Past exam of the metric spaces and complex analysis course of the University of Oxford / 2015 / 3 / a / Solution

One standard form of the Cauchy integral formula is this: if $f$ is holomorphic on an open set containing a contour that is a simple closed curve $\Gamma$ and its interior, and $\Gamma$ has positive orientation of a contour, then for every point $w$ inside it,The hypothesis includes the contour itself; singularities on the contour are excluded. In particular, the formula applies on a circle whose closed disk is contained in the domain of holomorphy.