Solution
= Solution
For $|z_0|<1$ and $k\geq0$, the <Cauchy integral formula> for derivatives is
$$
\boxed{f^{(k)}(z_0)=\frac{k!}{2\pi i}\int_\gamma\frac{f(z)}{(z-z_0)^{k+1}}\,dz.}
$$
The formula applies because the closed unit disc lies inside the domain of holomorphy. For $k=0$ this is the ordinary value formula, with $0!=1$.