The gravitational force and potential of the finite Mestel disk
  Mestel determined the surface mass distribution of the finite disk for which
the circular velocity is constant in the disk and found the gravitational field
for points in the $z=0$ plane. Here we find the exact closed form solutions for
the potential and the gravitational field of this disk in cylindrical
coordinates over all the space. The Finite Mestel Disk (FMD) is characterized
by a cuspy mass distribution in the inner disk region and by an exponential
distribution in the outer region of the disk. The FMD is quite different from
the better known exponential disk or the untruncated Mestel disk which, being
infinite in extent, are not realistic models of real spiral galaxies. In
particular, the FMD requires significantly less mass to explain a measured
velocity curve.
