Original Post
I saw this post at these forums and it''s been bugging me, it''s not a question for me but I can''t seem to get the answer!
Prove the Residue Theorem
Residue Theorem:
Given a closed contour Gamma contained in an open set A in the Complex plane that is homotopic to a point, a function that is analytic on A except for finitely many points z1,z2,...,zn and that z1,...,zn are isolated singularities, the integral along Gamma is 2PIi times the sum of the residues of f at z1,....zn, times the index of Gamma around z1,...,zn.
I''ll be easy on you and let you Prove the easiest part; when Gamma is a simple contour.