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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149188 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862731437886668800 |
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| author | Roffelsen, P. |
| author_facet | Roffelsen, P. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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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| first_indexed | 2025-12-07T19:25:52Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149188 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:25:52Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials Roffelsen, P. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149188 |
| work_keys_str_mv | AT roffelsenp onthenumberofrealrootsoftheyablonskiivorobevpolynomials |