Designer basis functions for potentials in galactic dynamics

Existing methods for the solution of Poisson’s equation using basis functions can be made considerably more flexible, yet simpler, by using non-orthogonal basis functions. The first part of this paper describes how such basis sets can be constructed. The second part gives explicit formulas (up to quadratures and matrix inversions) for basis functions as products of spherical harmonic and radial functions; two basis sets in the literature appear as special cases.