An Exact Solution of Milne's Problem with a General Scattering Law

The solution of transport problems in semi-infinite media when the scattering function is an N'th-order polynomial is considered. Case's singular eigenfunction expansion is used to obtain a compact solution of Milne's problem in the nonconservative case in terms of an appropriate X function. The coefficients of the M + 1 discrete eigenfunctions are found by solving a nonhomogeneous set of N + M + 1 algebraic linear equations. The coefficient of the continuum of eigenfunctions and the emergent flux are at last reported.