Uniform relations between the Gauss-Legendre nodes and weights
Numerical Analysis
2025-01-23 v3 Numerical Analysis
Classical Analysis and ODEs
Abstract
Four different relations between the Legendre nodes and weights are presented which, unlike the circle and trapezoid theorems for Gauss-Legendre quadrature, hold uniformly in the whole interval . These properties are supported by strong asymptotic evidence. The study of these results was originally motivated by the role some of them play in certain finite difference schemes used in the discretization of the angular Fokker-Planck diffusion operator.
Cite
@article{arxiv.2305.19128,
title = {Uniform relations between the Gauss-Legendre nodes and weights},
author = {Óscar López Pouso and Javier Segura},
journal= {arXiv preprint arXiv:2305.19128},
year = {2025}
}