Self-Similar Bootstrap of Divergent Series

Details Self-Similar Bootstrap of Divergent Series Self-Similar Bootstrap of Divergent Series

1997-06-07

arxiv.org/abs/cond-mat/9706072v1

Phys. Rev. E 55 (1997) 6552-6565

Physics

Condensed Matter

Statistical Mechanics

1 file, 22 pages, RevTex

Scientific paper

10.1103/PhysRevE.55.6552

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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