코시-구르사_정리,Cauchy-Goursat_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
$\oint_C f(z)dz=0.$

(Zill AEM 18.2)