论文标题
Turán决定因素的正交多项式II的阳性率II
Positivity of Turán determinants for orthogonal polynomials II
论文作者
论文摘要
多项式$ p_n $正交在间隔$ [-1,1]上，$由$ p_n（1）= 1标准化，如果$ p_n^2（x）-p_ {n-1}（x）-p_ {n-1}（x）p_ {n+1}（x）（x）\ ge 0 $ for $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ x $ n $ x $ n $ n $ x $ n $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $我们给出了正交多项式的一般标准，以满足Turán的不平等。这基本上扩展了\ cite {szw}的结果。特别是，通过检查其复发关系，可以将结果应用于许多类别的正交多项式。
The polynomials $p_n$ orthogonal on the interval $[-1,1],$ normalized by $p_n(1)=1,$ satisfy Turán's inequality if $p_n^2(x)-p_{n-1}(x)p_{n+1}(x)\ge 0$ for $n\ge 1$ and for all $x$ in the interval of orthogonality. We give a general criterion for orthogonal polynomials to satisfy Turán's inequality. This extends essentially the results of \cite{szw}. In particular the results can be applied to many classes of orthogonal polynomials, by inspecting their recurrence relation.
