Abstrakt
The task of finding the potential of a thin circular disk with power-law radial density profile is revisited. The result, given in terms of infinite Legendre-type series in the above reference, has now been obtained in closed form thanks to the method of Conway employing Bessel functions.
Starting from a closed-form expression for the potential generated by the elementary density term rho (2l ), we cover more generic-finite solid or infinite annular-thin disks using superposition and/or inversion with respect to the rim. We check several specific cases against the series-expansion form by numerical evaluation at particular locations.
Finally, we add a method to obtain a closed-form solution for finite annular disks whose density is of "bump" radial shape, as modeled by a suitable combination of several powers of radius. Density and azimuthal pressure of the disks are illustrated on several plots, together with radial profiles of free circular velocity.