The classical problem of time-independent slowing down and transport of neutrons in an infinite planar homogeneous medium with constant cross sections is revisited. By applying a Laplace transform with respect to the lethargy variable, the Boltzmann equation describing this problem is brought into the form of a parameter-dependent monoenergetic transport equation with anisotropic scattering to all orders in terms of Legendre polynomials. This equation is solved by expansion in singular eigenfunctions. An original expression encompassing previously derived Gaussian and exponential-type formulas is obtained for the asymptotic scalar flux. The phase-space region where the scalar flux changes its behavior from a Gaussian to an exponential type is derived analytically as a function of the scatterer’s atomic mass. Analytical comparisons with currently available expressions for the scalar flux are also presented.