Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them
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| Creator |
Roffelsen, P.
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| 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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| Date |
2019-02-09T19:38:40Z
2019-02-09T19:38:40Z 2010 |
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| Type |
Article
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| Identifier |
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 http://dspace.nbuv.gov.ua/handle/123456789/146510 |
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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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