I'd like to expand a 3D scalar function I'm working with, ##f(r,\theta,\phi)##, in an orthogonal spherical 3D basis set. For the angular component I intend to use spherical harmonics, but what should I do for the radial direction? Close to zero, ##f(r)\propto r##, and above a fuzzy threshold ##r_0## I don't really care about the value of f anymore. So I can make it go to zero exponentially, polynomially, or just cut it off suddenly depending on which allows me to have the best numerical computation time for the expansion I obtain. It seems like I have a number of options, like the normalized hydrogenic radial wavefunctions since they're automatically orthonormal by virtue of being the solution of schrodinger's equation. This seems silly though since my scalar has nothing to do with hydrogen or schrodinger's equation. Maybe the spherical bessel functions, but they don't seem to converge when I integrate them, since they go to zero to slowly. I suppose I could just do a fourier expansion with a cutoff at ##r_0## and just divide the basis functions by r so that when I do the spherical integral the ##r^2## in the Jacobean gives me the usual fourier orthogonality. Anything wrong with this way?