### Abstract

Let w(z) be an arbitrary transcendental solution of the fourth (respectively, second) Painlevé equation. Concerning the frequency of poles in |z| ≤ r, it is shown that n(r,w) ≫ r^{2} (respectively, n(r,w) ≫ r^{3/2}), from which the growth estimate T(r,w) ≫ r ^{2} (respectively, T(r,w) ≫ r^{3/2}) immediately follows.

Original language | English |
---|---|

Pages (from-to) | 231-249 |

Number of pages | 19 |

Journal | Proceedings of the Edinburgh Mathematical Society |

Volume | 47 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2004 Feb 1 |

### Fingerprint

### Keywords

- Characteristic function
- Elliptic functions
- Growth order
- Painlevé transcendents

### ASJC Scopus subject areas

- Mathematics(all)