Green function for the Poisson equation in a general case of astrophysical interest

In present paper we suggest exact solution of the Poisson problem which appears in frequently addressed applications regarding calculation of the gravitational potential of spiral galaxies. We suggest an analytical solution for the problem in cylindrical coordinates by using the finite integral transform technique. The final solution is presented as expansion on the eigenfunctions of the corresponding Sturm-Liouville problem. Green function of the problem is constructed.