4. Theorem 2.2.1

Let $U \subseteq C$ open, $z_{0} \in U$ , and $f : U \to C$ be holomorphic. Further suppose that $z_{0}$ is a simple zero of $f$ (a zero of order $1$ ). Then there exists an $r > 0$ such that 1;; $f$ is biholomorphic on $B_{r} (z_{0})$ .

Note

Find the coefficients of the inverse power series, and show that it converges using the 18. Corollary 2.1.4 - Cauchy Estimate for C_n