A DIRECT NUMERICAL APPROACH TO THE CHANDRASEKHAR H-FUNCTIONS FOR ARBITRARY CHARACTERISTIC FUNCTIONS

The purpose of this paper is to present a numerical technique to directly compute the Chandrasekhar's H(mu)-function for anisotropic scattering in terms of the roots of the characteristic equation as well as the quadrature points of a certain degree n employed to approximate the definite integral involved in the basic equation. The principal feature of the algorithm proposed here is a compact computer code to enumerate (n)C(m) combinations of n distinct integers {1,...,n} taken m at a time. With these quantities available, the coefficients of the polynomial equation of the characteristic equation can be readily computed for any given characteristic function, so that a standard technique such as the Laguerre method can be applied to find all the roots. It is shown that the results obtained for some representative H(mu)-functions using the present technique with relatively low-order formula (e.g., n = 7) are sufficiently accurate for all practical purposes.