用三角有理傅里叶级数的部分和逼近函数| sinx |s

N. Y. Kazlouskaya, Y. A. Rovba
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引用次数: 1

摘要

本文考虑用有理三角傅立叶级数的部分和逼近函数| sinx |s。得到了上述近似的积分表示、一致估计和点估计。在此基础上,研究了几种特殊的极点选择情况。在用多项式三角傅立叶级数的部分和逼近的情况下,发现了一个渐近等式。对几何上不同的固定数量的极点进行了详细的研究。
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Approximation of the function |sin x| s by the partial sums of the trigonmometric rational fourier series
In the present article, the approximation of the function |sin x| s by the partial sums of the rational trigonometric Fourier series is considered. An integral representation, uniform and point estimates for the above-mentioned approximation were obtained. Based on them, several special cases of the selection of poles were studied. In the case of the approximation by the partial sums of the polynomial trigonometric Fourier series, an asymptotic equality was found. A detailed study is made of a fixed number of geometrically different poles.
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