Cauchy-Riemann equation

English

Etymology

Named after mathematicians Template:W (1789-1857) and Template:W (1826-1866).

Noun

1. Template:Lb Given a complex-valued function f and real-valued functions u and v such that f(z) = u(z) + iv(z), either of the equations $\frac{\partial u}{\partial x}=\frac{\partial v}{\partial y}$ or $\frac{\partial u}{\partial y}=-\frac{\partial v}{\partial x}$, which together form part of the criteria that f be complex-differentiable.
2. Template:Lb The equivalent single equation $\frac{\partial f}{\partial x}+i\frac{\partial f}{\partial y}=0$.