  An analytic solution for a Fokker-Planck equation that describes propagation
of energetic particles through a scattering medium is obtained. The solution is
found in terms of an infinite series of mixed moments of particle distribution.
The spatial dispersion of a particle cloud released at t=0 evolves through
three phases, ballistic (t<Tc), transdiffusive (t~Tc) and diffusive (t>>Tc),
where Tc is the collision time.The ballistic phase is characterized by a
decelerating expansion of the initial point source in form of a "box"
distribution with thickening walls. The next, transdiffusive phase is marked by
the box walls thickened to its size and a noticeable slow down of expansion.
Finally, the evolution enters the conventional diffusion phase.
