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періодичних видань НАН України
періодичних видань НАН України
Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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| dc.contributor.author | Roffelsen, P. | |
| dc.date.accessioned | 2019-02-09T19:38:40Z | |
| dc.date.available | 2019-02-09T19:38:40Z | |
| dc.date.issued | 2010 | |
| dc.identifier.citation | 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. | uk_UA |
| dc.identifier.issn | 1815-0659 | |
| dc.identifier.other | 2010 Mathematics Subject Classification: 34M55 | |
| dc.identifier.other | DOI:10.3842/SIGMA.2010.095 | |
| dc.identifier.uri | http://dspace.nbuv.gov.ua/handle/123456789/146510 | |
| dc.description.abstract | 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. | uk_UA |
| dc.description.sponsorship | 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. | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | Інститут математики НАН України | uk_UA |
| dc.relation.ispartof | Symmetry, Integrability and Geometry: Methods and Applications | |
| dc.title | Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them | uk_UA |
| dc.type | Article | uk_UA |
| dc.status | published earlier | uk_UA |
