Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them
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 Yab...
Saved in:
Date: | 2010 |
---|---|
Main Author: | |
Format: | Article |
Language: | English |
Published: |
Інститут математики НАН України
2010
|
Series: | Symmetry, Integrability and Geometry: Methods and Applications |
Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/146510 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
Cite this: | Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them / P. Roffelsen // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 13 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of UkraineSummary: | 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. |
---|