Further Discussion on the Calculation of Fourier Series

• 作者: Caixia Zhang
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: FOURIER COEFFICIENTS Fouries SERIES Period SERIES EXPANSION EXTENSION
• 年，卷（期）: yysxyw_2015,（3）
• 页码范围: 594-598
• 页数: 5页
• 分类号: O1

摘要

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.