  Recently it has been proposed that the coefficient of the three-point
function of the BMN operators in N=4 supersymmetric Yang-Mills theory is
related to the three-string interactions in the pp-wave background. We
calculate three-point functions of these operators to the first order in the
effective Yang-Mills coupling lambda' = g_{YM}^2 N/J^2 in planar perturbation
theory. On the string theory side, we derive the explicit expressions of the
Neumann matrices to all orders in 1/(\mu p^+ \alpha')^2. This allows us to
compute the corresponding three-string scattering amplitudes. This provides an
all orders prediction for the field theory three-point functions. We compare
our field theory results with the string theory results to the subleading order
in 1/(\mu p^+ \alpha')^2 and find perfect agreement.
