Weighted averaged Gaussian quadrature rules for modified Chebyshev measures

This paper is concerned with the approximation of integrals of a real-valued integrand over the interval [−1,1] by Gauss quadrature. The averaged and optimal averaged quadrature rules ([13], [21]) provide a convenient method for approximating the error in the Gauss quadrature. However, they are applicable to all integrands that are continuous on the interval [−1,1] only if their nodes are internal, i.e. if they belong to this interval.