The method of orthogonal polynomials in linear transport theory

The problem of solving the linear transport equation by approximating the angular dependence of the solution by a finite sum of orthogonal polynomials is investigated. Under plane-symmetry conditions and for a polynomial scattering function an explicit form of approximate eigenfunctions is obtained, and thecharacteristic equation for the spectrum of eigenvalues of the problem is defined and analyzed. The convergence of the eigenfunctions to Keyes functions, and the identity of the limit and precise spectra are proved. Sufficient criteria for orthogonal polynomials to be applicable transport theory are established.