  We report a simple method to generate potential/surface density pairs in flat
axially symmetric finite size disks. Potential/surface density pairs consist of
a ``homogeneous'' pair (a closed form expression) corresponding to a uniform
disk, and a ``residual'' pair. This residual component is converted into an
infinite series of integrals over the radial extent of the disk. For a certain
class of surface density distributions (like power laws of the radius), this
series is fully analytical. The extraction of the homogeneous pair is
equivalent to a convergence acceleration technique, in a matematical sense. In
the case of power law distributions, the convergence rate of the residual
series is shown to be cubic inside the source. As a consequence, very accurate
potential values are obtained by low order truncation of the series. At zero
order, relative errors on potential values do not exceed a few percent
typically, and scale with the order N of truncation as 1/N**3. This method is
superior to the classical multipole expansion whose very slow convergence is
often critical for most practical applications.
