On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2012
• 1. Verfasser: Roffelsen, P.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2012
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/149188
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials / P. Roffelsen // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 8 назв. — англ.

We study the real roots of the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlevé equation. It has been conjectured that the number of real roots of the nth Yablonskii-Vorob'ev polynomial equals [(n+1)/2]. We prove thi...