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ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2010, том 6, 095, 11 стр. (Mi sigma553)

Эта публикация цитируется в 4 статьях

Irrationality of the Roots of the Yablonskii–Vorob'ev Polynomials and Relations between Them

Pieter Roffelsen

Radboud Universiteit Nijmegen, IMAPP, FNWI, Heyendaalseweg 135, 6525 AJ Nijmegen, the Netherlands

Аннотация: 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.

Ключевые слова: second Painlevé equation; rational solutions; power series expansion; irrational roots; Yablonskii–Vorob'ev polynomials.

MSC: 34M55

Поступила: 13 ноября 2010 г.; в окончательном варианте 8 декабря 2010 г.; опубликована 14 декабря 2010 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2010.095



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