### 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 |

### Fingerprint

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*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

**Generalities on the Painlevé equations.** / Guest, Martin; Hertling, Claus.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

}

TY - CHAP

T1 - Generalities on the Painlevé equations

AU - Guest, Martin

AU - Hertling, Claus

PY - 2017

Y1 - 2017

N2 - The Painlevé equations are six families PI, PII, PIII, PIV, PV, PVI of second order differential equations in U = ℂ, ℂ* = ℂ -{0}, or ℂ - {0, 1} of the form fxx = R(x,f,fx) where R is holomorphic for x ∈ U and rational in f and fx.

AB - The Painlevé equations are six families PI, PII, PIII, PIV, PV, PVI of second order differential equations in U = ℂ, ℂ* = ℂ -{0}, or ℂ - {0, 1} of the form fxx = R(x,f,fx) where R is holomorphic for x ∈ U and rational in f and fx.

UR - http://www.scopus.com/inward/record.url?scp=85032027445&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85032027445&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-66526-9_9

DO - 10.1007/978-3-319-66526-9_9

M3 - Chapter

AN - SCOPUS:85032027445

VL - 2198

T3 - Lecture Notes in Mathematics

SP - 87

EP - 92

BT - Lecture Notes in Mathematics

PB - Springer Verlag

ER -