Abstract
A method for extrapolating perturbative power series to infinity is described. It is a Borel partial resummation stabilized by a variational parameter. Two kinds of series relative to the anharmonic oscillators ‖x‖k, k>0, are extrapolated in order to illustrate the effectiveness of the method: the Rayleigh–Schrödinger series, on the one hand, which, after extrapolation, provides the strong coupling expansion of the energy levels, and their lattice expansion, on the other hand, from which is extracted the continuum limit.
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