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復(fù)合函數(shù)的孤立奇點與留數(shù)計算
復(fù)合函數(shù)的孤立奇點與留數(shù)計算
摘要
復(fù)合函數(shù)的孤立奇點與留數(shù)計算是留數(shù)理論應(yīng)用中的重要內(nèi)容，對于1些復(fù)雜的復(fù)合函數(shù)，如果直接討論其孤立奇點的類型與留數(shù)計算往往極為困難，為了解決這1問題，本文將復(fù)合函數(shù)分解為兩個簡單函數(shù)來研究，首先建立了復(fù)合函數(shù)的孤立奇點類型與其內(nèi)外函數(shù)的孤立奇點類型的關(guān)系，在1定意義下，所得結(jié)果具有普遍性。然后，根據(jù)某些孤立奇點的特性，并利用留數(shù)的定義，建立了若干個用內(nèi)外函數(shù)的留數(shù)或某些Laurent系數(shù)來表示復(fù)合函數(shù)的留數(shù)的公式，并舉例介紹了其應(yīng)用，從列舉的例子中可以看到所得公式在簡化復(fù)合函數(shù)留數(shù)計算中的作用。
關(guān)鍵詞：復(fù)合函數(shù)，孤立奇點，可去奇點，極點，本性奇點，留數(shù)。
Abstract
Compound functions isolated singularity and residue computation is the substantial content of residue theorys application, to several complicated compound function, if we discuss it directly, it is difficulty. To solve this problem, this passage will put compound function into two parts. Firstly, constitute compound functions isolated singularity and relation of interior function and external function. In a degree, the result is ripeness. Where after. We can use certain isolated singularitys property and define of fluxion, constitute several interior function and external functions fluxion or several Laurent quotient to show compound functions flexion’s expressions. Take some example to solve compound function.
Key words: Compound function, isolated singularity, removable singularity, vertex, essential singularity, residue.
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