Cauchy-Riemann equation

Etymology
Named after mathematicians (1789-1857) and  (1826-1866).

Noun

 * 1)  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 $$\textstyle \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}$$ or $$\textstyle \frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x}$$, which together form part of the criteria that f be complex-differentiable.
 * 2)  The equivalent single equation $$\textstyle \frac{\partial f}{\partial x} + i\frac{\partial f}{\partial y} = 0$$.