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Mathematica > Mathematics and Algorithms > Mathematical Functions > Special Functions >

Built-in Mathematica Symbol

SphericalHarmonicY

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gives the spherical harmonic

The spherical harmonics are orthonormal with respect to integration over the surface of the unit sphere.

For certain special arguments, SphericalHarmonicY automatically evaluates to exact values.

Evaluate for complex arguments and orders:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

SphericalHarmonicY threads element-wise over lists:

SphericalHarmonicY can be applied to a power series:

SphericalHarmonicY is an eigenfunction of the spherical part of the Laplace operator:

] for half-integers

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