Really need help for this one. Cheers! 1. The problem statement, all variables and given/known data Question: calculate function z/(1-cos z) integrated in ac ounterclockwise circular contour given by |z-2pi|= 1 2. Relevant equations 3. The attempt at a solution Clearly the pole in the given contour is 2pi. But the problem is: if it's a simple pole, then apply formula we have Residue=lim (z-2pi) * z/(1-cos z) where z->2pi. This limit does not exist. So I reckon 2pi might be a higher order pole but this actually makes no sense and even if it's true, there is a really nasty differentiation. Any thoughts.?