The integro-differential diffusion equation of the multiple scattering problem in an infinite, homogeneous, medium, is studied without the usual small-angle approximation. An expansion in spherical harmonics is carried out which is rapidly convergent in the case of large-angle scattering, whose coefficients can be exactly determined, and which leads to expressions for the various moments of the spatial and angular distributions. The latter alone has previously been obtained by Goudsmit and Saunderson, and, in the small-angle approximation, by Snyder and Scott. Our results are shown to include these.