  We calculate analytically the proportionality constant in the pressure law of
a membrane between parallel walls from the strong-coupling limit of variational
perturbation theory up to third order. Extrapolating the zeroth to third
approximations to infinity yields the pressure constant alpha=0.0797149. This
result lies well within the error bounds of the most accurate available
Monte-Carlo result 0.0798 +- 0.0003.
