#noindex
함수 $f$ 가 단순 닫힌 경로 $C$ 와 그 안쪽의 모든 점에서 해석적이면 다음이 성립한다. [* https://dreamlab1.tistory.com/m/182]
 $\int_C f(z)dz=0$
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Cauchy-Goursat Theorem

●  If $f$ is analytic in a simply connected domain $D,$
for every simple closed contour $C$ in $D$
 $\oint_C f(z)dz=0$
or
●  If $f$ is analytic at all points within and on a simple closed contour $C,$ then
 $\oint_C f(z)dz=0$

(Beelee)
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'''Cauchy's Theorem''' (1825)
Suppose that a function $f$ is analytic in a simply connected domain $D$ and that $f'$ is continuous in $D.$ Then for every simple closed contour $C$ in $D:$
 $\oint_C f(z)dz=0$

'''Cauchy-Goursat Theorem''' (1883)
$f'$ 의 연속성을 가정하지 않고도 코시 정리가 성립함을 증명.
Suppose a function $f$ is analytic in a simply connected domain $D.$ Then for every simple closed contour $C$ in $D:$
 $\oint_C f(z)dz=0$
If $f$ is analytic at all points within and on a simple closed contour $C,$ then
 $\oint_C f(z)dz=0.$

(Zill AEM 18.2)
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= Related =
[[경로적분,contour_integral]]
[[복소해석,complex_analysis]]학의 중요한 정리임.

= Twins =
복소해석에서의 코시 정리 증명 Proof of Cauchy's Theorem
https://freshrimpsushi.github.io/posts/proof-of-cauchys-theorem/

http://blog.naver.com/freshmeat/91343548

"코시 구르사 정리"
Ndict:"코시 구르사 정리"
Google:"코시 구르사 정리"

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Up: [[복소해석,complex_analysis]] [[정리,theorem]]