MathLiveCauchy–Riemann equations
These two partial differential equations give the condition a complex function f = u + iv must satisfy to be holomorphic (complex differentiable). They are used to test holomorphy and in complex analysis generally.
\begin{aligned}\frac{\partial u}{\partial x}&=\frac{\partial v}{\partial y}\\\frac{\partial u}{\partial y}&=-\frac{\partial v}{\partial x}\end{aligned}What the symbols mean
| real part of the complex variable z = x + iy | |
| imaginary part of the complex variable z = x + iy | |
| real part of the function f = u + iv | |
| imaginary part of the function f = u + iv |
About this formula
- FieldMathematics
- TopicComplex analysis
- LevelUniversity
- Also calledCauchy-Riemann conditions, d'Alembert–Euler conditions, Cauchy–Riemann conditions
- SourceWikidata Q622741
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