Explicit form of the Yablonskii - Vorob'ev polynomials

Details Explicit form of the Yablonskii - Vorob'ev polynomials Explicit form of the Yablonskii - Vorob'ev polynomials

2006-03-22

arxiv.org/abs/nlin/0603044v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

21 pages

Scientific paper

Special polynomials associated with rational solutions of the second
Painlev\'{e} equation and other members of its hierarchy are discussed. New
approach, which allows one to construct each polynomial is presented. The
structure of the polynomials is established. Formulas of their coefficients are
found. Correlations between the roots of every polynomial are obtained.

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