Concise and accurate solutions for Chandrasekhar's X and Y functions

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Chandrasekhar Equation, Isotropic Media, Radiative Transfer, Scattering Functions, Algebra, Linear Equations, Singular Integral Equations

Scientific paper

Chandrasekhar (1950) was able to express, for the case of isotropic scattering, the solution to his standard problem in radiative transfer in terms of two basic functions, including the X and Y functions. Mullikin (1962) showed that the X and Y functions, for isotropic scattering, are the unique solutions to singular integral equations. The present investigation is concerned with the derivation of solutions for the X and Y functions by means of an approach considered by Siewert and Benoist (1979). Use is also made of an improvement in the F(N) method reported by Garcia and Siewert (1982). In the calculation of the numerical results, a collocation strategy described by Garcia and Siewert (1981) is employed. The obtained values for the X and the Y function are presented in two tables. The results have been compared with calculations reported by Chandrasekhar et al. (1952) and others.

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