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. Here spherical monogenics are polynomial solutions of the Dirac equation.

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 formul' of generating functions in by induction on the dimension m.

Keywords

• Spherical harmonics
• spherical monogenics
• Gelfand-Tsetlin basis
• orthogonal basis
• generating function