The properties of the polynomials hl(ν) which appear in the spherical-harmonics expansion of the eigen-solution φν(μ)=∑l=0∞12(2l+1)Pl(μ)hl(ν) in plane-symmetric one-speed transport problems with anisotropic scattering are reviewed and further investigated. These polynomials are shown to be orthogonal in the Stieltjes sense with a weight distribution which contains a continuous as well as a discrete portion. Some further properties of the hl(ν) are listed, taken from the Tchebycheff theory of orthogonal polynomials.