SIMBAD references

Exact analytical solutions are given for the three finite disks with surface density Σ_n= σ₀(1 - R ²/α²)^ n-1/2^withn = 0, 1, 2. Closed-form solutions in cylindrical coordinates are given using only elementary functions for the potential and for the gravitational field of each of the disks. The n = 0 disk is the flattened homeoid for which. Improved results are presented for this disk. The n = 1 disk is the Maclaurin disk for which. The Maclaurin disk is a limiting case of the Maclaurin spheroid. The potential of the Maclaurin disk is found here by integrating the potential of the n = 0 disk over α, exploiting the linearity of Poisson's equation. The n = 2 disk has the surface density Σ_D2= σ₀(1 - R ²/α²)^3/2. The potential is found by integrating the potential of the n = 1 disk.