  The one-dimensional, ordinary differential equation (ODE) by Hur\'e & Hersant
(2007) that satisfies the midplane gravitational potential of truncated, flat
power-law disks is extended to the whole physical space. It is shown that
thickness effects (i.e. non-flatness) can be easily accounted for by
implementing an appropriate "softening length" $\lambda$. The solution of this
"softened ODE" has the following properties: i) it is regular at the edges
(finite radial accelerations), ii) it possesses the correct long-range
properties, iii) it matches the Newtonian potential of a geometrically thin
disk very well, and iv) it tends continuously to the flat disk solution in the
limit $\lambda \rightarrow 0$. As illustrated by many examples, the ODE,
subject to exact Dirichlet conditions, can be solved numerically with
efficiency for any given colatitude at second-order from center to infinity
using radial mapping. This approach is therefore particularly well-suited to
generating grids of gravitational forces in order to study particles moving
under the field of a gravitating disk as found in various contexts (active
nuclei, stellar systems, young stellar objects). Extension to non-power-law
surface density profiles is straightforward through superposition. Grids can be
produced upon request.
