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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:494

Article

Gil, A.¹  Segura, J.²  Temme, N. M.^3,4 

[1] Univ Cantabria, ETSI Caminos, Dept Matemat Aplicada & CC Computac, Santander 39005, Spain

[2] Univ Cantabria, Dept Matemat Estadist & Computac, Santander 39005, Spain

[3] IAA, NL-1825 BD Alkmaar 25, Netherlands

[4] Ctr Wiskunde Informat CWI, Sci Pk 123, NL-1098 XG Amsterdam, Netherlands

关键词: Jacobi polynomials;    Asymptotic expansion;    Gauss quadrature;    Estimates of zeros of Jacobi;    polynomials;   

DOI  :  10.1016/j.jmaa.2020.124642

来源: Elsevier

【 摘 要 】

Asymptotic approximations of Jacobi polynomials are given in terms of elementary functions for large degree n and parameters alpha and beta. 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. (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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