Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2010
• Main Author: Roffelsen, P.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2010
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146510
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them / P. Roffelsen // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 13 назв. — англ.

We study the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlevé equation. Divisibility properties of the coefficients of these polynomials, concerning powers of 4, are obtained and we prove that the nonzero roots of the Yab...