In spherical coordinates, you get tex2html_wrap124 as tex2html_wrap125 . This seperates via tex2html_wrap126 with tex2html_wrap127 and associated legendre polynomials in tex2html_wrap128 . The radial equation is tex2html_wrap129 . The tex2html_wrap128 equation transforms via x=cos( tex2html_wrap128 ) to tex2html_wrap132 . 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: tex2html_wrap133

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