  In this paper, we study shifted Schur functions $S_\mu^\star$, as well as a
new family of shifted symmetric functions $\mathfrak{K}_\mu$ linked to Kostka
numbers. We prove that both are polynomials in multi-rectangular coordinates,
with nonnegative coefficients when written in terms of falling factorials. We
then propose a conjectural generalization to the Jack setting. This conjecture
is a lifting of Knop and Sahi's positivity result for usual Jack polynomials
and resembles recent conjectures of Lassalle. We prove our conjecture for
one-part partitions.
