论文标题
经典正交多项式的渐近计算
Asymptotic computation of classical orthogonal polynomials
论文作者
论文摘要
经典的正交多项式（Hermite，Laguerre和Jacobi）参与了大量物理和工程应用。当需要大度$ n $时，使用递归来计算多项式不是计算的好策略，建议使用更有效的方法，例如使用渐近扩展。在本文中，我们概述了[8]中考虑的用于计算laguerre多项式的渐近扩展$ l^{（α）} _ n（x）$用于参数$α$的有界值。此外，我们展示了$ l^{（α）} _ n（x）$的渐近扩展的计算性能示例，适用于$α$和$ n $的大值。在[6]中使用了这种扩展作为获得零近似值的起点。最后，我们分析了[9]，[10]和[11]中考虑的扩展，以计算大型$ n $的雅各比多项式。
The classical orthogonal polynomials (Hermite, Laguerre and Jacobi) are involved in a vast number of applications in physics and engineering. When large degrees $n$ are needed, the use of recursion to compute the polynomials is not a good strategy for computation and a more efficient approach, such as the use of asymptotic expansions,is recommended. In this paper, we give an overview of the asymptotic expansions considered in [8] for computing Laguerre polynomials $L^{(α)}_n(x)$ for bounded values of the parameter $α$. Additionally, we show examples of the computational performance of an asymptotic expansion for $L^{(α)}_n(x)$ valid for large values of $α$ and $n$. This expansion was used in [6] as starting point for obtaining asymptotic approximations to the zeros. Finally, we analyze the expansions considered in [9], [10] and [11] to compute the Jacobi polynomials for large degrees $n$.
