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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Trigonometric integral ： ウィキペディア英語版 Trigonometric integral In mathematics, the trigonometric integrals are a family of integrals involving trigonometric functions. A number of the basic trigonometric integrals are discussed at the list of integrals of trigonometric functions. ==Sine integral== The different sine integral definitions are ::$\backslash operatorname(x)\; =\; \backslash int\_0^x\backslash frac\backslash ,dt$ ::$\backslash operatorname(x)\; =\; -\backslash int\_x^\backslash infty\backslash frac\backslash ,dt.$ By definition, is the antiderivative of which is zero for ; and is the antiderivative of which is zero for . Their difference is given by the Dirichlet integral, :$\backslash operatorname(x)\; -\; \backslash operatorname(x)\; =\; \backslash int\_0^\backslash infty\backslash frac\backslash ,dt\; =\; \backslash frac\; ~.$ Note that is the , and also the zeroth spherical Bessel function. In signal processing, the oscillations of the sine integral cause overshoot and ringing artifacts when using the sinc filter, and frequency domain ringing if using a truncated sinc filter as a low-pass filter. Related is the Gibbs phenomenon: if the sine integral is considered as the convolution of the sinc function with the heaviside step function, this corresponds to truncating the Fourier series, which is the cause of the Gibbs phenomenon. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Trigonometric integral」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.