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

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

2010-10-23

arxiv.org/abs/1010.4839v1

Astronomy and Astrophysics

Astrophysics

Earth and Planetary Astrophysics

12 pages, 1 table, Accepted for publication in Astrophysics and Space Science

Scientific paper

10.1007/s10509-010-0512-x

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.

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