Cauchy's integral theorem
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important statement about line integrals for holomorphic functions in the complex plane. Essentially, it says that if two different paths connect the same two points, and a function is holomorphic everywhere in between the two paths, then the two path integrals of the function will be the same.
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1825 in scienceAbel–Plana formulaAntiderivative (complex analysis)Augustin-Louis CauchyCauchy's Integral TheoremCauchy's integral formulaCauchy-GoursatCauchy-Goursat theoremCauchy GoursatCauchy Integral TheoremCauchy integralCauchy integral theoremCauchy theoremCauchy–Goursat theoremCauchy–Riemann equationsComplex analysisContour integrationDavid HestenesField-theoretic simulationFokas methodFourier transformFunction of several complex variablesFundamental theorem of algebraGiacinto MoreraGiovanni Battista RizzaHenry W. GouldHolomorphic functionInfinite-dimensional holomorphyLine integralLippmann–Schwinger equationList of French inventions and discoveriesList of complex analysis topicsList of mathematical proofsList of theoremsList of things named after Augustin-Louis CauchyMorera's theoremNeumann–Poincaré operatorNormal familyPolymer field theoryPrime number theorem
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Cauchy's integral theorem
In mathematics, the Cauchy integral theorem (also known as the Cauchy–Goursat theorem) in complex analysis, named after Augustin-Louis Cauchy (and Édouard Goursat), is an important statement about line integrals for holomorphic functions in the complex plane. Essentially, it says that if two different paths connect the same two points, and a function is holomorphic everywhere in between the two paths, then the two path integrals of the function will be the same.
has abstract
Cauchyova–Goursatova věta (tak ...... křivek C1, ..., Cn. Pak platí
@cs
Cauchys integralsats i komplex ...... ed samma start- och slutpunkt:
@sv
Der cauchysche Integralsatz (n ...... Aussage aus der Topologie aus.
@de
El teorema de la integral de C ...... integral de variable complexa.
@ca
En analyse complexe, le théorè ...... ivant ces chemins sont égales.
@fr
En matemáticas, el teorema int ...... integral de variable compleja.
@es
Il teorema integrale di Cauchy è un teorema di analisi complessa.
@it
In mathematics, the Cauchy int ...... the function will be the same.
@en
Na análise complexa, o teorema ...... nte conexos no plano complexo.
@pt
Twierdzenie podstawowe Cauchy’ ...... matem Goursata w teorii grup).
@pl
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p/c020900
@en
title
Cauchy Integral Theorem
@en
Cauchy integral theorem
@en
urlname
CauchyIntegralTheorem
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comment
Cauchyova–Goursatova věta (tak ...... upravit pomocí Greenovy věty:
@cs
Cauchys integralsats i komplex ...... ed samma start- och slutpunkt:
@sv
Der cauchysche Integralsatz (n ...... nd des Residuensatzes benutzt.
@de
El teorema de la integral de C ...... integral de variable complexa.
@ca
En analyse complexe, le théorè ...... ivant ces chemins sont égales.
@fr
En matemáticas, el teorema int ...... integral de variable compleja.
@es
Il teorema integrale di Cauchy è un teorema di analisi complessa.
@it
In mathematics, the Cauchy int ...... the function will be the same.
@en
Na análise complexa, o teorema ...... nte conexos no plano complexo.
@pt
Twierdzenie podstawowe Cauchy’ ...... matem Goursata w teorii grup).
@pl
label
Cauchy's integral theorem
@en
Cauchyova–Goursatova věta
@cs
Cauchys integralsats
@sv
Cauchyscher Integralsatz
@de
Koŝia integrala teoremo
@eo
Teorema de integral de Cauchy
@pt
Teorema de la integral de Cauchy
@ca
Teorema integral de Cauchy
@es
Teorema integrale di Cauchy
@it
Théorème intégral de Cauchy
@fr