復合函數的孤立奇點(diǎn)與留數計算

復合函數的孤立奇點(diǎn)與留數計算

摘要

復合函數的孤立奇點(diǎn)與留數計算是留數理論應用中的重要內容，對于1些復雜的復合函數，如果直接討論其孤立奇點(diǎn)的類(lèi)型與留數計算往往極為困難，為了解決這1問(wèn)題，本文將復合函數分解為兩個(gè)簡(jiǎn)單函數來(lái)研究，首先建立了復合函數的孤立奇點(diǎn)類(lèi)型與其內外函數的孤立奇點(diǎn)類(lèi)型的關(guān)系，在1定意義下，所得結果具有普遍性。然后，根據某些孤立奇點(diǎn)的特性，并利用留數的定義，建立了若干個(gè)用內外函數的留數或某些Laurent系數來(lái)表示復合函數的留數的公式，并舉例介紹了其應用，從列舉的例子中可以看到所得公式在簡(jiǎn)化復合函數留數計算中的作用。

關(guān)鍵詞：復合函數，孤立奇點(diǎn)，可去奇點(diǎn)，極點(diǎn)，本性奇點(diǎn)，留數。

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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