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Translation of real solid spherical harmonics



General formulae for the translation of both regular and irregular real solid harmonics are derived from the addition theorems of complex harmonics. The resultant expressions, being too complicated for practical purposes, are rewritten in a more compact and friendly manner. The usefulness of these simplified expressions is illustrated with two examples: the potential generated by sets of charges and multipoles in points placed far away, and the expansion in regular harmonics of the long-range potential inside a region surrounded by pointwise charge distributions. © 2012 Wiley Periodicals, Inc.