(* <listing> *)
SphericalHarmonicY[l, m, theta, phi] gives the spherical
   harmonic Ylm(theta, phi).

SphericalHarmonicY[1, 0, theta, phi] 
SphericalHarmonicY[1, 1, theta, phi] 
SphericalHarmonicY[1, -1, theta, phi] 

TeXForm[SphericalHarmonicY[1, 0, theta, phi] ]

SphericalHarmonicY[10, -6, theta, phi] 

TeXForm[SphericalHarmonicY[10, 5, theta, phi] ]

{{3003\,{e^{5\,i\,\phi }}\,
     \left( -15\,\cos (\theta ) + 
       170\,{{\cos (\theta )}^3} - 
       323\,{{\cos (\theta )}^5} \right) \,
     {{\sin (\theta )}^5}}\over {256\,{\sqrt{1001\,\pi }}}
   }