### Abstract

The Painlevé equations are six families P_{I}, P_{II}, P_{III}, P_{IV}, P_{V}, P_{VI} of second order differential equations in U = ℂ, ℂ* = ℂ -{0}, or ℂ - {0, 1} of the form f_{xx} = R(x,f,f_{x}) where R is holomorphic for x ∈ U and rational in f and f_{x}.

Original language | English |
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Title of host publication | Lecture Notes in Mathematics |

Publisher | Springer Verlag |

Pages | 87-92 |

Number of pages | 6 |

Volume | 2198 |

DOIs | |

Publication status | Published - 2017 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 2198 |

ISSN (Print) | 0075-8434 |

### ASJC Scopus subject areas

- Algebra and Number Theory

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## Cite this

Guest, M., & Hertling, C. (2017). Generalities on the Painlevé equations. In

*Lecture Notes in Mathematics*(Vol. 2198, pp. 87-92). (Lecture Notes in Mathematics; Vol. 2198). Springer Verlag. https://doi.org/10.1007/978-3-319-66526-9_9