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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 Half range Fourier series ： ウィキペディア英語版 Half range Fourier series A half range Fourier series is a Fourier series defined on an interval $()$ instead of the more common $()$, with the implication that the analyzed function $f(x),\; x\backslash in()$ should be extended to $()$ as either an even (f(-x)=f(x)) or odd function (f(-x)=-f(x)). This allows the expansion of the function in a series solely of sines (odd) or cosines (even). The choice between odd and even is typically motivated by boundary conditions associated with a differential equation satisfied by $f(x)$. Example Calculate the half range Fourier sine series for the function $f(x)=\backslash cos(x)$ where Since we are calculating a sine series, $a\_n=0\backslash \; \backslash quad\; \backslash forall\; n$ Now, $b\_n=\; \backslash frac\; \backslash int\_0^\backslash pi\; \backslash cos(x)\backslash sin(nx)\backslash ,\backslash mathrmx$ = \frac\quad \forall n\ge 2 When n is odd, $b\_n=0\backslash$ When n is even, $b\_n=$ thus $b\_=$ With the special case $b\_1=0$, hence the required Fourier sine series is $\backslash cos(x)\; =\; \backslash sum\_^\; \backslash sin(2nx)\}$ } 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「Half range Fourier series」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.