Orthogonality of a Set of Polynomials Encountered in Neutron-Transport and Radiative-Transfer Theories

The properties of the polynomials h_l(ν) which appear in the spherical‐harmonics expansion of the eigen‐solution ${\phi }_{\nu }{\mathrm{(\mu )=\sum }}_{\text{l=0}}^{\infty }\frac{1}{2}{\text{(2l+1)P}}_l{\mathrm{(\mu )h}}_l\mathrm{(\nu )}$ 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 h_l(ν) are listed, taken from the Tchebycheff theory of orthogonal polynomials.