MathLiveCauchy's integral formula
It expresses the value of a holomorphic function at an interior point as a contour integral of the function divided by (z - z_0) around a simple closed curve enclosing that point. It also yields integral formulas for all derivatives of the function.
f(z_0) = \frac{1}{2 \pi \mathrm{i}} \oint_{C} \frac{f(z)}{z - z_0} \, \mathrm{d}zWhat the symbols mean
| a holomorphic function of the complex variable z | |
| a point inside the contour C | |
| the complex variable of integration | |
| a simple closed contour, positively oriented, enclosing z_0 | |
| the imaginary unit | |
| the constant pi |
About this formula
- FieldMathematics
- TopicComplex analysis
- LevelUniversity
- Also calledholomorphic function contour integral, value of holomorphic function from contour integral, derivatives of holomorphic function integral formula, Cauchy formula complex analysis
- SourceWikidata Q913764
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