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Resummation of QED Perturbation Series by Sequence Transformations and the Prediction of Perturbative Coefficients

U. D. Jentschura·J. Becher·E. J. Weniger·G. Soff
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Abstract

We propose a method for the resummation of divergent perturbative expansions in quantum electrodynamics and related field theories. The method is based on a nonlinear sequence transformation and uses as input data only the numerical values of a finite number of perturbative coefficients. The results obtained in this way are for alternating series superior to those obtained using Padé approximants. The nonlinear sequence transformation fulfills an accuracy-through-order relation and can be used to predict perturbative coefficients. In many cases, these predictions are closer to available analytic results than predictions obtained using the Padé method.

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U. D. Jentschura, J. Becher, E. J. Weniger, G. Soff. 2000-08-06. Resummation of QED Perturbation Series by Sequence Transformations and the Prediction of Perturbative Coefficients. https://doi.org/10.1103/physrevlett.85.2446

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