Yablonskiii-Vorob 'ev多项式根的无理性及其关系
Irrationality of the Roots of the Yablonskii-Vorob'ev Polynomials and Relations between Them
摘要：
研究了第二类Painlevé方程的有理解的特殊多项式--Yablonskiii-Vorob 'ev多项式。这些多项式的系数的整除性质，涉及4的权力，我们得到的Yablonskiii-Vorob 'ev多项式的非零根是无理的。进一步，通过对第二类Painlevé方程的有理解进行幂级数展开，得到了这些多项式的连续次数根之间的关系.
英文摘要：
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.
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