Cauchy's integral formula

Last updated Jan 9, 2023

Cauchys integral formula

Let $f$ be holomorphic and $\gamma$ a closed curve in the complex plane $$\int_\gamma \frac{f(z)}{z-z_0} dz = 2\pi if(z_0)$$ and $$\int_\gamma \frac{f(z)}{(z-z_0)^n} dz = \frac{2\pi i}{(n-1)!}f^{(n-1)}(z_0)$$