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
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.
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收藏
页数:9
相关论文
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