Internality of generalized averaged Gaussian quadrature rules and truncated variants for modified Chebyshev measures of the second kind

Abstract

Generalized averaged Gaussian quadrature rules associated with some measure, and truncated variants of these rules, can be used to estimate the error in Gaussian quadrature rules. However, the former quadrature rules may have nodes outside the interval of integration and, therefore, it may not be possible to apply them when the integrand is defined on the interval of integration only. This paper investigates whether generalized averaged Gaussian quadrature rules associated with modified Chebyshev measures of the second kind, and truncated variants of these rules, are internal, i.e. if all nodes of these quadrature rules are in the interval of integration.