  Some formulae are presented for finding two-integral distribution functions
(DFs) which depends only on the two classical integrals of the energy and the
magnitude of the angular momentum with respect to the axis of symmetry for
stellar systems with known axisymmetric densities. They come from an
combination of the ideas of
  Eddington and Fricke and they are also an extension of those shown by Jiang
and Ossipkov for finding anisotropic DFs for spherical galaxies. The density of
the system is required 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 about the axis of symmetry. The product of
the density and its radial velocity dispersion can be also expressed as a sum
of products of functions of the potential and of the radial coordinate. It can
be further known that the density multipied by its rotational velocity
dispersion is equal to a sum of products of functions of the potential and of
the radial coordinate minus the product of the density and the square of its
mean rotational velocity. These formulae can be applied to the Binney and the
Lynden-Bell models. An infinity of the odd DFs for the Binney model can be also
found under the assumption of the laws of the rotational velocity.
