Deaño Cabrera, Alfredo2021-02-232021-02-232018-10-03SIGMA, (2018), v.14, 107, [19] p.1815-0659https://hdl.handle.net/10016/32004This paper is a contribution to the Special Issue on Painlevé Equations and Applications in Memory of Andrei Kapaev. The full collection is available at https://www.emis.de/journals/SIGMA/Kapaev.htmlIn this paper we obtain large z asymptotic expansions in the complex plane forthe tau function corresponding to special function solutions of the Painlevé II differentialequation. Using the fact that these tau functions can be written as n × n Wronskiandeterminants involving classical Airy functions, we use Heine's formula to rewrite them asn-fold integrals, which can be asymptotically approximated using the classical method ofsteepest descent in the complex plane.19engThe authors retain the copyright for their papers published in SIGMA under the terms of the Creative Commons Attribution-ShareAlike LicenseAtribución-NoComercial-SinDerivadas 3.0 EspañaPainlevé equationsAsymptotic expansionsAiry functionsresearch articleMatemáticashttps://doi.org/10.3842/SIGMA.2018.107open access110719Symmetry Integrability and Geometry: Methods and Applications14AR/0000026483