Methods of Retrieving Large-Variable Exponents

TL;DR

This paper analyzes various advanced summation methods to accurately determine characteristic exponents for large variables from small-variable asymptotic expansions, demonstrating their effectiveness and consistency across typical problems.

Contribution

It compares multiple summation techniques, including Padé and self-similar methods, for estimating large-variable exponents, highlighting their agreement and reliability.

Findings

All methods provide close estimates for large-variable exponents.

Reliable estimates occur when different summation methods agree.

The methods are effective across typical problems.

Abstract

Methods of determining, from small-variable asymptotic expansions, the characteristic exponents for variables tending to infinity are analyzed. The following methods are considered: diff-log Pad\'e summation, self-similar factor approximation, self-similar diff-log summation, self-similar Borel summation, and self-similar Borel-Leroy summation. Several typical problems are treated. The comparison of the results shows that all these methods provide close estimates for the large-variable exponents. The reliable estimates are obtained when different methods of summation are compatible with each other.