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We prove that under an explicit condition on the parameters in the isotropic-scattering linear transport equation for an exponential atmosphere, the continuum eigensolutions developed by Millikin and Siewert are complete on the half range 0<μ⩽1. We also treat numerically the equation for the outgoing flux, which can be derived using these eigenfunctions, and we show that excellent numerical results are obtained if the above condition is satisfied, while poor results are obtained if the condition is sufficiently violated. Finally, we describe a method for constructing elementary solutions of the anisotropic-scattering transport equation for an exponential atmosphere.

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