Fourier series of higher-order Bernoulli functions and their applications

Taekyun Kim; Dae San Kim; Seog-Hoon Rim; Dmitry V Dolgy

doi:10.1186/s13660-016-1282-y

Fourier series of higher-order Bernoulli functions and their applications

J Inequal Appl. 2017;2017(1):8. doi: 10.1186/s13660-016-1282-y. Epub 2017 Jan 5.

Authors

Taekyun Kim¹, Dae San Kim², Seog-Hoon Rim³, Dmitry V Dolgy⁴

Affiliations

¹ Department of Mathematics, Kwangwoon University, Seoul, 139-701 Republic of Korea ; Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin, 300160 China.
² Department of Mathematics, Sogang University, Seoul, 121-742 Republic of Korea.
³ Department of Mathematics Education, Kyungpook National University, Taegu, 702-701 Republic of Korea.
⁴ Hanrimwon, Kwangwoon University, Seoul, 139-701 Republic of Korea ; School of Natural Sciences, Far Eastern Federal University, 690950 Vladivostok, Russia.

Abstract

In this paper, we study the Fourier series related to higher-order Bernoulli functions and give new identities for higher-order Bernoulli functions which are derived from the Fourier series of them.

Keywords: Bernoulli functions; Bernoulli polynomials; Fourier series.