Abstract
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 Painleve 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 Painleve equation and, equivalently, the canonical normal form equation to which the first Painleve 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 Painleve equation.
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