# Cauchy-Riemann equation

> English word · Noun

## Definitions
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 (∂u)/(∂x)=(∂v)/(∂y) or (∂u)/(∂y)=-(∂v)/(∂x), which together form part of the criteria that f be complex-differentiable.
2. The equivalent single equation (∂f)/(∂x)+i(∂f)/(∂y)=0.

## Etymology
Named after mathematicians Augustin Cauchy (1789-1857) and Bernhard Riemann (1826-1866).

## Source
Compiled from Wiktionary via kaikki.org (CC BY-SA). Data vintage: 2026-05-06.
Canonical page: https://plainspell.com/en/word/cauchy-riemann-equation