkeyFollow
Mehmet Acikgoz, Department of Mathematics, Faculty of Science and Arts, Gaziantep University, TR-27310 Gaziantep, TurkeyFollow

Author Country (or Countries)

Turkey

Abstract

In this paper, we firstly consider the properties of Genocchi polynomials, Fourier series and Zeta functions. In the special cases, we see that the Fourier series yield Zeta functions. From here, we show that zeta functions for some special values can be computed by Genocchi polynomials. Secondly, we consider the Fourier series of periodic Genocchi functions. For odd indexes of Genocchi functions, we construct good links between Genocchi functions and Zeta function. Finally, since Genocchi functions reduce to Genocchi polynomials over the interval [0,1), we see that Zeta functions have integral representations in terms of Genocchi polynomials.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/120508

Recommended Citation

Araci, Serkan and Acikgoz, Mehmet (2018) "Applications of Fourier Series and Zeta Functions to Genocchi Polynomials," Applied Mathematics & Information Sciences: Vol. 12: Iss. 5, Article 8.
DOI: http://dx.doi.org/10.18576/amis/120508
Available at: https://digitalcommons.aaru.edu.jo/amis/vol12/iss5/8