Generation of leading coefficients of orthogonal polynomials with an application to anisotropic scattering of neutrons

Abstract

A simple method to generate leading coefficients for high-order sets of orthogonal polynomials, by derivation of recurrence expressions for these coefficients, is developed. The method is applied to Legendre, Hermite, Chebyshev and Laguerre polynomials. The method may be used in calculations of high anisotropic neutron-scattering transfer cross-sections, where the angular distribution of the scattered neutrons is given in the ENDF/B files for most materials as coefficients of an expansion into Legendre polynomials.