Discrete approximations to spherically symmetric distributions

Summary We consider the approximation of spherically symmetric distributions in ^d by linear combinations of Heaviside step functions or Dirac delta functions. The approximations are required to faithfully reproduce as many moments as possible. We discuss stable methods of computing such approximations, taking advantage of the close connection with Gauss-Christoffel quadrature. Numerical results are presented for the distributions of Maxwell, Bose-Einstein, and Fermi-Dirac.Dedicated to Fritz Bauer on the occasion of his 60th birthdayWork supported in part by the National Science Foundation under Grant MCS-7927158A1