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：sup ...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：sup n≥1｜｜∑^n k=1sin kx/k｜｜=∫^x 0sin x/x dx=1.85194, which is better than that in[1].展开更多
基金Foundation item： the Natural Science Foundation of Zhejiang Province （No. 102058）.
文摘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：sup n≥1｜｜∑^n k=1sin kx/k｜｜=∫^x 0sin x/x dx=1.85194, which is better than that in[1].
