Large $z$ Asymptotics for Special Function Solutions of Painlev\'e II in the Complex Plane
Classical Analysis and ODEs
2018-10-04 v4
Abstract
In this paper we obtain large asymptotic expansions in the complex plane for the tau function corresponding to special function solutions of the Painlev\'e II differential equation. Using the fact that these tau functions can be written as Wronskian determinants involving classical Airy functions, we use Heine's formula to rewrite them as -fold integrals, which can be asymptotically approximated using the classical method of steepest descent in the complex plane.
Keywords
Cite
@article{arxiv.1804.00563,
title = {Large $z$ Asymptotics for Special Function Solutions of Painlev\'e II in the Complex Plane},
author = {Alfredo Deaño},
journal= {arXiv preprint arXiv:1804.00563},
year = {2018}
}