Truncated Solutions For The First Painlevé Equation
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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).
KeywordsRiemann Surface Holomorphic Function Entire Function Domain Versus Convolution Equation
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