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

作者：Xiang, Shuhuang^*

来源：Journal of Mathematical Analysis and Applications, 2012, 393(2): 434-444.

DOI：10.1016/j.jmaa.2012.03.056

• Asymptotic
• Laguerre polynomial
• Hermite polynomial
• Truncated error
• Gauss-type quadrature

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.

• 出版日期2012-9-15
• 单位中南大学