  In this paper, we investigate properties of Gelfand-Tsetlin bases mainly for
spherical monogenics, that is, for spinor valued or Clifford algebra valued
homogeneous solutions of the Dirac equation in the Euclidean space. Recently it
has been observed that in dimension 3 these bases form an Appell system. We
show that Gelfand-Tsetlin bases of spherical monogenics form complete
orthogonal Appell systems in any dimension. Moreover, we study the
corresponding Taylor series expansions for monogenic functions. We obtain
analogous results for spherical harmonics as well.
