### Abstract

For a solution y(x) of the fifth (resp. third) Painlevé equation, the function w(z) = y(e^{z}) is meromorphic in ℂ. It is proved that T(r, w)=O(e^{Λr}) (resp. O(e^{Λr})), where Λ (resp. Λ) is some positive number independent of w(z). Moreover, using this result, we estimate the proximity functions m(r, w), m(r, 1/(w-c)) (cℂ).

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

Pages (from-to) | 231-247 |

Number of pages | 17 |

Journal | Forum Mathematicum |

Volume | 16 |

Issue number | 2 |

Publication status | Published - 2004 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Forum Mathematicum*,

*16*(2), 231-247.

**Growth of modified Painlevé transcendents of the fifth and the third kind.** / Shimomura, Shun.

Research output: Contribution to journal › Article

*Forum Mathematicum*, vol. 16, no. 2, pp. 231-247.

}

TY - JOUR

T1 - Growth of modified Painlevé transcendents of the fifth and the third kind

AU - Shimomura, Shun

PY - 2004

Y1 - 2004

N2 - For a solution y(x) of the fifth (resp. third) Painlevé equation, the function w(z) = y(ez) is meromorphic in ℂ. It is proved that T(r, w)=O(eΛr) (resp. O(eΛr)), where Λ (resp. Λ) is some positive number independent of w(z). Moreover, using this result, we estimate the proximity functions m(r, w), m(r, 1/(w-c)) (cℂ).

AB - For a solution y(x) of the fifth (resp. third) Painlevé equation, the function w(z) = y(ez) is meromorphic in ℂ. It is proved that T(r, w)=O(eΛr) (resp. O(eΛr)), where Λ (resp. Λ) is some positive number independent of w(z). Moreover, using this result, we estimate the proximity functions m(r, w), m(r, 1/(w-c)) (cℂ).

UR - http://www.scopus.com/inward/record.url?scp=1042279096&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1042279096&partnerID=8YFLogxK

M3 - Article

VL - 16

SP - 231

EP - 247

JO - Forum Mathematicum

JF - Forum Mathematicum

SN - 0933-7741

IS - 2

ER -