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

TL;DR

This paper derives an exact analytical Green function solution for the Poisson equation in cylindrical coordinates, applicable to calculating gravitational potentials in spiral galaxies, using finite integral transforms and Sturm-Liouville eigenfunctions.

Contribution

It introduces a novel analytical solution for the Poisson problem in astrophysics, specifically for gravitational potential calculations in spiral galaxies.

Findings

Derived an explicit Green function for the Poisson equation in cylindrical coordinates.

Provided an analytical solution using finite integral transforms and Sturm-Liouville eigenfunctions.

Facilitates more accurate gravitational potential computations in astrophysical models.

Abstract

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.