A New Derivation of the Integro-Differential Equations for Chandrasekhar's X and Y Functions

The X and Y functions of Chandrasekhar are of great importance in the theory of multiple scattering in a finite slab. Their properties are best determined analytically through the use of integral equations. From the computational view, however, they are best treated as solutions of a system of integro-differential equations. The authors' purpose is to produce a derivation from first principles that illuminates the nature of the integro-differential equations and that will aid in computational studies of transport processes. A knowledge of integral equations and Chandrasekhar's book, Radiative Transfer, is assumed.