论文标题
在雅各比多项式的极端零上
On the extreme zeros of Jacobi polynomials
论文作者
论文摘要
通过将Euler--rayleigh方法应用于雅各比多项式的特定表示，我们为其最大的零零获得了新的界限。特别是，我们以$ 1-x_ {nn}^2（λ）$的价格得出上限和下限，其中$ x_ {nn}（λ）$是$ n $ th $ n $ th超球$ p_n^{（λ）} $的最大零。对于每个固定的$λ> -1/2 $，我们的上限和下限$ 1-x_ {nn}^2（λ）$的比率不超过$ 1.6 $。本文是[1]的延续。
By applying the Euler--Rayleigh methods to a specific representation of the Jacobi polynomials as hypergeometric functions, we obtain new bounds for their largest zeros. In particular, we derive upper and lower bound for $1-x_{nn}^2(λ)$, with $x_{nn}(λ)$ being the largest zero of the $n$-th ultraspherical polynomial $P_n^{(λ)}$. For every fixed $λ>-1/2$, the limit of the ratio of our upper and lower bounds for $1-x_{nn}^2(λ)$ does not exceed $1.6$. This paper is a continuation of [1].
