14. Theorem 2.1.3 - Integral Formula of Cauchy

Let $U \subseteq C$ be open, and $f : U \to C$ be holomorphic. Fix $z_{0} \in U$ , and choose $r > 0$ such that $\overset{―}{B_{r} (z_{0})} \subseteq U$ . Then for any $a \in B_{r} (z_{0})$ , we have:
:?:

f (a) = \frac{1}{2 π i} \oint_{| z - z_{0} | = r} \frac{f (z)}{z - a} d z

In particular,

f (z_{0}) = \frac{1}{2 π} \int_{0}^{2 π} f (z_{0} + r e^{i t}) d t