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Truncated Solutions For The First Painlevé Equation

  • Eric Delabaere
Chapter
  • 797 Downloads
Part of the Lecture Notes in Mathematics book series (LNM, volume 2155)

Abstract

In the previous chapters, we studied the unique formal solution of the first Painlevé equation then we introduced its formal integral. In this chapter, we show that formal series components of the formal integral are 1-Gevrey and their minors have analytic properties quite similar to those for the minor of the formal series solution we started with (Sect. 6.1). We then make a focus on the transseries solution and we show their Borel-Laplace summability (Sect. 6.2). This provides the truncated solutions by Borel-Laplace summation (Sect. 6.4).

Keywords

Riemann Surface Holomorphic Function Entire Function Domain Versus Convolution Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Eric Delabaere
    • 1
  1. 1.Département de MathématiquesUniversité d’AngersAngersFrance

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