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{title2=$Y_\ell^m$}
{wiki}

A spherical harmonic is an eigenfunction of the Laplacian on the unit sphere:
$$
\nabla_{S^2}^2Y_\ell^m=-\ell(\ell+1)Y_\ell^m.
$$


Spherical harmonic

Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 314 / 2 / b / Solution

{wiki=Spherical_harmonics}

Correspond to the angular part of <Laplace's equation> in spherical coordinates after using <separation of variables> as shown at: https://en.wikipedia.org/wiki/Spherical_harmonics#Laplace's_spherical_harmonics

Spherical harmonic ( $Y_{ℓ}^{m}$ )

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Spherical harmonic (Yℓm​)

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