Geodesic
Irrationality of the Roots of the Yablonskii–Vorob'ev Polynomials and Relations between Them
Symmetry, integrability and geometry: methods and applications, Tome 6 (2010) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: second Painlevé equation; rational solutions; power series expansion; irrational roots; Yablonskii–Vorob'ev polynomials. 
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     title = {Irrationality of the {Roots} of the {Yablonskii{\textendash}Vorob'ev} {Polynomials} and {Relations} between {Them}},
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     url = {http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a94/}
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Pieter Roffelsen. Irrationality of the Roots of the Yablonskii–Vorob'ev Polynomials and Relations between Them. Symmetry, integrability and geometry: methods and applications, Tome 6 (2010). http://geodesic.mathdoc.fr/item/SIGMA_2010_6_a94/

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