  We apply Pade summation to the \beta(\lambda) function for the quartic Higgs
coupling \lambda in the standard electroweak model. We use the \beta function
calculated to five loops in the minimal subtraction scheme to demonstrate the
improvement resulting from the summation, and then apply the method to the more
physical on-mass-shell renormalization scheme where \beta is known to three
loops. We conclude that the OMS \beta function and the running coupling
\lambda(\mu) are reliably known over the range of energies and Higgs-boson
masses of current interest.
