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Self-Similar Bootstrap of Divergent Series

V. I. Yukalov·S. Gluzman
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Abstract

A method is developed for calculating effective sums of divergent series. This approach is a variant of the self-similar approximation theory. The novelty here is in using an algebraic transformation with a power providing the maximal stability of the self-similar renormalization procedure. The latter is to be repeated as many times as it is necessary in order to convert into closed self-similar expressions all sums from the series considered. This multiple and complete renormalization is called self-similar bootstrap. The method is illustrated by several examples from statistical physics.

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BibTeXRIS

V. I. Yukalov, S. Gluzman. 1997-06-07. Self-Similar Bootstrap of Divergent Series. https://doi.org/10.1103/physreve.55.6552

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