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Abstract and Applied Analysis
Volume 2014, Article ID 856491, 4 pages
http://dx.doi.org/10.1155/2014/856491
Research Article

Fourier Series of the Periodic Bernoulli and Euler Functions

1Department of Mathematics, Hannam University, Daejeon 306-791, Republic of Korea
2Department of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
3Department of Applied Mathematics, Kangnam University, Yongin 446-702, Republic of Korea

Received 16 April 2014; Revised 16 July 2014; Accepted 16 July 2014; Published 5 August 2014

Academic Editor: Ming Mei

Copyright © 2014 Cheon Seoung Ryoo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give some properties of the periodic Bernoulli functions and study the Fourier series of the periodic Euler functions which are derived periodic functions from the Euler polynomials. And we derive the relations between the periodic Bernoulli functions and those from Euler polynomials by using the Fourier series.