On the Radius of Convergence of the Simplest Power Series Solution of Painleve-I equation II(A Singular Solution)

In our previous paper [1] we considered the simplest power series solution of the Painleve-I equation which is regular at the origin. This note is a sequel to it. Here we consider another simplest Laurent series solution which is singular at the origin. Important feature of this solution is the location of the singularities. The location of the nearest singularity from the origin is given by the radius S of convergence of this Laurent series. The value of S is calculated numerically by the same method as in [1]. We obtained S = 2.56.... Various theoretical bounds for S are also obtained. The mathematical part of this work was done by Kametaka and the numerical part by Noda.

公開日:2010年1月24日で登録したコンテンツは、国立情報学研究所において電子化したものです。