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In present paper we suggest exact solution of the Poisson problem whichappears in frequently addressed applications regarding calculation of thegravitational potential of spiral galaxies. We suggest an analytical solutionfor the problem in cylindrical coordinates by using the finite integraltransform technique. The final solution is presented as expansion on theeigenfunctions of the corresponding Sturm-Liouville problem. Green function ofthe problem is constructed.

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