Lower estimates for the growth of the fourth and the second painlevé transcendents

Shun Shimomura

Research output: Contribution to journal › Article

5 Citations (Scopus)

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) ≫ r2 (respectively, n(r,w) ≫ r3/2), from which the growth estimate T(r,w) ≫ r 2 (respectively, T(r,w) ≫ r3/2) immediately follows.

Original languageEnglish
Pages (from-to)231-249
Number of pages19
JournalProceedings of the Edinburgh Mathematical Society
Volume47
Issue number1
DOIs
Publication statusPublished - 2004 Feb

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Transcendental
Immediately
Pole
Arbitrary
Estimate

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Lower estimates for the growth of the fourth and the second painlevé transcendents. / Shimomura, Shun.

In: Proceedings of the Edinburgh Mathematical Society, Vol. 47, No. 1, 02.2004, p. 231-249.

Research output: Contribution to journal › Article

Shimomura, S 2004, 'Lower estimates for the growth of the fourth and the second painlevé transcendents', Proceedings of the Edinburgh Mathematical Society, vol. 47, no. 1, pp. 231-249. https://doi.org/10.1017/S0013091503000440
Shimomura S. Lower estimates for the growth of the fourth and the second painlevé transcendents. Proceedings of the Edinburgh Mathematical Society. 2004 Feb;47(1):231-249. https://doi.org/10.1017/S0013091503000440
Shimomura, Shun. / Lower estimates for the growth of the fourth and the second painlevé transcendents. In: Proceedings of the Edinburgh Mathematical Society. 2004 ; Vol. 47, No. 1. pp. 231-249.
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