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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

Abstract: Asymptotic approximations of Jacobi polynomials are given in terms of elementary functions for large degree n and parameters ? and ?. From these new results, asymptotic expansions of the zeros are derived and methods are given to obtain the coefficients in the expansions. These approximations can be used as initial values in iterative methods for computing the nodes of Gauss?Jacobi quadrature for large degree and parameters. The performance of the asymptotic approximations for computing the nodes and weights of these Gaussian quadratures is illustrated with numerical examples.

Otras publicaciones de la misma revista o congreso con autores/as de la Universidad de Cantabria

 Fuente: Journal of Mathematical Analysis and Applications, 2021, 494(2), 124642

Editorial: Academic Press Inc.

 Fecha de publicación: 15/02/2021

Nº de páginas: 14

Tipo de publicación: Artículo de Revista

 DOI: 10.1016/j.jmaa.2020.124642

ISSN: 0022-247X,1096-0813

Proyecto español: MTM2015-67142-P

Url de la publicación: https://doi.org/10.1016/j.jmaa.2020.124642

Autores/as

TEMME, NICO M.