We present the derivation of distribution functions for the first four
members of a family of disks, previously obtained in (MNRAS, 371, 1873, 2006),
which represent a family of axially symmetric galaxy models with finite radius
and well behaved surface mass density. In order to do this we employ several
approaches that have been developed starting from the potential-density pair
and, essentially using the method introduced by Kalnajs (Ap. J., 205, 751,
1976) we obtain some distribution functions that depend on the Jacobi integral.
Now, as this method demands that the mass density can be properly expressed as
a function of the gravitational potential, we can do this only for the first
four discs of the family. We also find another kind of distribution functions
by starting with the even part of the previous distribution functions and using
the maximum entropy principle in order to find the odd part and so a new
distribution function, as it was pointed out by Dejonghe (Phys. Rep., 133, 217,
1986). The result is a wide variety of equilibrium states corresponding to
several self-consistent finite flat galaxy models.Comment: 12 pages, 7 figures, updated version, accepted for publication in
Rev. Acad. Colomb. Cienc. Ex. Fis. Na
