Uniform relations between the Gauss–Legendre nodes and weights

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 ) $(-1,1)$ . These properties are supported by strong asymptotic evidence. The study of...

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Bibliographic Details

Published in:	Journal of Inequalities and Applications
Main Authors:	Óscar López Pouso, Javier Segura
Format:	Article
Language:	English
Published:	SpringerOpen 2025-03-01
Subjects:	Gauss–Legendre quadrature Asymptotic expansions Uniform relations Finite difference schemes Angular Fokker–Planck diffusion operator
Online Access:	https://doi.org/10.1186/s13660-025-03283-w