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

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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Main Author: Roffelsen, P.
Format: Article
Language:English
Published: Інститут математики НАН України 2012
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/149188
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spelling irk-123456789-1491882019-02-20T01:24:42Z On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials Roffelsen, P. 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. 2012 Article On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials / P. Roffelsen // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 8 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34M55 DOI: http://dx.doi.org/10.3842/SIGMA.2012.099 http://dspace.nbuv.gov.ua/handle/123456789/149188 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description 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.
format Article
author Roffelsen, P.
spellingShingle Roffelsen, P.
On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Roffelsen, P.
author_sort Roffelsen, P.
title On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials
title_short On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials
title_full On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials
title_fullStr On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials
title_full_unstemmed On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials
title_sort on the number of real roots of the yablonskii-vorob'ev polynomials
publisher Інститут математики НАН України
publishDate 2012
url http://dspace.nbuv.gov.ua/handle/123456789/149188
citation_txt On the Number of Real Roots of the Yablonskii-Vorob'ev Polynomials / P. Roffelsen // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 8 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT roffelsenp onthenumberofrealrootsoftheyablonskiivorobevpolynomials
first_indexed 2023-05-20T17:31:26Z
last_indexed 2023-05-20T17:31:26Z
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