  The super-Jack polynomials, introduced by Kerov, Okounkov and Olshanski, are
polynomials in $n+m$ variables, which reduce to the Jack polynomials when $n=0$
or $m=0$ and provide joint eigenfunctions of the quantum integrals of the
trigonometric deformed Calogero-Moser-Sutherland system. We prove that the
super-Jack polynomials are orthogonal with respect to a bilinear form of the
form $(p,q)\mapsto (L_pq)(0)$, with $L_p$ quantum integrals of the rational
deformed Calogero-Moser-Sutherland system. In addition, we provide a new proof
of the Lassalle-Nekrasov correspondence between trigonometric and rational
harmonic deformed Calogero-Moser-Sutherland systems and infer orthogonality of
super-Hermite polynomials, which provide joint eigenfunctions of the latter
system.
