Empty plot when calling the SphericalHarmonicY function in Plot or SphericalPlot3D [duplicate]

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.

• Sin (theta) should be Sin[theta], right? Nov 5, 2014 at 14:51
• Yes, thank you. Nov 5, 2014 at 14:53
• Because it is complex function. So you have to decide what to plot.
– Kuba
Nov 5, 2014 at 14:58
• possible duplicate of Plotting Complex Quantity Functions Nov 5, 2014 at 19:33

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]