  Recently-developed variational perturbation expansions converge exponentially
fast for positive coupling constants. They do not, however, possess the correct
left-hand cut in the complex coupling constant plane, implying a wrong
large-order behavior of their Taylor expansion coefficients. We correct this
deficiency and present a method of resumming divergent series with their proper
large-order behavior. For a given set of expansion coefficients, knowledge of
the large-order behavior considerably improves the quality of the
approximation.
