  Spaces of homogeneous spherical monogenics in dimension 3 can be considered
naturally as sl(2,C)-modules. As finite-dimensional irreducible
sl(2,C)-modules, they have canonical bases which are, by construction,
orthogonal. In this note, we show that these orthogonal bases form the Appell
system and coincide with those constructed recently by S. Bock and K.
Guerlebeck. Moreover, we obtain simple expressions of elements of these bases
in terms of the Legendre polynomials.
