  A method is presented for finding anisotropic distribution functions for
stellar systems with known, spherically symmetric, densities, which depends
only on the two classical integrals of the energy and the magnitude of the
angular momentum. It requires the density to be expressed as a sum of products
of functions of the potential and of the radial coordinate. The solution
corresponding to this type of density is in turn a sum of products of functions
of the energy and of the magnitude of the angular momentum. The products of the
density and its radial and transverse velocity dispersions can be also
expressed as a sum of products of functions of the potential and of the radial
coordinate. Several examples are given, including some of new anisotropic
distribution functions. This device can be extended further to the related
problem of finding two-integral distribution functions for axisymmetric
galaxies.
