Cauchy-Riemann equations (redirected from Cauchy-Riemann conditions)

Cauchy-Riemann equations [kō·shē ′rē‚män i′kwā·zhənz]

(mathematics)

A pair of partial differential equations that is satisfied by the real and imaginary parts of a complex function ƒ(z) if and only if the function is analytic: ∂u/∂x= ∂v/∂yand ∂u/∂y= - ∂v/∂x,where ƒ(z) =u+ivandz=x+iy.