Can anyone offer advice on how one might use the residue of gamma to show the integral gamma (z) dz=-4piei/3 where C=(z:z[Z+2-i]=2).......or am I on the right track at all?
It says here that the residue of the gamma function at the simple pole z=–n is If C is meant to be the circle of radius 2 centred at –2+i then the poles inside the circle are at –1, –2 and –3, and times the sum of the residues given by that formula is indeed .