View source for Cauchy-Riemann equation

==English==
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===Etymology===
Named after mathematicians {{w|Augustin Cauchy}} (1789-1857) and {{w|Bernhard Riemann}} (1826-1866).

===Noun===
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# {{lb|en|mathematics|complex analysis|always plural}} 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 <math>\textstyle \frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}</math> or <math>\textstyle \frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x}</math>, which together form part of the criteria that ''f'' be [[complex-differentiable]].
# {{lb|en|complex analysis}} The equivalent single equation <math>\textstyle \frac{\partial f}{\partial x} + i\frac{\partial f}{\partial y} = 0</math>.

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