Radial function

In mathematics, a radial function is a function defined on a Euclidean space R whose value at each point depends only on the distance between that point and the origin. For example, a radial function Φ in two dimensions has the form

where φ is a function of a single non-negative real variable. Radial functions are contrasted with spherical functions, and any decent function (e.g., continuous and rapidly decreasing) on Euclidean space can be decomposed into a series consisting of radial and spherical parts: the solid spherical harmonic expansion.