Let F = P/Q be a rational generating function in d real variables. The Taylor coefficients in the expansion F = sum_R a_R X^R represent quantities of interest -- here X = (x_1 , ... , x_d) and R = (r_1 , ... , r_d). Cauchy's formula gives a_R as an integral, so estimates of a_R come down to whether we can do the harmonic analysis. The integral can be made to look like a Fourier transform but it is only formal until we get rid of divergent integrals. To do so requires the apparatus of generalized functions as well as some clever topological tricks, stolen from great sources. When the smoke clears, one must still evaluate the generalized Fourier transform. By now we know what the picture is supposed to look like, and the answer emerges after a little computation.