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arXiv · 1208.2337

On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials

Pieter Roffelsen
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Abstract

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 this conjecture using an interlacing property between the roots of the Yablonskii-Vorob'ev polynomials. Furthermore we determine precisely the number of negative and the number of positive real roots of the nth Yablonskii-Vorob'ev polynomial.

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Pieter Roffelsen. 2012-12-14. On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials. https://doi.org/10.3842/sigma.2012.099

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