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.
Cite this paper
Zhang, C. (2015) Further Discussion on the Calculation of Fourier Series. Applied Mathematics, 6, 594-598. doi: 10.4236/am.2015.63054.
 Department of Mathematics of East China Normal University (2010) Mathematical Analysis. 4th Edition, Higher Education Press, Beijing, 62-72. (In Chinese)
 He, G.Z. (2008) Discussion on a Style of Fourier Series Expansion. Journal of Leshan Teachers College, 23, 27-28. (In Chinese)
 Zheng, C. and Qiu, W.G. (2010) Integration Techniques Based on Fourier. Studies in College Mathematics, 13, 31-32. (In Chinese)
 Wang, B.Y. and Qi, X.S. (2011) Two Methods for Summing Trigonometric Series. Studies in College Mathematics, 14, 33-34. (In Chinese)
 Jiao, H.Y. and Liu, W.H. (2011) Fourier Expansion and a Class of Series. Studies in College Mathematics, 14, 35-36. (In Chinese)
 Ding, X.H. (2004) Several Problems of Fouries Series Expansion. Journal of Daxian Teachers College (Natural Sci ence Edition), 14, 1-4. (In Chinese)