MR3241905 Kohei IWAKI Kohei IWAKI Parametric Stokes Phenomenon for the Second Painlevé Equation Funkcialaj Ekvacioj. Serio Internacia 57 2014 173--243 http://fe.math.kobe-u.ac.jp/FE/FullPapers/57-2/57_173.pdf http://www.ams.org/mathscinet-getitem?mr=MR3241905 The second Painlevé equation with a large parameter ($P_{\rm II}$) is analyzed from the viewpoint of the exact WKB analysis. The purpose of this study is to investigate a new kind of Stokes phenomena which we call “parametric Stokes phenomenon”, occurring to transseries solutions of ($P_{\rm II}$). To analyze the parametric Stokes phenomenon, we introduce the “Voros coefficient” for ($P_{\rm II}$) and derive the connection formula for transseries solutions of ($P_{\rm II}$) through the analysis of the Voros coefficient. We also show that the connection formula can be derived by completely different method: the isomonodromic deformation. The second Painlevé equation, Exact WKB analysis, Parametric Stokes phenomenon, $P$-Voros coefficient. 34M55, 34M60, 34M40. 57-173 2014 Parametric Stokes Phenomenon for the Second Painlevé Equation Kohei IWAKI Kohei IWAKI
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