Abstract
The internality of quadrature rules ensures the approximation of integrals whose integrands are defined only on the support interval of corresponding measure. Previous studies addressed the internality of averaged Gauss and optimal averaged Gauss quadratures for Jacobi measures modified by a linear factor or divisor. In this paper we extend the analysis to Jacobi measures modified by a quadratic factor or divisor of the form $(t - z)(t - \overline{z})$, where $z = x + iy$ with $y> 0$. We prove that, under certain conditions and for sufficiently many nodes, these quadratures are internal. Special focus is given to Chebyshev measures of the first and third kinds.
