Whittaker Functions as Solutions for a Background of (2+1)-DIMENSIONAL Dust

2+1 gravity is studied for a situation in which the usual point matter source has been regularized by replacing it with a smooth extended source. This leads to a solution of the Einstein equations for a perfect fluid with positive mass density and zero pressure: dust. With this background, the Klein-Gordon equation for a scalar field is solved explicitly in terms of Whittaker functions.