On the remainder term of Gauss-Radau quadratures for analytic functions

[摘要] For analytic functions the remainder term of Gauss-Radau quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points I and a sum of semi-axes q > 1 for the Chebyshev weight function of the second kind. Starting from explicit expressions of the corresponding kernels the location of their maximum modulus on ellipses is determined. The corresponding Gautschi's conjecture from [On the remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadratures, Rocky Mountain J. Math. 21 (1991), 209-226] is proved. (C) 2007 Elsevier B.V. All rights reserved.

[发布日期] 2008-09-01

[效力级别]  Proceedings Paper

[关键词] Gauss-Radau quadrature formula;Chebyshev weight function;error bound;remainder term for analytic functions;contour integral representation