  Exact analytical solutions are given for the three finite disks with surface
density $\Sigma_n=\sigma_0 (1-R^2/\alpha^2)^{n-1/2} \textrm{with} n=0, 1, 2$.
Closed-form solutions in cylindrical co-ordinates are given using only
elementary functions for the potential and for the gravitational field of each
of the disks.
  The n=0 disk is the flattened homeoid for which $\Sigma_{hom} =
\sigma_0/\sqrt{1-R^2/\alpha^2}$. Improved results are presented for this disk.
The n=1 disk is the Maclaurin disk for which $\Sigma_{Mac} = \sigma_0
\sqrt{1-R^2/\alpha^2}$. The Maclaurin disk is a limiting case of the Maclaurin
spheroid. The potential of the Maclaurin disk is found here by integrating the
potential of the n=0 disk over $\alpha$, exploiting the linearity of Poisson's
equation. The n=2 disk has the surface density $\Sigma_{D2}=\sigma_0
(1-R^2/\alpha^2)^{3/2}$. The potential is found by integrating the potential of
the n=1 disk.
