  In this paper we study the asymptotic behavior of the Jack rational functions
as the number of variables grows to infinity. Our results generalize the
results of A. Vershik and S. Kerov obtained in the Schur function case
(theta=1). For theta=1/2,2 our results describe approximation of the spherical
functions of the infinite-dimensional symmetric spaces $U(\infty)/O(\infty)$
and $U(2\infty)/Sp(\infty)$ by the spherical functions of the corresponding
finite-dimensional symmetric spaces.
