Deaño, Alfredo (2018) Large z Asymptotics for Special Function Solutions of Painlevé II in the Complex Plane. Symmetry, Integrability and Geometry: Methods and Applications, 14 (107). Article Number 107. ISSN 1815-0659. (doi:10.3842/SIGMA.2018.107) (KAR id:69536)
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Official URL: https://doi.org/10.3842/SIGMA.2018.107 |
Abstract
In this paper we obtain large z asymptotic expansions in the complex plane for the tau function corresponding to special function solutions of the Painlevé II differential equation. Using the fact that these tau functions can be written as n×n Wronskian determinants involving classical Airy functions, we use Heine's formula to rewrite them as n-fold integrals, which can be asymptotically approximated using the classical method of steepest descent in the complex plane.
Item Type: | Article |
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DOI/Identification number: | 10.3842/SIGMA.2018.107 |
Uncontrolled keywords: | Painlev´e equations; asymptotic expansions; Airy functions |
Subjects: | Q Science > QA Mathematics (inc Computing science) |
Divisions: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Depositing User: | Alfredo Deano Cabrera |
Date Deposited: | 12 Oct 2018 08:25 UTC |
Last Modified: | 04 Mar 2024 16:30 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/69536 (The current URI for this page, for reference purposes) |
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