On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2012 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149188 |
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| Cite this: | 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. |
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Roffelsen, P. 2019-02-19T18:23:01Z 2019-02-19T18:23:01Z 2012 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 https://nasplib.isofts.kiev.ua/handle/123456789/149188 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials |
| spellingShingle |
On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials Roffelsen, P. |
| title_short |
On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials |
| title_full |
On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials |
| title_fullStr |
On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials |
| title_full_unstemmed |
On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials |
| title_sort |
on the number of real roots of the yablonskii-vorob'ev polynomials |
| author |
Roffelsen, P. |
| author_facet |
Roffelsen, P. |
| publishDate |
2012 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/149188 |
| citation_txt |
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. |
| work_keys_str_mv |
AT roffelsenp onthenumberofrealrootsoftheyablonskiivorobevpolynomials |
| first_indexed |
2025-12-07T19:25:52Z |
| last_indexed |
2025-12-07T19:25:52Z |
| _version_ |
1850878777133891584 |