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

Andrew A. Rawlinson
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Abstract

We introduce a transformation for converting a series in a parameter, λ, to a series in the inverse of the parameter λ^{-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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Andrew A. Rawlinson. 2003-09-18. Converting a series in λto a series in λ^{-1}. https://doi.org/10.1088/0305-4470%2F36%2F40%2F006

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