  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.
