Fourier series of finite products of Bernoulli and Genocchi functions

Taekyun Kim; Dae San Kim; Gwan-Woo Jang; Jongkyum Kwon

doi:10.1186/s13660-017-1431-y

Fourier series of finite products of Bernoulli and Genocchi functions

J Inequal Appl. 2017;2017(1):157. doi: 10.1186/s13660-017-1431-y. Epub 2017 Jun 30.

Authors

Taekyun Kim^{1

2}, Dae San Kim³, Gwan-Woo Jang¹, Jongkyum Kwon⁴

Affiliations

¹ Department of Mathematics, Kwangwoon University, Seoul, 139-701 Republic of Korea.
² Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin, 300160 China.
³ Department of Mathematics, Sogang University, Seoul, 121-742 Republic of Korea.
⁴ Department of Mathematics Education and RINS, Gyeongsang National University, Jinju, Gyeongsangnamdo 52828 Republic of Korea.

Abstract

In this paper, we consider three types of functions given by products of Bernoulli and Genocchi functions and derive some new identities arising from Fourier series expansions associated with Bernoulli and Genocchi functions. Furthermore, we will express each of them in terms of Bernoulli functions.

Keywords: Bernoulli function; Fourier series; Genocchi function; finite product.