Large z Asymptotics for Special Function Solutions of Painlevé II in the Complex Plane - Deaño, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2018)
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.