Fourier series of sums of products of Bernoulli functions and their applications

Volume 10, Issue 5, pp 2798--2815 http://dx.doi.org/10.22436/jnsa.010.05.46

Publication Date: May 25, 2017 Submission Date: December 19, 2016

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Authors

Taekyun Kim - Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, 300387, China. - Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea. Dae San Kim - Department of Mathematics, Sogang University, Seoul 121-742, Republic of Korea. Lee-Chae Jang - Graduate School of Education, Konkuk University, Seoul 143-701, Republic of Korea. Gwan-Woo Jang - Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea.

Abstract

We consider three types of sums of products of Bernoulli functions and derive their Fourier series expansions. In addition, we express each of them in terms of Bernoulli functions.

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Keywords

• Fourier series
• Bernoulli polynomials
• Bernoulli functions.

MSC

•  11B68
•  11S80
•  05A19
•  05A30

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