关于解析函数中的一个问题

A Problem Concerning the Analytic Function

给出已知调和函数,不用计算出其共轭调和函数,直接写出对应的解析函数的简便方法。

Given a harmonic function u(x,y),the common way for finding out the analytic function with u(x,y)as its real part is to use curve integration and indefinite integration for obtaining the conjugate harmonic function of v(x,y)so as to analyze f(z)=u(x,y)+iv(x,y).The present paper introduces a simplified method for directly getting the analytic function in correspondence with a given harmonic function without calculating its conjuate harmonic function.