Asymptotic expansions of Jacobi polynomials and of the nodes and weights of Gauss-Jacobi quadrature for large degree and parameters in terms of elementary functions

DOI10.1016/j.jmaa.2020.124642zbMath1461.65030arXiv2007.10748OpenAlexW3089871805MaRDI QIDQ2227589

Amparo Gil, Javier Segura, Nico M. Temme

Publication date: 15 February 2021

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.10748

zbMATH Keywords

asymptotic expansionJacobi polynomialsGauss quadratureestimates of zeros of Jacobi polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Numerical quadrature and cubature formulas (65D32)

Related Items (3)

Asymptotic computation of classical orthogonal polynomials ⋮ Fast and reliable high-accuracy computation of Gauss-Jacobi quadrature ⋮ Chebyshev polynomials of sixth kind for solving nonlinear fractional PDEs with proportional delay and its convergence analysis

Uses Software

• DLMF
• FastGaussQuadrature

Cites Work

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• Approximations of orthogonal polynomials in terms of Hermite polynomials
• Asymptotic expansions of Jacobi polynomials for large values of \(\beta\) and of their zeros
• Fast, reliable and unrestricted iterative computation of Gauss-Hermite and Gauss-Laguerre quadratures
• Asymptotic behaviour of Jacobi polynomials and their zeros
• Fast computation of Gauss quadrature nodes and weights on the whole real line
• Iteration-Free Computation of Gauss--Legendre Quadrature Nodes and Weights
• Reliable Computation of the Zeros of Solutions of Second Order Linear ODEs Using a Fourth Order Method
• Asymptotic Methods for Integrals
• Whittaker functions with both parameters large: uniform approximations in terms of parabolic cylinder functions
• Noniterative Computation of Gauss--Jacobi Quadrature
• Asymptotic Approximations to the Nodes and Weights of Gauss–Hermite and Gauss–Laguerre Quadratures
• Fast and Accurate Computation of Gauss--Legendre and Gauss--Jacobi Quadrature Nodes and Weights

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