  We present a non-perturbative resummation of the asymptotic strong-coupling
expansion for the dressing phase factor of the AdS_5xS^5 string S-matrix. The
non-perturbative resummation provides a general form for the coefficients in
the weak-coupling expansion, in agreement with crossing symmetry and
transcendentality. The ambiguities of the non-perturbative prescription are
discussed together with the similarities with the non-perturbative definition
of the c=1 matrix model.
