  Following Rankin's method, D. Zagier computed the $n$-th Rankin-Cohen bracket
of a modular form $g$ of weight $k_1$ with the Eisenstein series of weight
$k_2$ and then computed the inner product of this Rankin-Cohen bracket with a
cusp form $f$ of weight $k = k_1+k_2+2n$ and showed that this inner product
gives, upto a constant, the special value of the Rankin-Selberg convolution of
$f$ and $g$. This result was generalized to Jacobi forms of degree 1 by Y.
Choie and W. Kohnen. In this paper, we generalize this result to Jacobi forms
defined over ${\mathcal H} \times {\mathbb C}^{(g, 1)}$.
