thanks , but there is something wrong , 'cause should be independent of n . the equality is required to be true for any positive integer ... so - obviously - should be independent of n .
here is what i did :
assume is smooth and analytic at , then it can be expanded in terms of a power series . now setting the correct relations on both RH and LH parts , and integrating over T , we end up with something like this :
now the program is to solve for in general .. so , is this doable ?