Cauchy-Riemann equations (polar coordinates)

Suppose A is an open set in and f(z)=f(reiθ)=u(r,θ)+iv(r,θ):A is a function. If the derivative of f(z) exists at z0=(r0,θ0). Then the functions u, v at z0 satisfy:

ur = 1rvθ
vr = -1ruθ

which are called Cauchy-Riemann equationsMathworldPlanetmath in polar form.

Title Cauchy-Riemann equations (polar coordinatesMathworldPlanetmath)
Canonical name CauchyRiemannEquationspolarCoordinates
Date of creation 2013-03-22 14:03:58
Last modified on 2013-03-22 14:03:58
Owner Daume (40)
Last modified by Daume (40)
Numerical id 8
Author Daume (40)
Entry type Definition
Classification msc 30E99
Related topic TangentialCauchyRiemannComplexOfCinftySmoothForms
Related topic ACRcomplex