Semiclassical methods and the summation of the scattering partial wave series.

The Hilb formula, an asymptotic continuous approximation in l for the Legendre polynomials that is valid from forward angles to nearly 180/sup 0/, is tested numerically in semiclassical summations of scattering amplitudes. It works remarkably well even when the amplitude oscillates and falls by many orders of magnitude so long as the S matrix varies slowly with l. We generalize the Hilb formula to the associated Legendre functions.