@modus_ponens
Yes, this is Cauchy’s integral formula, the contour is closed since it is the boundary of Omega. The only assumptions needed are that Omega must be a simply connected open subset (or an open star domain) of C, f is holomorphic over Omega and z is in the interior of Omega.
Hjalp! Fell asleep during the lecture! What integral is that? Its appearance is screaming to have “Cauchy” written all over it. Ah hmm, is it Cauchy’s integral formula? But wait, is the contour closed here? Also, do we assume the function to be holomorphic? Aaa daamn… going to struggle bad with home exercises this time.
Yes, this is Cauchy’s integral formula, the contour is closed since it is the boundary of Omega. The only assumptions needed are that Omega must be a simply connected open subset (or an open star domain) of C, f is holomorphic over Omega and z is in the interior of Omega.