Cauchy's [[Integration|Integral]] Formula is one relating a [[Holomorphic Function]] defined on a [[Closed Disk]] $D$ in the [[Complex Plane]] to its evalauation at the boundary of said $D$. $\huge \begin{align} D &=\setbuild{z \in \C}{|z-z_{0}| \leq r} \\ a &\in \op{Interior}(D) \\ f(a) &= \frac{1}{2\pi i} \oint \frac{f(z)}{z-a}\d z \end{align} $