So we have a function $f$ which has an isolated singularity at $z_0$.
We define $$\text{Res}(f, z_0) = \frac{1}{2\pi i} \int_{B_{\varepsilon}(z_0)} f(\eta) d\eta $$
for $\varepsilon > 0$ sufficiently small.
Now I want to show this is equal to $$\text{Res}(f, z_0) = \lim_{z\rightarrow z_0} \frac{1}{(n-1)!)} \frac{d^n}{dz^n}((z-z_0)^n f(z_0)) $$
Bit unsure of how to do this.
I know that the residue is the coefficient of $a_{-1}$ of the Laurent series.
And I can write $g(z) = (z-z_0)^n f(z)$ which is holomorphic at $z_0$. But I'm struggling to make the connection to the final result...