复变函数的洛必达法则

复变函数的洛必达法则

摘要

本文通过对数学分析中洛必达法则相关定理的分析，将实数域中的洛必达法则推广到复数域中，得到复变函数的洛必达法则．首先给出并证明❧复变函数中洛必达法则的相关定理及推论，从而使复变函数中不定式的极限问题变得容易解决．接着从两个主要方面讨论复变函数中洛必达法则的应用：孤立奇点的判定和求解析函数在孤立奇点处的留数．

关键词：洛必达法则；不定式；解析函数；孤立奇点

Thツe 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 applica♀tions of the law of LHospital in complღex functions, namely, the isolated points classi❥fication and residues calculation for the isolated singularity.

Key word: The law of LHospital; Function limit; Analytic function; Isolated singularity