留數是複變函數中的一個重要概念,指解析函式沿著某一圓環域內包圍某一孤立奇點的任一正向簡單閉曲線的積分值除以2πi。留數數值上等於解析函式的洛朗展開式中負一次冪項的係數。根據孤立奇點的不同,採用不同的留數計算方法。留數常套用在某些特殊類型的實積分中,從而大大簡化積分的計算過程。
基本介紹
- 中文名:留數
- 外文名:Residue
- 所屬學科:複變函數
- 數值上等於:解析函式洛朗展開負一次冪項係數
- 留數計算:根據孤立奇點採用不同的計算方法
- 套用:簡化某些類型的實積分的計算過程
- 定理名稱:留數定理
洛朗展開
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定義
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留數定理
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留數的計算
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