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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 095, 11 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.095 (Mi sigma553) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Irrationality of the Roots of the Yablonskii–Vorob'ev Polynomials and Relations between Them

Pieter Roffelsen

Radboud Universiteit Nijmegen, IMAPP, FNWI, Heyendaalseweg 135, 6525 AJ Nijmegen, the Netherlands
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DOI: https://doi.org/10.3842/SIGMA.2010.095
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.
Keywords: second Painlevé equation; rational solutions; power series expansion; irrational roots; Yablonskii–Vorob'ev polynomials.
Received: November 13, 2010; in final form December 8, 2010; Published online December 14, 2010
Bibliographic databases:
Document Type: Article
MSC: 34M55
Language: English
Citation: Pieter Roffelsen, “Irrationality of the Roots of the Yablonskii–Vorob'ev Polynomials and Relations between Them”, SIGMA, 6 (2010), 095, 11 pp.
Citation in format AMSBIB
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