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

Shun Shimomura

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

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).

Original languageEnglish
Pages (from-to)231-247
Number of pages17
JournalForum Mathematicum
Volume16
Issue number2
Publication statusPublished - 2004

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M-function
Meromorphic
Proximity
Estimate

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Forum Mathematicum, Vol. 16, No. 2, 2004, p. 231-247.

Research output: Contribution to journalArticle

Shimomura, Shun. / Growth of modified Painlevé transcendents of the fifth and the third kind. In: Forum Mathematicum. 2004 ; Vol. 16, No. 2. pp. 231-247.
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