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In mathematics, a radial function is a real-valued function defined on a Euclidean space whose value at each point depends only on the distance between that point and the origin. The distance is usually the Euclidean distance. 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 descent function on Euclidean space can be decomposed into a series consisting of radial and spherical parts: the solid spherical harmonic expansion.
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