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復(fù)變函數(shù)的洛必達(dá)法則論文
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摘要：
本文通過(guò)對(duì)數(shù)學(xué)分析中洛必達(dá)法則相關(guān)定理的分析，將實(shí)數(shù)域中的洛必達(dá)法則推廣到復(fù)數(shù)域中，得到復(fù)變函數(shù)的洛必達(dá)法則．首先給出并證明復(fù)變函數(shù)中洛必達(dá)法則的相關(guān)定理及推論，從而使復(fù)變函數(shù)中不定式的極限問(wèn)題變得容易解決．接著從兩個(gè)主要方面討論復(fù)變函數(shù)中洛必達(dá)法則的應(yīng)用：孤立奇點(diǎn)的判定和求解析函數(shù)在孤立奇點(diǎn)處的留數(shù)．
關(guān)鍵詞：洛必達(dá)法則；不定式；解析函數(shù)；孤立奇點(diǎn)
The Law of LHospital in Complex Functions
ABSTRACT
The paper get the law of LHospital in complex functions through earnestly analysing correlative theorems of the law of LHospital in the mathematic analysis, as a result, the law of LHospital was extended to the complex number field. Firstly, the related theorems and the deduction of the law of LHospital in complex functions were given and proved in this article. It causes function limit to change easily to solve in complex functions. Then we elaborate two applications of the law of LHospital in complex functions, namely, the isolated points classification and residues calculation for the isolated singularity.
Key word: The law of LHospital; Function limit; Analytic function; Isolated singularity
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