18. Corollary 2.1.4 - Cauchy Estimate for C

Let $f : U \to C$ be holomorphic, with $U \subseteq C$ open. Let $z_{0} \in U$ , and pick $r > 0$ such that $\overset{―}{B_{r} (z_{0})} \subseteq U$ . Suppose that $| f (z) | \leq M$ for $| z - z_{0} | = r$ . Then by 15. Theorem 2.1.4 - power series expansion, we have:

\sum_{n = 0}^{\infty} c_{n} (z - z_{0})^{n}

with where we estimate $c_{n}$ by:
:?:

| c_{n} | \leq \frac{M}{r^{n}}