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...
| Autores: | , |
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| 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 |
| 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. |
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