I think these two ideas are simmilar (if not closely related) Spherical Radial Functions and Zonal Spherical Functions. I know they both have something to do with radial solutions to laplaces equations. Wikipedia wasn't very helpful, http://en.wikipedia.org/wiki/Zonal_spherical_function as the description is done in very high level mathematics. I believe these functions are used in this paper. http://www.google.ca/url?sa=t&source=web&ct=res&cd=9&url=http%3A%2F%2Fwww.math.uni-luebeck.de%2Fkeiner%2Fpublications%2Fdiploma_thesis.ps&ei=VdeJSqykPJCuswOj_uziAg&usg=AFQjCNHa2vYgn8yL8NchpXEnFEfJYCyq0Q&sig2=Jt6on7lunZjTUSeJelG5jw [Broken] which I find interesting because it discusses using non uniform fast Fourier transforms to find the spherical harmonic components. I wouldn't mind a simplified description of these functions, and some simple examples of using these as basis functions.