A special case of a Plummer-Kuzmin model for the gravitational potential of a galaxy with an infinitely thin disk corresponding to b = 0. It was proposed by Kuzmin (1956) and gives an axisymmetric potential of the form

The Laplacian in cylindrical coordinates is given by

so computing the first term gives

and the second term gives

Therefore, does indeed satisfy Laplace's equation

The surface density of this model is given by

Differentiation leads to Toomre's models.