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Variational Resummation of Divergent Series with known Large-Order Behavior

H. Kleinert
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Abstract

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.

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H. Kleinert. 1995-07-17. Variational Resummation of Divergent Series with known Large-Order Behavior. https://doi.org/10.1016/0370-2693(95)01117-9

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