Internality of generalized averaged Gaussian quadrature rules and truncated variants for measures induced by Chebyshev polynomials

Abstract

Generalized averaged Gaussian quadrature rules and truncated variants associated with a nonnegative measure with support on a real open interval {t : a lt t lt b} may have nodes outside this interval, in other words the rules may fail to be internal. Such rules cannot be applied when the integrand is defined on {t : a lt t lt b} only. This paper investigates whether generalized averaged Gaussian quadrature rules and truncated variants are internal for measures induced by Chebyshev polynomials. Our results complement those of Notaris [13] for Gauss-Kronrod quadrature formulas for the same kind of measures.