Asymptotic representation of the weights in the Gauss quadrature formula
type: Item
instance of: scholarly article
title: Asymptotic representation of the weights in the Gauss quadrature formula
zbMATH Open document ID: 0733.41033
DOI: 10.1007/BF01163817
author: A. L. Marshak
published in: Mathematical Notes
publication date: 1990-01-01T00:00:00Z
review text: Consider the quadrature formula of Gauss-Jacobi for Legendre's weight dx on [0,1]. Given n, let \(\lambda_{n,j}\), \(j=1,2,...,n\), be the Christoffel coefficient corresponding to the zero \(x_{n,j}\), \(j=1,2,...,n\), of the nth Legendre orthogonal polynomial. Set cos \(\theta\) \({}_{n,j}=x_{n,j}\). It is proved that \[ \lambda_{n,j}=\frac{\pi}{2n+1}\sin \theta_{n,j}+O(\frac{1}{n^ 3\sin \theta_{n,j}}). \]
Mathematics Subject Classification ID: 41A55
zbMATH DE Number: 4212703
zbMATH Keywords: quadrature formula
zbMATH Keywords: Legendre's weight
reviewed by: Guillermo López Lagomasino
MaRDI profile type: Publication
cites work: Q3847247
cites work: Error Bounds for Gaussian Quadrature and Weighted-$L^1$ Polynomial Approximation
cites work: Q5533728
full work available at URL: https://doi.org/10.1007/bf01163817
OpenAlex ID: W2030705039
description: scientific article; zbMATH DE number 4212703