复变函数不定式的几个结论

The limit problems of complex functions

在讨论复变函数的极限问题时,我们常遇到"不定式"的问题。但由于复变函数极限的本质是两个二元函数的极限,所以其极限问题是比较复杂的。因此在复变函数中处理极限问题就缺少有的工具,特别是不定式问题。本文对解析函数及解析函数在其孤立奇点所产生的"不定式"问题加以讨论,得出类似于一元函数的罗比塔法则的几个结论,但它较之更"完美"些,这无疑地对我们处理复变函数的极限提供了一条途径。

In dealing with the lirut of complex function,sometimes the problem of "indefinite" will be encountered.As the limits of complex functions are the limits of two binary functions in essence, this problem will become much eoplieate due to the wles and criterions of limits in monadie func- tions hold no more.Lacking of prowerful mears to handle those limit problems in complex func- tions,especially in the ease of indefinite,will be usually experienced. Inthe paper,the problem of "indefinite" arising in analytic functions and at the isolated sin- gular points in such functions is discussed and several sults similar to Del'Hospital Rule in monadie function are concluded with rather more "consummate" nature than the latter.This will provide a substanial approach to manipulate.