Abstract
Some systematics which exist between eigenfunctions and adjoint singular integral equations arising in the solution of the transport equation in slab geometry are illustrated. The transport equation is shown to obey a singular integral equation and its relationship to the eigenfunction expansion-method solution is shown. A new method for solving for the expansion coefficients in the eigenfunction expansion method is illustrated by solving Milne's problem. The role adjoint singular integral equations play in finding appropriate weight functions for use in orthogonality relations between the eigenfunctions of the transport equation is briefly discussed.
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