| 关于一个典型函数Fourier级数的Gibbs现象 |
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| 引用本文： | 项雪艳,何倩. 关于一个典型函数Fourier级数的Gibbs现象[J]. 数学研究及应用, 2008, 28(2): 347-352. DOI: 10.3770/j.issn.1000-341X.2008.02.014 |
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| 作者姓名： | 项雪艳 何倩 |
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| 作者单位： | 丽水学院数学物理系, 浙江 丽水 323000; 浙江师范大学数理信息工程学院, 浙江 金华 321004;浙江师范大学数理信息工程学院, 浙江 金华 321004 |
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| 摘 要： | In this paper,we point out that the Fourier series of a classical function∑∞k=1 sin kx/k has the Gibbs phenomenon in the neighborhood of zero.Furthermore,we estimate the upper bound of its partial sum and get:supn≥1‖n∑k=1sin kx/k‖∫x0sin x/xdx=1.85194,which is better than that in[1].
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| 关 键 词： | Fourier series partial sum upper bound. 函数 Fourier Series 级数 Gibbs phenomenon 现象 Function better estimate upper bound partial sum neighborhood zero point Fourier series function paper |
| 收稿时间： | 2006-03-20 |
| 修稿时间： | 2006-03-20 |
On the Gibbs Phenomenon of Fourier Series of a Classical Function |
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| XIANG Xue Yan and HE Qian. On the Gibbs Phenomenon of Fourier Series of a Classical Function[J]. Journal of Mathematical Research with Applications, 2008, 28(2): 347-352. DOI: 10.3770/j.issn.1000-341X.2008.02.014 |
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| Authors: | XIANG Xue Yan and HE Qian |
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| Affiliation: | 1. Department of Mathematics and Physics,Lishui University,Zhejiang 323000,China;Department of Mathematics,Zhejiang Normal University,Zhejiang 321004,China
2. Department of Mathematics,Zhejiang Normal University,Zhejiang 321004,China |
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| Abstract: | In this paper, we point out that the Fourier series of a classical function $sum_{k=1}^{infty}{frac{sin kx}k}$ has the Gibbs phenomenon in the neighborhood of zero. Furthermore, we estimate the upper bound of its partial sum and get: $sup_{ngeq 1} {big|sum_{k=1}^n{frac{sin kx}k}big|=int_0^{pi}{frac {sin x}xd x}}doteq 1.85194,$ which is better than that in [1]. |
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| Keywords: | Fourier series partial sum upper bound. |
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