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Cauchy's integral formula
Sign in to saveprovides integral formulas for all derivatives of a holomorphic function
Wikidata facts
- Instance of
- theorem
- Named after
- Augustin-Louis Cauchy
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- Wikipedia:Vital articles/Level/4
- different from
- Cauchy's integral theorem
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- WikiProject Mathematics
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Encyclopedic overview
In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk, and it provides integral formulas for all derivatives of a holomorphic function. Cauchy's formula shows that, in complex analysis, "differentiation is equivalent to integration": complex differentiation, like integration, behaves well under uniform limits – a result that does not hold in real analysis.
Theorem
Excerpted from Wikipedia’s “Cauchy's integral formula” article, available under the CC BY-SA 4.0 licence.