Asymptotic Expansions of Jacobi Polynomials for Large Values of β and of Their Zeros

被引：1

作者：

Gil, Amparo ^{[1
]}

Segura, Javier ^{[1
]}

Temme, Nico M. ^{[2
,3
]}

机构：

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

[2] IAA, 1825 BD 25, Alkmaar, Netherlands

[3] CWI, Sci Pk 123, NL-1098 XG Amsterdam, Netherlands

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2018年 / 14卷

关键词：

Jacobi polynomial; large-beta asymptotics; Laguerre polynomial;

D O I：

10.3842/SIGMA.2018.073

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Asymptotic approximations of Jacobi polynomials are given for large values of the beta-parameter and of their zeros. The expansions are given in terms of Laguerre polynomials and of their zeros. The levels of accuracy of the approximations are verified by numerical examples.

引用

页数：9

共 4 条

[1] ASYMPTOTIC BEHAVIOUR OF JACOBI POLYNOMIALS AND THEIR ZEROS [J].

Dimitrov, Dimitar K. ;

dos Santos, Eliel J. C. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (02) :535-545

[2]

Gil A., ARXIV180407076

[3] Asymptotic Approximations to the Nodes and Weights of Gauss-Hermite and Gauss-Laguerre Quadratures [J].

Gil, Amparo ;

Segura, Javier ;

Temme, Nico M. .

STUDIES IN APPLIED MATHEMATICS, 2018, 140 (03) :298-332

[4]

Koornwinder T.H., 2010, NIST Handbook of Mathematical Functions. Ed. by

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