Dynamics of Flat Galaxies. II. Biorthonormal Surface Density-Potential Pairs for Finite Disks

Poisson's equation in the flat disk geometry becomes an integral equation, and it can be solved by series expansions in biorthonormal as well as orthonormal functions. A method for generating complete sets of biorthonormal surface density-potential pairs by means of Abel transforms of orthonormal sets is developed. When applied to Jacobi polynomials, it produces surface densities which vanish outside a finite disk, and their corresponding potentials which on the disk are polynomials in the Cartesian coordinates. Subject headings: galaxies: internal motions - galaxies: structure - stars: stellar dynamics