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Modified Spherical Harmonics

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摘要

A modification of the classical theory of spherical harmonics is presented. The unit sphere S in is replaced by the half-sphere S (+) in the upper half space, the Euclidean scalar product on S by a non-Euclidean one on S (+), and the Laplace equation by the equation . It will be shown that most results from the theory of spherical harmonics in stay valid in this modified setting.

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