GroupTheory`
GroupTheory`
GTCartesianSphericalHarmonicY
GTCartesianSphericalHarmonicY[l,m,x,y,z]
gives the spherical harmonic 
in cartesian form.
Details and Options
- With the help of the associate Legendre polynomials
(see LegendreP) the spherical harmonics can be calculated in cartesian form, with the help of the following equation: -
- The result is normalized using the following pre-factor:
. - See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, Appendix A.