Extrapolation of power series by self-similar factor and root approximants

Details Extrapolation of power series by self-similar factor and root approximants Extrapolation of power series by self-similar factor and root approximants

2004-12-02

arxiv.org/abs/cond-mat/0412046v1

Int. J. Mod. Phys. B 18 (2004) 3027-3046

Physics

Condensed Matter

Statistical Mechanics

21 pages, Latex file

Scientific paper

10.1142/S0217979204026330

The problem of extrapolating the series in powers of small variables to the region of large variables is addressed. Such a problem is typical of quantum theory and statistical physics. A method of extrapolation is developed based on self-similar factor and root approximants, suggested earlier by the authors. It is shown that these approximants and their combinations can effectively extrapolate power series to the region of large variables, even up to infinity. Several examples from quantum and statistical mechanics are analysed, illustrating the approach.

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