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Phys Rev Lett. 2000 Sep 18;85(12):2446-9.

Resummation of QED perturbation series by sequence transformations and the prediction of perturbative coefficients

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Institut fur Theoretische Physik, TU Dresden, D-01062 Dresden, Germany.


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 Pade 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 Pade method.

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