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

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dc.contributor.authorDeaño, A.
dc.date.accessioned2025-11-27T14:53:57Z
dc.date.issued2018
dc.description.abstractIn 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.
dc.description.sponsorshipThe author acknowledges financial support from the EPSRC grant "Painlevé equations: analytical properties and numerical computation", reference EP/P026532/1, and from the project MTM2015-65888-C4-2-P from the Spanish Ministry of Economy and Competitiveness. The author wishes to thank M. Fasondini, D. Huybrechs, A. Iserles, A.R. Its, A.B.J. Kuijlaars, A.F. Loureiro, C. Pech, and W. Van Assche for stimulating discussions on the topic and scope of this paper, as well as the organizers of the workshop "Painlevé Equations and Applications" held at the University of Michigan, August 25-29, 2017, for their hospitality. The comments, remarks, and corrections of the anonymous referees have led to an improved version of the paper, and they are greatly appreciated.
dc.identifier.citationLarge z Asymptotics for Special Function Solutions of Painlevé II in the Complex Plane / A. Deaño // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 35 назв. — англ.
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2018.107
dc.identifier.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 34M55; 34E05; 33C10; 30E10
dc.identifier.otherarXiv: 1804.00563
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/209850
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleLarge z Asymptotics for Special Function Solutions of Painlevé II in the Complex Plane
dc.typeArticle

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