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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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Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them
Інший ID:
2010 Mathematics Subject Classification: 34M55
DOI:10.3842/SIGMA.2010.095
DOI:10.3842/SIGMA.2010.095
Посилання:
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.
Підтримка:
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.
Дата:
2010
Переглядів:
502
Завантажень:
262
Анотація:
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.
