The remainder term for analytic functions of Gauss-Radau and Gauss-Lobatto quadrature rules with multiple end points

摘要

A study is undertaken of the kernels in the contour integral representations of the remainder terms for Gauss-Radau and Gauss-Lobatto quadrature rules over the interval [−1, 1]. It is assumed that the respective end points in these rules have multiplicity two, and that integration is with respect to one of the four Chebyshev weight functions. Of particular interest is the location on the contour where the modulus of the kernel attains its maximum value. Only elliptic contours are considered having foci at the points ± 1.