Abstract
This chapter aims at introducing the reader to properties of the first Painleve equation and its general solution. The definition of the first Painleve equation is recalled (Sect. 2.1). We precise how the Painleve property translates for the first Painleve equation (Sect. 2.2), a proof of which being postponed to an appendix. We explain how the first Painleve equation also arises as a condition of isomonodromic deformations for a linear ODE (Sect. 2.3 and Sect. 2.4). Some symmetry properties are mentioned (Sect. 2.5). We spend some times describing the asymptotic behaviour at infinity of the solutions of the first Painleve equation and, in particular, we introduce the truncated solutions (Sect. 2.6). We eventually briefly comment the importance of the first Painleve transcendents for models in physics (Sect. 2.7).
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