Truncated Solutions For The First Painlevé Equation

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 m...

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Bibliographic Details
Published inDivergent Series, Summability and Resurgence III Vol. 2155; pp. 129 - 146
Main Author Delabaere, Eric
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 01.01.2016
Springer International Publishing
SeriesLecture Notes in Mathematics
Subjects
Calculus & mathematical analysis
Complex analysis
Convolution Equation
Differential equations
Domain Versus
Entire Function
Holomorphic Function
Riemann Surface
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Summary: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).
ISBN:9783319289991
3319289993
ISSN:0075-8434
1617-9692
DOI:10.1007/978-3-319-29000-3_6