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We apply Pade summation to the \beta(\lambda) function for the quartic Higgscoupling \lambda in the standard electroweak model. We use the \beta functioncalculated to five loops in the minimal subtraction scheme to demonstrate theimprovement resulting from the summation, and then apply the method to the morephysical on-mass-shell renormalization scheme where \beta is known to threeloops. We conclude that the OMS \beta function and the running coupling\lambda(\mu) are reliably known over the range of energies and Higgs-bosonmasses of current interest.Comment: 14 pages, RevTeX, 6 figure

Perturbative stability of the Padé-summed Higgs-boson coupling in the standard electroweak model