Transseries And Formal Integral For The First Painlevé Equation
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Abstract This chapter has two purposes. Our first goal is to construct the socalled “formal transseries solutions” for the prepared form associated with the first Painlevé equation, which will be used later on to get the truncated solutions : this is done in Sect. 5.3, after some preliminaries in Sect. 5.1 and Sect. 5.2. Our second goal is to build the formal integral for the first Painlevé equation and, equivalently, the canonical normal form equation to which the first Painlevé equation is formally conjugated. This is what we do in Sect. 5.4. These informations will be used in a next chapter to investigate the resurgent structure for the first Painlevé equation.
KeywordsFormal Solution Formal Integral Formal Series Linear Differential Operator Newton Polygon
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