This research effort determined how to numerically represent the scattering kernel for x-ray scattering from a relativistic Maxwellian distribution of electrons in a multigroup discrete Sn treatment of the equation of radiative transfer. An ordinary four-term Legendre polynomial expansion of the scattering kernel was used in the study. Ten sets of 134 group-averaged Wien-weighted cross-section coefficients were calculated for electron temperatures between 0.5 and 20 keV, with photon energies between 0.05 and 400 keV. The first Legendre coefficients satisfy conservation and detailed balance at equilibrium neglecting induced effects. These 134-group cross sections were then collapsed to 10-, 20-, and 40-group cross-section sets for use in parametric transmission studies using a discrete Sn transport code. These studies involved the transmission of a source of x rays through a thin slab of free electrons, varying the source and electron temperatures, the angular behavior of the source, the number of energy groups, the degree of angular quadrature, and the degree of kernel expansion. Steady-state transmission studies in which the source and electron temperatures were equal showed that the kernel is adequately represented by a two-term Legendre polynomial expansion. In optically thin regions, an S8 angular quadrature is sufficient for near-isotropic sources, while S16 or higher quadratures are necessary for highly anisotropic sources. Steady-state transmission studies in which the source temperature did not equal the electron temperature, but in which the cross sections were deliberately weighted by an equilibrium photon distribution, indicated that for 20 energy-group models, for example, the ratio of source temperature to electron-distribution temperature must lie in the interval 0.8 ≤ T/Te ≤ 1.8 if spectral errors are to be limited to 5% or less.