# 調和共軛

${\displaystyle \Omega }$區間內，${\displaystyle v}$${\displaystyle u}$共軛函數的充份必要條件是${\displaystyle u}$${\displaystyle v}$滿足柯西－黎曼方程

${\displaystyle {\partial u \over \partial x}={\partial v \over \partial y}}$
${\displaystyle {\partial u \over \partial y}=-{\partial v \over \partial x}.}$

## 參考資料

• Brown, James Ward; Churchill, Ruel V. Complex variables and applications 6th. New York: McGraw-Hill. 1996: 61. ISBN 0-07-912147-0. If two given functions u and v are harmonic in a domain D and their first-order partial derivatives satisfy the Cauchy-Riemann equations (2) throughout D, v is said to be a harmonic conjugate of u.