In two variable Calculus, you learnt the following result: let and be two functions defined on the same simply connected domain . Suppose that and are continuous on the interior of and that, for every Jordan curve in , the following equation holds:

Then in .

Using this result we can prove the following converse to Cauchy-Goursat theorem:

Another converse of Cauchy-Goursat theorem, stronger than Proposition 6.1 is Morera's theorem:

Noah Dana-Picard 2007-12-24