Generating functions for spherical harmonics and spherical monogenics
Abstract
In this paper, we study generating functions for the standard orthogonal bases of spherical harmonics and spherical monogenics in Rm. Here spherical monogenics are polynomial solutions of the Dirac equation in Rm. In particular, we obtain the recurrence formula which expresses the generating function in dimension m in terms of that in dimension m-1. Hence we can find closed formulae of generating functions in Rm by induction on the dimension m.
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