A polynomial quadrature method for half-range neutron transport problems

The properties of the two orthonormal polynomial sets associated with the two half-range weight functions in neutron transport problems are further investigated. Transformation formulae from one set to the other are generalized and thence a limit expression for one of the weight functions is obtained in the form of a polynomial quotient. The two highest algebraic degree of precision quadrature systems related to the two orthonormal polynomial sets are then applied (with special provisos) to singular-type transport integrals and to the representation, in terms of quadrature sums, of the extended orthogonality and completeness relations for the Case eigenfunctions. The quadrature formalism is finally exemplified on the standard half-range transport problems. Tables for nodes and quadrature coefficients are given, and an appendix deals with the interconnection between the moments of different order of a weight function