Find The Zero-pole Points Of Meromorphic Function Using Argument Principle

In this dissertation,we apply the generalized argument principle to find the zero-pole points of meromorphic function.To be more accessible and consistent,we first introduce the basic properites of meromorphic function.Based on the theory of meromorphic function on the complex surface,we derive the generalized argument principle.Then we show that how to use the generalized argument principle to prove some fundamental theorems of meromorphic functions,which are important in what follows.We focus on the baisic theory of finding zero-pole points of meromorphic function using generalized argument principle.This part provides the fundamental basis for this dissertation.Then we give two different algorithms to handle the zero-pole problem of meromorphic functions,with simple error analysis.Finaly,we illustrate these algorithms by example,and the common considerations.