  The partial differential equation governing the formation of the radiation
spectrum in the shocked plasma accreting onto an x-ray pulsar is solved to
obtain the associated Green's function describing the scattering of
monochromatic radiation injected into the plasma at a fixed altitude above the
star. Collisions between the photons and the infalling electrons cause both the
ordered and random components of the plasma energy to be transferred to the
radiation, which escapes by diffusing through the walls of the accretion
column. The analytical solution for the Green's function provides important
physical insight into the formation of the observed spectra in x-ray pulsars.
Interesting mathematical aspects of the problem include the establishment of a
new summation formula involving the Laguerre polynomials, based on the
calculation of the photon number density via integration of the Green's
function.
