2014/04/15 by Paula Cerejeiras, Cerejeiras, Paula, Uwe Kaehler +3
Mathematics · #30G35 #33C45 #33C55 #Complex Variables (math.CV) #FOS: Mathematics #math.CV #msc:30G35 #msc:33C45 #msc:33C55
paper · pdf · doi:10.48550/arxiv.1404.4066
submitted to Advances in Applied Clifford Algebras
arxiv created 2014/04/15 · arxiv updated 2014/04/17
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.