利用调和函数构造解析函数的两种变量替换法

Two variable substitution methods for conforming analytic function by harmonic function

目的寻求利用调和函数构造解析函数的简便方法。方法根据Cauchy-Riemann方程的等价条件和解析函数唯一性定理分别推导。结果与结论得到利用调和函数构造解析函数的两种简便实用的变量替换法,同时还得到判别函数解析以及将复变函数的二元实函数形式转化为一元复函数形式的简便方法。

Objective—To search for simple methods for conforming analytic function by harmonic function.Methods—The aforesaid methods respectively derives by using equivalent condition of Cauchy-Riemann equation and uniqueness theorem of analytic function.Results and Conclusion—Herein are obtained two variable substitution methods which are more simple and convenient for conforming analytic function by harmonic function.Also are obtained simple methods for distinguishing analyticity of functions and converting analytic functions from binary real function form to complex function form.