  Clifford-Legendre and Clifford-Gegenbauer polynomials are eigenfunctions of
certain differential operators acting on functions defined on $m$-dimensional
euclidean space ${\mathbb R}^m$ and taking values in the associated Clifford
algebra ${\mathbb R}_m$. New recurrence and Bonnet type formulae for these
polynomials are proved, as their Fourier transforms are computed. Explicit
representations in terms of spherical monogenics and Jacobi polynomials are
given, with consequences including the interlacing of the zeros. In the case
$m=2$ we describe a degeneracy between the even- and odd-indexed polynomials.
