Jack symmetric polynomials are known to be generalizations of Shur fuctions, for which powerful Weyl determinant formulas are known. Are there any generalizations of determinant formulas for general Jack symmetric functions?

Jack symmetric polynomials are known to be generalizations of Schur functions $\chi_\lambda$, for which powerful Weyl determinant formulas are known. Are there any generalizations of two determinant formulas for general Jack symmetric $P^\alpha_\lambda(x)$ functions?

The first determinant (Jacobi-Trudi) formula represents the character of the irrep GL(N) given by the partition $\lambda$ $$ \chi_\lambda(x)=\det_{i,j} s_{\lambda_i-i+j} $$ where $s_k$ are elementary Schur function and the second one gives the same function as determinant $$ \chi_\lambda(x)=\frac{\det_{i,j} x_i^{\lambda_j+N-j}}{\det_{i,j} x_i^{N-j}} $$ Jack symmetric polynomials are natural generalizations of Schur polynomials, and probably, to operate with them it would be useful to have as simple as possible analogs of Weyl formulas.