spherical harmonics

In mathematics, spherical harmonics are a series of special functions defined on the surface of a sphere used to solve some kinds of differential equations. As Fourier series are a series of functions used to represent functions on a circle, spherical harmonics are a series of functions that are used to represent functions defined on the surface of a sphere. Spherical harmonics are functions defined in terms of spherical coordinates and are organized by angular frequency, as seen in the rows of functions in the illustration on the right.