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Cauchy's integral formula
| Mathematical analysis → Complex analysis |
| Complex analysis |
|---|
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| Complex numbers |
| Complex functions |
| Basic theory |
| Geometric function theory |
| People |
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.
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صيغة كوشي التكاملية Arabic Fórmula integral de Cauchy AST Кошиҙың интеграль формулаһы BA Fórmula de la integral de Cauchy Catalan فورمووڵی تەواوکاریی کۆشی CKB Cauchyův vzorec Czech Cauchysche Integralformel German Ολοκληρωτικός τύπος του Κωσύ Greek Koŝia integrala formulo EO Fórmula integral de Cauchy Spanish
