Large z Asymptotics for Special Function Solutions of Painlevé II in the Complex Plane
Large z Asymptotics for Special Function Solutions of Painlevé II in the Complex Plane
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DOI：
10.3842/sigma.2018.107
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发表时间：
2018-04
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影响因子：
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通讯作者：
A. Deaño
中科院分区：
文献类型：
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作者：
A. Deaño
本文得到了Painlev ′ e Ⅱ型微分方程的特函数解所对应的τ函数在复平面上的大z渐近展开式.利用这些tau函数可以写成n × n的包含经典Airy函数的Wronskian行列式的事实，我们使用海涅公式将它们重写为n重积分，可以使用复平面中的经典最速下降法来渐近近似。
In this paper we obtain large z asymptotic expansions in the complex plane for the tau function corresponding to special function solutions of the Painlev´e 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.