Velocity-density twin transforms in thin disk model
  Ring mass density and the corresponding circular velocity in thin disk model are known to be integral transforms of one another. But it may be less familiar that the transforms can be reduced to one-fold integrals with identical weight functions. It may be of practical value that the integral for the surface density does not involve the velocity derivative, unlike the equivalent and widely known Toomre's formula. 
{\L}ukasz Bratek, Szymon Sikora, Joanna Ja{\l}ocha, Marek Kutschera
astro-ph.GA