  A generalization of associated Legendre functions is proposed and used to
describe the scattering states of the Rosen-Morse potential. The functions are
then given explicit formulas in terms of the hypergeometric function, their
asymptotic behavior is examined and shown to match the requirements for states
in the regions of total and partial reflection. Elementary expressions are
given for reflection and transmission coefficients, and an integral identity
for the generalized Legendre functions is proven, allowing the calculation of
the spectral measure of the induced integral transform for the scattering
states. These methods provide a complete classical solution to the potential,
without need of path integral techniques.
