Abstract Let Wα,ρ = xα(1 – x2)ρe–Q(x), where α > – 12 $\begin{array}{} \displaystyle \frac12 \end{array}$ and Q is continuous and increasing on [0, 1), with limit ∞ at 1. This paper deals with orthogonal polynomials for the weights Wα,ρ2 $\begin{array}{} \displaystyle W^2_{\alpha, \rho} \end{array}$ and gives bounds on orthogonal polynomials, zeros, Christoffel functions and Markov inequalities. In addition, estimates of fundamental polynomials of Lagrange interpolation at the zeros of the orthogonal polynomial and restricted range inequalities are obtained.

中文翻译：

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[0, 1) 上指数权重 x2α(1 – x2)2ρe–2Q(x) 的正交多项式

摘要 让 Wα,ρ = xα(1 – x2)ρe–Q(x)，其中 α > – 12 $\begin{array}{} \displaystyle \frac12 \end{array}$ 并且 Q 是连续的并且在 [ 0, 1)，极限 ∞ 为 1。 本文处理权重 Wα,ρ2 $\begin{array}{} \displaystyle W^2_{\alpha, \rho} \end{array}$ 和给出正交多项式、零点、克里斯多夫函数和马尔可夫不等式的界限。此外，还获得了正交多项式零点处的拉格朗日插值基本多项式和有限范围不等式的估计。