Asymptotics on Laguerre or Hermite polynomial expansions and their applications in Gauss quadrature

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:393

Article

Xiang, Shuhuang

关键词: Asymptotic;    Laguerre polynomial;    Hermite polynomial;    Truncated error;    Gauss-type quadrature;   

DOI  :  10.1016/j.jmaa.2012.03.056

来源: Elsevier

【 摘 要 】

In this paper, we present asymptotic analysis on the coefficients of functions expanded in forms of Laguerre or Hermite polynomial series, which shows the decay of the coefficients and derives new error bounds on the truncated series. Moreover, by applying the asymptotics, new estimates on the errors for Gauss-Laguerre, Radau-Laguerre and Gauss-Hermite quadrature are deduced. These results show that Gauss-Laguerre-type and Gauss-Hermite-type quadratures are nearly of same convergence rates. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free