Converting a series in λto a series in λ^{-1}

Details Converting a series in λto a series in λ^{-1} Converting a series in λto a series in λ^{-1}

2003-05-07

arxiv.org/abs/hep-th/0305047v3

J.Phys.A36:10215-10225,2003

Physics

High Energy Physics

High Energy Physics - Theory

7 pages, Latex, 3 figures; Typos corrected. To appear in Journal of Physics A: Math and Gen

Scientific paper

10.1088/0305-4470/36/40/006

We introduce a transformation for converting a series in a parameter, \lambda, to a series in the inverse of the parameter \lambda^{-1}. By applying the transform on simple examples, it becomes apparent that there exist relations between convergent and divergent series, and also between large- and small-coupling expansions. The method is also applied to the divergent series expansion of Euler-Heisenberg-Schwinger result for the one-loop effective action for constant background magnetic (or electric) field. The transform may help us gain some insight about the nature of both divergent (Borel or non-Borel summable series) and convergent series and their relationship, and how both could be used for analytical and numerical calculations.

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