15. Theorem 2.1.4 - power series expansion

Let $U \subseteq C$ be open, and $f : U \to C$ holomorphic. Using 14. Theorem 2.1.3 - Integral Formula of Cauchy, fix $z_{0} \in U$ . Then $\forall r > 0$ such that $\overset{―}{B_{r} (z_{0})} \subseteq U$ , the function $f$ can be written uniquely as
:?:
A convergent power series (on $\overset{―}{B_{r} (z_{0})}$ ). That is:

\sum_{n = 0}^{\infty} c_{n} (z - z_{0})^{n} w h e r e c_{n} = \frac{1}{2 π i} \oint_{| z - z_{0} | = r} \frac{f (z)}{(z - z_{0})^{n + 1}} d z