This powerful statement may be easily derived from the connectedness of the domain in question,  Green's theorem, and its namesake's integral theorem, assuming that the function in question obeys the set  of equations named for Riemann and its namesake. Under certain hypotheses, this lemma can be turned on  its head to find the leading term of the 
This powerful statement may be easily derived from the connectedness of the domain in question,  Green's theorem, and its namesake's integral theorem, assuming that the function in question obeys the set  of equations named for Riemann and its namesake. Under certain hypotheses, this lemma can be turned on  its head to find the leading term of the Laurent expansion of a function singular at 8 [infinity] by enclosing all finite point singularities and reversing the conventional direction of integration. For ten points name the theorem that states that the positive closed contour integral of an analytic function with a finite number of isolated singularities is equal to 2pi "two pie eye" times the sum of the residues of that function at those 2  singularities enclosed by the contour.
This powerful statement may be easily derived from the connectedness of the domain in question,  Green's theorem, and its namesake's integral theorem, assuming that the function in question obeys the set  of equations named for Riemann and its namesake.
Cauchy’s residue theorem