  In the setting of global geometric Langlands, we show that miraculous duality
on the stack of principal bundles on a curve intertwines the functor of
Poincare series with the dual functor to Whittaker coefficients. We construct,
for arbitrary parabolic subgroups, Jacquet functors controlling constant terms
of Poincare series and Whittaker coefficients of Eisenstein series in local
terms.
