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.