Further Discussion on the Calculation of Fourier Series

Caixia Zhang

College of Mathematics and Statistics, Northeast Petroleum University, Daqing, China.

DOI: 10.4236/am.2015.63054                

Abstract

Fourier series is an important mathematical concept. It is well known that we need too much computation to expand the function into Fourier series. The existing literature only pointed that its Fourier series is sine series when the function is an odd function and its Fourier series is cosine series when the function is an even function. And on this basis, in this paper, according to the function which satisfies different conditions, we give the different forms of Fourier series and the specific calculation formula of Fourier coefficients, so as to avoid unnecessary calculation. In addition, if a function is defined on [0,a], we can make it have some kind of nature by using the extension method as needed. So we can get the corresponding form of Fourier series.

Keywords

Fourier Coefficients, Fouries Series, Period, Series Expansion, Extension

Conflicts of Interest

The authors declare no conflicts of interest.

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