POTENTIAL DENSITY PAIRS FOR FLAT DISKS

We simplify Lynden-Bell's extension to non-axisymmetric discs of Mestel's method of flattened spheroids for finding potential-density pairs. We use it to find a large family of potential-density pairs, which is described by a pair of generalized hypergeometric functions. We then explore a portion of this family, finding some new pairs, as well as recovering many already known ones. Among the new pairs found are ones related to non-axisymmetric distortions of the Kuzmin-Toomre, Gaussian, Kalnajs-Mestel, and isochrone discs, and which should be useful for stability analyses of these discs.