Values inside a disc are boundary averages against the Cauchy kernel.Suggest a slogan
Let \(D\subseteq\CC\) be an open disc, let \(U\) be an open set containing its closure \(\overline D\), and let \(f\) be holomorphic on \(U\). Then for every \(z\in D\), \[ f(z) = {1 \over 2\pi i} \int_{\bd D} {f(\xi) \over \xi - z} \,d\xi, \] where the circle \(\bd D\) is oriented counterclockwise.
State the Cauchy integral formula for $f(z)$.