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

Shun Shimomura

doi:10.1515/form.2004.011

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

Shun Shimomura

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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
DOIs	https://doi.org/10.1515/form.2004.011
Publication status	Published - 2004 Jan 1

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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abstract = "For a solution y(x) of the fifth (resp. third) Painlev{\'e} 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).",

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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).

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

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