解析函数f(z)=u(r,θ)+iv(r,θ)中u(r,θ),v(r,θ)高阶偏导的一般式及推论  

General Expression and Corollary on Higher-Order Partial Derivatives of u(r,θ),v(r,θ)in Analytic Function f(z)=u(r,θ)+iv(r,θ)

作　　者：胡平[1] 

机构地区：[1]青海师范大学数学与信息科学系,青海西宁810008

出　　处：《青海师范大学学报（自然科学版）》2010年第2期6-9,共4页Journal of Qinghai Normal University(Natural Science Edition)

摘　　要：本文在复函数解析时,将自变量表成指数形式,推导了解析函数实虚部的高阶偏导数的递推公式,并发现实虚部的偏导公式有着完全相同的形式,另外在推论中给出了解析函数在此种形式下的一个充要条件.With expressing the complex variables in exponential form,this paper analyzes bivariate complex functions and gives a recurrence formula on higher-order partial derivatives of real part and imaginary part of bivariate analytic function. The paper also obtains that the partial derivative formula of the real part has same expression as of the imaginary part. Furthermore,a sufficient and necessary condition that is possessed by analytic function in such form is presented in the corollary.

关 键 词：解析函数 二元函数 偏导数 调和函数 共轭调和函数 

分 类 号：O174.5[理学—数学]