Power series expansion of a holomorphic function on a disc

Let \(\Omega\subseteq\CC\) be open, let \(f\) be holomorphic on \(\Omega\), and let \(z_0\in\Omega\) and \(R>0\) satisfy \(\overline{D_R(z_0)}\subseteq\Omega\). Then for every \(z\in D_R(z_0)\), \[ f(z)=\sum_{n=0}^{\infty}a_n(z-z_0)^n, \] where for every \(n\geq0\) and every \(r\in(0,R]\), \[ a_n=\frac{f^{(n)}(z_0)}{n!}=\frac{1}{2\pi r^n}\int_0^{2\pi}f(z_0+re^{i\theta})e^{-in\theta}\dtheta. \]