  We use the weighted integral form of spherical Bessel functions, and
introduce a new analytical set of complete and biorthogonal potential--density
basis functions. The potential and density functions of the new set have finite
central values and they fall off, respectively, similar to $r^{-(1+l)}$ and
$r^{-(4+l)}$ at large radii where $l$ is the latitudinal quantum number of
spherical harmonics. The lowest order term associated with $l=0$ is the perfect
sphere of de Zeeuw. Our basis functions are intrinsically suitable for the
modeling of three dimensional, soft-centred stellar systems and they complement
the basis sets of Clutton-Brock, Hernquist & Ostriker and Zhao. We test the
performance of our functions by expanding the density and potential profiles of
some spherical and oblate galaxy models.
