We examine the large-order behavior of perturbation theory for the anharmonic oscillator, a simple quantum-field-theory model. New analytical techniques are exhibited and used to derive formulas giving the precise rate of divergence of perturbation theory for all energy levels of the x2N oscillator. We compute higher-order corrections to these formulas for the x⁴ oscillator with and without Wick ordering.
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Bender et al. (1971) studied this question.
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