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Cauchy's integral formula
Sign in to saveprovides integral formulas for all derivatives of a holomorphic function
In the Vinony graph
Vinony's link graph records 109 inbound references to Cauchy's integral formula, and connects out to Cauchy's integral theorem, holomorphic function and Cauchy–Riemann equations.
It sits within the topics Augustin-Louis Cauchy and Theorems in complex analysis.
Vinony links it to 41 Wikipedia language editions.
Wikidata facts
- Instance of
- theorem
- Named after
- Augustin-Louis Cauchy
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- on focus list of Wikimedia project
- Wikipedia:Vital articles/Level/4
- different from
- Cauchy's integral theorem
- maintained by WikiProject
- 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.