论文标题
雅各比多项式的渐近膨胀以及高级雅各比的节点和权重，在基本功能方面用于大程度和参数
Asymptotic expansions of Jacobi polynomials and of the nodes and weights of Gauss-Jacobi quadrature for large degree and parameters in terms of elementary functions
论文作者
论文摘要
Jacobi多项式的渐近近似是根据$ n $的基本功能和参数$α$和$β$给出的。从这些新结果中，得出了零的渐近扩展，并给出了在扩展中获得系数的方法。这些近似值可以用作迭代方法中的初始值，用于计算高度和参数的jacobi正交的节点。性能 用数值示例说明了用于计算这些高斯四肢的节点和权重的渐近近似值。
Asymptotic approximations of Jacobi polynomials are given in terms of elementary functions for large degree $n$ and parameters $α$ and $β$. From these new results, asymptotic expansions of the zeros are derived and methods are given to obtain the coefficients in the expansions. These approximations can be used as initial values in iterative methods for computing the nodes of Gauss--Jacobi quadrature for large degree and parameters. The performance of the asymptotic approximations for computing the nodes and weights of these Gaussian quadratures is illustrated with numerical examples.
