  We present an algebraic construction of the orthogonal eigenfunctions of the
supersymmetric extension of the rational Calogero-Moser-Sutherland model with
harmonic confinement. These eigenfunctions are the superspace extension of the
generalized Hermite (or Hi-Jack) polynomials. The conserved quantities of the
rational supersymmetric model are related to their trigonometric relatives
through a similarity transformation. This leads to a simple expression between
the corresponding eigenfunctions: the generalized Hermite superpolynomials are
written as a differential operator acting on the corresponding Jack
superpolynomials. As an aside, the maximal superintegrability of the
supersymmetric rational Calogero-Moser-Sutherland model is demonstrated.
