广义Cauchy-Riemann条件和n元调和函数

Generalized Cauchy-Riemann equations and the n-variate harmonic function

由于解析函数实部和虚部为调和函数,只适用于二元函数,不具有广泛性,因此,应用Jacobi行列式定义n元函数的广义Cauchy-Riemann条件,将二元函数的广义Cauchy-Riemann条件推广到n元函数,由此给出一类n元调和函数,并在三维几何空间中导出这类函数,其具有三维变换保正交性的优越特性.

Analytic functions are the important research area in complex variable functions.It is not extensive because the real and imaginary parts of the analytic functions are harmonic functions with only two variables.Therefore,this paper proposes the Generalized Cauchy-Riemann equations with n variables by the Jacobian determinant.The Generalized Cauchy-Riemann equations with two variables are extended to n variables as well as the harmonic function.This kind of function has the superiority of conformal orthogonality in three dimensional geometric space.