Work

Uniform relations between the Gauss–Legendre nodes and weights

Year: 2025

Type: article

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 $(-1,1)$ . 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.

Source: Journal of Inequalities and Applications

DOI: 10.1186/s13660-025-03283-w

Authors: Óscar López Pouso, Javier Segura

Institutions: Universidade de Santiago de Compostela, Universidad de Cantabria

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,190

Funders: Ministerio de Ciencia e Innovación, Xunta de Galicia, Agencia Estatal de Investigación