Variational resummation of divergent series with known large-order behavior

Recently-developed variational perturbation expansions converge exponentially fast for positive coupling constants. They do not, however, possess the proper 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 for resumming divergent series in which the leading large-order behavior is incorporated. For a given set of expansion coefficients, knowledge of the large-order behavior considerably improves the quality of the approximation.