Multipole expansion

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A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles used in the spherical coordinate system (the polar and azimuthal angles) for three-dimensional Euclidean space, R 3 {\displaystyle \mathbb {R} ^{3}} . Multipole expansions are useful because, similar to Taylor series, often times only the first few terms are needed to provide a good approximation of the original function. The function being expanded may be real- or complex-valued and is defined either on R 3 {\displaystyle \mathbb {R} ^{3}} , or less often on R n {\displaystyle \mathbb {R} ^{n}} for some other...

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