17. Corollary 2.1.3 - Theorem of Goursat

Suppose $f : U \to C$ is holomorphic with $U \subseteq C$ open. Then by 15. Theorem 2.1.4 - power series expansion, we have that $f$ is
:?:
$C^{\infty} (U)$ where the coefficients of the taylor series are as follows:

\frac{f^{(n)} (z)}{n!} = \frac{1}{2 π i} \oint \frac{f (ζ)}{(ζ - z)^{n + 1}} d ζ