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

dc.contributor.author	Roffelsen, P.
dc.date.accessioned	2019-02-19T18:23:01Z
dc.date.available	2019-02-19T18:23:01Z
dc.date.issued	2012
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 34M55
dc.identifier.other	DOI: http://dx.doi.org/10.3842/SIGMA.2012.099
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/149188
dc.description.abstract	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 this conjecture using an interlacing property between the roots of the Yablonskii-Vorob'ev polynomials. Furthermore we determine precisely the number of negative and the number of positive real roots of the nth Yablonskii-Vorob'ev polynomial.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA