A series approximation for disk galaxies by means of the Epstein-Hubbell integral

In this paper, an exact series will be derived for the calculation of rotational velocities in homogeneous disk galaxies with finite thickness. The procedure is based on the Legendre polynomial expansion method for the solution of the Epstein-Hubbell integral. A ‘scaling’ method will also be given in order to derive approximate values for rotational velocities in disk galaxies with a nonuniform distribution. An interesting identity, which shows up in the analysis, has been proved.