Rational Approximation Formula for Chandrasekhar's H-function for Isotropic Scattering

Abstract

We first establish a simple procedure to obtain with 11-figure accuracy the values of Chandrasekhar's H-function for isotropic scattering using a closed-form integral representation and the Gauss-Legendre quadrature. Based on the numerical values of the function produced by this method for various values of the single scattering albedo and the cosine of the azimuth angle of the direction of radiation emergent from or incident upon a semi-infinite scattering-absorbing medium, we propose a rational approximation formula, which allows us to reproduce the correct values of the H-function within a relative error of 2.1/100000 without recourse to any iterative procedure or root-finding process.