Exponential approximation to Chandrasekhar's H-function for isotropic scattering

Abstract

In this paper, we generated a new integral equation by defining a G function to seek an analytic solution for the Chandrasekhar's H-function. Then, using shifted Legendre polynomials and modified spherical Bessel functions, the nonlinear integral equation was converted to a form that semi-analytic and numerical solutions for the H-function and its moments could be obtained. We believe this new initiative would cause scientists to solve the equation exactly. The numerical results obtained by the present method are in good agreement with those already reported in the existing literature and the differences between them range from 0.00-0.05% in case of H-function and 0.00-0.85% in case of its moments.