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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 Residue at infinity ： ウィキペディア英語版 Residue at infinity In complex analysis, a branch of mathematics, the residue at infinity is a residue of a holomorphic function on an annulus having an infinite external radius. The ''infinity'' $\backslash infty$ is a point added to the local space $\backslash mathbb\; C$ in order to render it compact (in this case it is a one-point compactification). This space noted $\backslash hat$ is isomorphic to the Riemann sphere.〔Michèle AUDIN, ''Analyse Complexe'', cursus notes of the university of Strasbourg (available on the web ), pp. 70–72〕 One can use the residue at infinity to calculate some integrals. ==Definition== Given a holomorphic function ''f'' on an annulus $A(0,\; R,\; \backslash infty)$ (centered at 0, with inner radius $R$ and infinite outer radius), the residue at infinity of the function ''f'' can be defined in terms of the usual residue as follows: :$\backslash mathrm(f,\backslash infty)\; =\; \backslash mathrm\backslash left(\; f\backslash left(\backslash right),\; 0\; \backslash right)$ Thus, one can transfer the study of $f(z)$ at infinity to the study of $f(1/z)$ at the origin. Note that $\backslash forall\; r\; >\; R$, we have :$\backslash mathrm(f,\; \backslash infty)\; =\; \backslash int\_\; f(z)\; \backslash ,\; dz$ 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「Residue at infinity」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.