Uniform relations between the Gauss–Legendre nodes and weights

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 origi...

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Detalhes bibliográficos
Autores: López Pouso, Óscar, Segura Sala, José Javier|||0000-0002-0841-5636
Tipo de documento: artigo
Data de publicação:2025
País:España
Recursos:Universidad de Cantabria (UC)
Repositório:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglês
OAI Identifier:oai:repositorio.unican.es:10902/38142
Acesso em linha:https://hdl.handle.net/10902/38142
Access Level:Acceso aberto
Palavra-chave:Gauss–Legendre quadrature
Asymptotic expansions
Uniform relations
Finite difference schemes
Angular Fokker–Planck diffusion operator
Descrição
Resumo: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.