  We derive a Jacobi-Trudi type formula for Jack functions of rectangular
shapes. In this formula, we make use of a hyperdeterminant, which is Cayley's
simple generalization of the determinant. In addition, after developing the
general theory of hyperdeterminants, we give summation formulae for Schur
functions involving hyperdeterminants, and evaluate Toeplitz-type
hyperdeterminants by using Jack function theory.
