Как работать с большими экспонентами
Интересные примеры из стат.физики, в том числе.
Methods of Retrieving Large-Variable Exponents https://arxiv.org/abs/2202.09565
V. I. Yukalov, S. Gluzman
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 Padé 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.
Comments: Latex file, 19 pages
Subjects: Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Phenomenology (hep-ph); Mathematical Physics (math-ph)
Methods of Retrieving Large-Variable Exponents https://arxiv.org/abs/2202.09565
V. I. Yukalov, S. Gluzman
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 Padé 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.
Comments: Latex file, 19 pages
Subjects: Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Phenomenology (hep-ph); Mathematical Physics (math-ph)