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We report a simple method to generate potential/surface density pairs in flataxially symmetric finite size disks. Potential/surface density pairs consist ofa ``homogeneous'' pair (a closed form expression) corresponding to a uniformdisk, and a ``residual'' pair. This residual component is converted into aninfinite series of integrals over the radial extent of the disk. For a certainclass of surface density distributions (like power laws of the radius), thisseries is fully analytical. The extraction of the homogeneous pair isequivalent to a convergence acceleration technique, in a matematical sense. Inthe case of power law distributions, the convergence rate of the residualseries is shown to be cubic inside the source. As a consequence, very accuratepotential values are obtained by low order truncation of the series. At zeroorder, relative errors on potential values do not exceed a few percenttypically, and scale with the order N of truncation as 1/N**3. This method issuperior to the classical multipole expansion whose very slow convergence isoften critical for most practical applications.

Generation of potential/surface density pairs in flat disks Power law distributions