MathLiveCauchy's integral theorem
For a function holomorphic on and inside a simple closed contour, the contour integral of the function around that contour is zero. It is a foundational result in complex analysis.
\oint_{C} f(z)\,\mathrm{d}z = 0What the symbols mean
| a holomorphic (complex-differentiable) function | |
| a simple closed contour in the complex plane | |
| complex variable of integration |
About this formula
- FieldMathematics
- TopicComplex analysis
- LevelUniversity
- Also calledCauchy's theorem, contour integral zero, holomorphic function contour integral, complex analysis closed contour integral
- SourceWikidata Q834025
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