  The prepotential in N=2 SUSY Yang-Mills theories enjoys remarkable
properties. One of the most interesting is its relation to the coordinate on
the quantum moduli space $u=< \tr \phi^2>$ that results into recursion
equations for the coefficients of the prepotential due to instantons. In this
work we show, with an explicit multi-instanton computation, that this relation
holds true at arbitrary winding numbers. Even more interestingly we show that
its validity extends to the case in which gravitational corrections are taken
into account if the correlators are suitably modified. These results apply also
to the cases in which matter in the fundamental and in the adjoint is included.
We also check that the expressions we find satisfy the chiral ring relations
for the gauge case and compute the first gravitational correction.
