On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials
We study the real roots of the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlevé equation. It has been conjectured that the number of real roots of the nth Yablonskii-Vorob'ev polynomial equals [(n+1)/2]. We prove thi...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2012-12-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://dx.doi.org/10.3842/SIGMA.2012.099 |