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

Google:코시+구르사+정리

"코시 구르사 정리"

Ndict:"코시 구르사 정리"

Google:"코시 구르사 정리"

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

함수 $f$ 가 단순 닫힌 경로 $C$ 와 그 안쪽의 모든 점에서 해석적이면 다음이 성립한다. [1]

$\int_C f(z)dz=0$

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)

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