复变函数教学中的几个注释

Several Notes in the Teaching of Complex Functions

摘要: 本文旨在对复变函数中求解特殊级数的收敛半径、幂函数乘指数函数原函数以及极点阶数等问题做一些补充说明，推广实函数中的相应结论，为计算带来方便。文中整理幂函数乘指数函数原函数的求解结果，并总结出统一的公式；求解极点阶数，推广实变函数中的洛必达法则以给出判断方法，并给予严格证明。

Abstract: The purpose of this paper is to give some remarks to the problems of finding the convergence ra-dius of some special series, the anti-derivative of power function multiplying exponential function and the order of polar points in return to generalize some relating consequences in real functions and then bring convenience to calculations. In this paper, we give the general result of the an-ti-derivative of power function multiplying exponential function; we also expand the L’hospital’s rule to find the order of some special polar points and give the proof.