# Spherical harmonic

From AMS Glossary

## spherical harmonic

An analytic basis function on the sphere that is commonly used in a spectral model.

A spherical harmonic is defined for each total wavenumber where The spherical harmonic basis functions satisfy the orthogonal relationship and they satisfy the elliptic equation on the sphere:

*n*and zonal wavenumber*m*as the following function of sine of latitude μ and longitude λ:*P*_{m,n}is the associated Legendre function defined as