gives the spherical harmonic .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- The spherical harmonics are orthonormal with respect to integration over the surface of the unit sphere.
- For , where is the associated Legendre function.
- For , .
- For certain special arguments, SphericalHarmonicY automatically evaluates to exact values.
- SphericalHarmonicY can be evaluated to arbitrary numerical precision.
- SphericalHarmonicY automatically threads over lists.
Examplesopen allclose all
Basic Examples (5)
Series expansion at Infinity:
Numerical Evaluation (4)
Specific Values (4)
Function Properties (7)
Domain of SphericalHarmonicY:
The range for SphericalHarmonicY:
SphericalHarmonicY is an even function with respect to θ and ϕ for even-order m:
SphericalHarmonicY is an odd function with respect to θ and ϕ for odd-order m:
SphericalHarmonicY is a periodic function with respect to θ and ϕ:
SphericalHarmonicY has the mirror property :
SphericalHarmonicY threads elementwise over lists:
Compute the indefinite integral using Integrate:
Generalizations & Extensions (1)
SphericalHarmonicY can be applied to a power series:
SphericalHarmonicY is an eigenfunction of the spherical part of the Laplace operator: