  In this paper we generalize the famous Jacobi's triple product identity,
considered as an identity for theta functions with characteristics and their
derivatives, to higher genus/dimension. By applying the results and methods
developed in our previous paper math.AG/0310085 several generalizations to
Siegel modular forms are obtained. These generalizations are identities
satisfied by theta functions with characteristics and their derivatives at
zero. Equating the coefficients of the Fourier expansion of these relations to
zero yields non-trivial combinatorial identities.
