Empty plot when calling the SphericalHarmonicY function in Plot or SphericalPlot3D

Question

I'm getting an empty plot for the following code:

SphericalPlot3D[
 2*Pi*Sin[theta]*SphericalHarmonicY[100, 50, theta, phi], {theta, 0, 2*Pi}, {phi, 0 , Pi}]

Also, if I set phi to a specific value and plot in 1D, an empty plot is printed.

Any thoughts? Thanks.

Answer 1

Grid[{{Abs, Re, Im}, 
  SphericalPlot3D[2 π Sin[θ] #@ 
       SphericalHarmonicY[10, 5, θ, φ], {θ, 0, 2 π}, {φ, 0, 2 π},
     PlotStyle -> Opacity[0.3],
     PlotPoints -> 40,PlotRange -> All,
     Mesh -> {5, 10},MeshStyle -> {Opacity[0.1], Darker@Purple},
     Boxed -> False, Axes -> False] & /@ {Abs, Re, Im}},
 Frame -> All]

SphericalHarmonicY[100, 50, θ, φ] takes so long time.

SphericalPlot3D[2 π Sin[θ] Abs@ 
   SphericalHarmonicY[100, 50, θ, φ], {θ, 0, 2 π}, {φ, 0, 2 π},
 PlotStyle -> Opacity[0.3],PlotPoints -> 150,
 PlotRange -> All, Mesh -> {50, 10},
 MeshStyle -> {Opacity[0.1], Darker@Purple},
 Boxed -> False, Axes -> False]