%0 Journal Article
%T Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them
%A Pieter Roffelsen
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2010
%I National Academy of Science of Ukraine
%X We study the Yablonskii-Vorob'ev polynomials, which are special polynomials used to represent rational solutions of the second Painlev¨¦ 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 Painlev¨¦ equation.
%K second Painlev¨¦ equation
%K rational solutions
%K power series expansion
%K irrational roots
%K Yablonskii-Vorob'ev polynomials
%U http://dx.doi.org/10.3842/SIGMA.2010.095