多值函数的单值解析分支

初等多值函数单值分支问题，历来是复变函数论中的一个难点，现有的文献大都较少谈及这一问题，而谈及的，也多半是利用个别例子的方式进行说明；即使涉及到幅角函数这一工具的，却也和对幅角函数理论本身并没有深刻阐述，也不去说明用这一工具的依据，从而使读者看完这些个别例子之后，还是难以从理论上的实践上掌握这类问题的一般规律。正是从理论上和实践上解决了这一问题。本文先是证明了幅角函数的几个重要定理，然后利用幅角函

The Single Value Analytical Branch of Multivalue Function

The problem of continuous branch of mul ti value function has been a difficult point of the theory of complex function.Few people have discussed it in the existing documents.Even if some have paid at tention to it,most of them only discussed with some special examples.Ones refere d to the means of amplitude function,but they could not go further in to the very principles and not showed why we should use ampli tude function.To solve the problem,we first prove a few important theorems on am pli tude function to prove the theorem about the branch of Logarithm function a nd r adical function.Then,we proceed to sum up the general method to fin d the continuous branch of multivalue function.And this method is easy to rememb er and apply.