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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 Borwein integral ： ウィキペディア英語版 Borwein integral In mathematics, a Borwein integral is an integral involving products of sinc(''ax''), where the sinc function is given by for ''x'' not equal to 0, and These integrals are notorious for exhibiting apparent patterns that eventually break down. An example is as follows: :$$ \begin & \int_0^\infty \frac \, dx=\pi/2 \\() & \int_0^\infty \frac\frac \, dx = \pi/2 \\() & \int_0^\infty \frac\frac\frac \, dx = \pi/2 \end This pattern continues up to :$\backslash int\_0^\backslash infty\; \backslash frac\backslash frac\backslash cdots\backslash frac\; \backslash ,\; dx\; =\; \backslash pi/2$ However at the next step the obvious pattern fails: :$$ \begin \int_0^\infty \frac\frac\cdots\frac \, dx &= \frac\pi \\ &= \frac - \frac\pi \\ &\simeq \frac - 2.31\times 10^ \end In general similar integrals have value whenever the numbers are replaced by positive real numbers such that the sum of their reciprocals is less than 1. In the example above, but An example for a longer series, :$\backslash int\_0^\backslash infty\; 2\; \backslash cos(x)\; \backslash frac\backslash frac\backslash cdots\backslash frac\; \backslash ,\; dx\; =\; \backslash pi/2,$ but : is shown in together with an intuitive mathematical explanation of the reason why the original and the extended series break down. In this case, but ==References== 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「Borwein 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.