On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials
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| Creator |
Roffelsen, P.
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| Description |
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.
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| Date |
2019-02-19T18:23:01Z
2019-02-19T18:23:01Z 2012 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2010 Mathematics Subject Classification: 34M55 DOI: http://dx.doi.org/10.3842/SIGMA.2012.099 http://dspace.nbuv.gov.ua/handle/123456789/149188 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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