In spherical coordinates, you get as . This seperates via with
and associated legendre polynomials in . The radial equation is
. The equation transforms via x=cos( ) to . l has to be integer
to get a convergent power series. This solution is legendre polynomials
for m=0 and associated legendre polynomials for other m. The solution
is typically written in terms of the spherical harmonics as:

source psfile jl@crush.caltech.edu index

spherical_coordinate_green_function

laplacian