Generating functions for spherical harmonics and spherical monogenics
Complex Variables
2014-04-17 v1
Abstract
In this paper, we study generating functions for the standard orthogonal bases of spherical harmonics and spherical monogenics in R^m. Here spherical monogenics are polynomial solutions of the Dirac equation in 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 formulae of generating functions in R^m by induction on the dimension m.
Cite
@article{arxiv.1404.4066,
title = {Generating functions for spherical harmonics and spherical monogenics},
author = {Paula Cerejeiras and Uwe Kaehler and Roman Lavicka},
journal= {arXiv preprint arXiv:1404.4066},
year = {2014}
}
Comments
submitted to Advances in Applied Clifford Algebras