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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| Дата: | 2012 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149188 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1491882019-02-20T01:24:42Z On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials Roffelsen, P. 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. 2012 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Roffelsen, P. |
| spellingShingle |
Roffelsen, P. On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Roffelsen, P. |
| author_sort |
Roffelsen, P. |
| title |
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_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 |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT roffelsenp onthenumberofrealrootsoftheyablonskiivorobevpolynomials |
| first_indexed |
2023-05-20T17:31:26Z |
| last_indexed |
2023-05-20T17:31:26Z |
| _version_ |
1796153484890865664 |