The product of a nonsymmetric Jack polynomial with a linear function

In this paper a decomposition in terms of the nonsymmetric Jack polynomials is given for the product of any nonsymmetric Jack polynomial $E_{\eta}(z)$ with $z_i$. This decomposition generalises a recurrence formula satisfied by single variable orthogonal polynomials on the unit circle. The decomposition also allows the evaluation of the generalised binomial coefficients $\binom{\eta}{\nu}$ associated with the nonsymmetric Jack polynomials for $\vert\eta\vert=\vert\nu\vert + 1$.