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 language | English |
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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 |
Keywords
- Characteristic function
- Elliptic functions
- Growth order
- Painlevé transcendents
ASJC Scopus subject areas
- Mathematics(all)