Effective resummation methods for an implicit resurgent function
Mathematical Physics
2007-05-23 v1 Analysis of PDEs
math.MP
Abstract
Our main aim in this self-contained article is at the same time to detail the relationships between the resurgence and the hyperasymptotic theories, and to demonstrate how these theories can be used for an implicit resurgent function. For this purpose we consider after Stokes the question of the effective Borel-resummation of an exact Bohr-Sommerfeld-like implicit resurgent function whose values on an explicit semi-lattice provide the zeros of the Airy function. The resurgent structure encountered resembles what one usually gets in nonlinear problems, so that the method described here is quite general.
Keywords
Cite
@article{arxiv.math-ph/0602026,
title = {Effective resummation methods for an implicit resurgent function},
author = {Eric Delabaere},
journal= {arXiv preprint arXiv:math-ph/0602026},
year = {2007}
}