In the form of spherical harmonics, they express the symmetry of the two-sphere under the action of the Lie group SO(3).
The set is the Riemann sphere, which is of major importance in complex analysis.
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In mathematics, Riemann's differential equation, named after Bernhard Riemann, is a generalization of the hypergeometric differential equation, allowing the regular singular points to occur anywhere on the Riemann sphere, rather than merely at 0, 1, and ∞.