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

TL;DR

This paper introduces a method using self-similar factor and root approximants to effectively extrapolate power series from small to large variables, including infinity, with applications in quantum and statistical physics.

Contribution

The authors develop and demonstrate a novel extrapolation technique based on self-similar approximants, extending the applicability of power series in physics.

Findings

Effective extrapolation to large variables demonstrated

Approximants work up to infinity in examples

Applicable to quantum and statistical mechanics

Abstract

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.