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Large z Asymptotics for Special Function Solutions of Painlevé II in the Complex Plane

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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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
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: 16 Feb 2021 13:58 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/69536 (The current URI for this page, for reference purposes)
Deaño, Alfredo: https://orcid.org/0000-0003-1704-247X
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