Many detailed multigroup transport calculations require group-to-group Legendre transfer coefficients to represent scattering processes in various nuclides. These (fine group) constants must first be generated from the basic data. This paper outlines an alternative technique for generating such data, given the total scattering cross section of a particular nuclide on a point-wise energy basis, σ(E'), and some information regarding the angular scattering distribution for each initial energy point. The evaluation of generalized multigroup transfer matrices for transport calculations requires a double integration extending over the primary and secondary energy groups where, for a given initial energy, the integration over the secondary energy group may be replaced by an integral over the possible scattering angles. In the present work, analytic expressions for these angular integrals are derived that are free of truncation error. Differences between the present method (as implemented in ROLAIDS) and other methods (as implemented in MINX and XLACS-2) will be explored. Of particular interest is the fact that, for hydrogen, the angular integration is shown to simplify to the point that, for many weight functions, the integration over the primary energy group might also be performed analytically. This completely analytic treatment for hydrogen has recently been implemented in NEWXLACS.