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

publication date

  • October 2018

start page

  • 1

end page

  • 19


  • 107


  • 14

International Standard Serial Number (ISSN)

  • 1815-0659


  • In 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.


  • Mathematics


  • painlevé equations; asymptotic expansions; airy functions