Methods of Retrieving Large-Variable Exponents

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 Pade 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.

Automated summary

This article analyzes the methods of determining the characteristic exponents for variables tending to infinity using small-variable asymptotic expansions. Several different methods of summation are compared, and it is found that reliable estimates are obtained when different summation methods are compatible with each other.