Abstract
In this paper, we study generating functions for the standard orthogonal bases of spherical harmonics and spherical monogenics in \({\mathbb{R}^{m}}\). Here spherical monogenics are polynomial solutions of the Dirac equation in \({\mathbb{R}^{m}}\). 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 formulæ of generating functions in \({\mathbb{R}^{m}}\) by induction on the dimension m.
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Cerejeiras, P., Kähler, U. & Lávička, R. Generating Functions for Spherical Harmonics and Spherical Monogenics. Adv. Appl. Clifford Algebras 24, 995–1004 (2014). https://doi.org/10.1007/s00006-014-0495-8
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DOI: https://doi.org/10.1007/s00006-014-0495-8