In this work , 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 combinations of \varpi _ { 0 } , the single scattering albedo , and \mu , the cosine of the azimuth angle \theta of the direction of radiation emergent from or incident upon a semi-infinite scattering-absorbing medium , we propose a rational approximation formula with \mu ^ { 1 / 4 } and \sqrt { 1 - \varpi _ { 0 } } as the independent variables .
This allows us to reproduce the correct values of H ( \varpi _ { 0 } , \mu ) within a relative error of 2.1 \times 10 ^ { -5 } without recourse to any iterative procedure or root-finding process .