Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them
We study the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlevé equation. Divisibility properties of the coefficients of these polynomials, concerning powers of 4, are obtained and we prove that the nonzero roots of the Yab...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2010 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146510 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them / P. Roffelsen // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 13 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862640674130624512 |
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| author | Roffelsen, P. |
| author_facet | Roffelsen, P. |
| citation_txt | Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them / P. Roffelsen // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We study the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlevé equation. Divisibility properties of the coefficients of these polynomials, concerning powers of 4, are obtained and we prove that the nonzero roots of the Yablonskii-Vorob'ev polynomials are irrational. Furthermore, relations between the roots of these polynomials for consecutive degree are found by considering power series expansions of rational solutions of the second Painlevé equation.
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| first_indexed | 2025-12-01T03:38:39Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146510 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-01T03:38:39Z |
| publishDate | 2010 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Roffelsen, P. 2019-02-09T19:38:40Z 2019-02-09T19:38:40Z 2010 Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them / P. Roffelsen // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 13 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34M55 DOI:10.3842/SIGMA.2010.095 https://nasplib.isofts.kiev.ua/handle/123456789/146510 We study the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlevé equation. Divisibility properties of the coefficients of these polynomials, concerning powers of 4, are obtained and we prove that the nonzero roots of the Yablonskii-Vorob'ev polynomials are irrational. Furthermore, relations between the roots of these polynomials for consecutive degree are found by considering power series expansions of rational solutions of the second Painlevé equation. I wish to thank Erik Koelink for his enlightening discussions and introducing me to the world
 of the Painlev´e equations. I am also grateful to Peter Clarkson for his interest and useful links to the literature. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them Article published earlier |
| spellingShingle | Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them Roffelsen, P. |
| title | Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them |
| title_full | Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them |
| title_fullStr | Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them |
| title_full_unstemmed | Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them |
| title_short | Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them |
| title_sort | irrationality of the roots of the yablonskii-vorob'ev polynomials and relations between them |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146510 |
| work_keys_str_mv | AT roffelsenp irrationalityoftherootsoftheyablonskiivorobevpolynomialsandrelationsbetweenthem |