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Comparison between the successive-perturbation method and the analytic-continuation method.

It is shown that our method of ``successive perturbations'' is closely related to the method of analytic continuation of perturbation series via reexpansion about a shifted origin [Silverman, Sudhindra, and Olbrich, Phys. Rev. A 30, 1554 (1984)], in that the former procedure arises from successive incremental applications of the latter. The theory is illustrated with a second-order application to the anharmonic oscillator.