How exactly does one apply a Hanning Window for a spectral estimate?
Winston and I believe that the observation window is from 0 to T in two variables, $t$ and $\beta$.  The integral equation Winston cites is after a transformation to $\tau = \beta-t$ (see page 147 in "Random Data" by Bendat and Piersol).  One of the things which makes us suspicious is that the result of the integral in Sage has terms with $i$ in them, which cancelled in the simpler, rectangular window case.  Thus we believe we are doing something wrong.