I'm looking to evaluate the infinite sum of 1/(n-f)^2 where n is the index of summation from 1 to infinity and f is a constant between zero and one.
I really have no clue where to start on this. I've seen the summation evaluated to pi^2/6 if f=0 by using a Fourier transform of x^2, but I can't see how to adapt this for an arbitrary constant.
Any ideas or hints would be appreciated.
That was my initial thought, but it doesn't really help. In the Fourier transform method when f=0, we end up finding that x^2 = pi^2/3 + 4 sum (-1)^n/n^2 cos nx. This becomes our sum when we let x=pi. If I try (x-f)^2 instead, I end up with some sin terms and a different constant offset, but the denominator is still n^2. (I get (x-f)^2 = pi^2/3 + f + 4 sum [(-1)^n/n^2 cos nx + f pi/n sin nx as the fourier series.)