Modified anti-Gauss and degree optimal average formulas for Gegenbauer measure

For the practical estimation of the error of Gauss quadrature rules, Gauss–Kronrod formulas are widely used; but, for the Gegenbauer measure, , real positive Gauss–Kronrod formulas do not exist for α>3 and n sufficiently large. Among the alternatives which are available in the literature, Gauss–Lobatto and anti-Gauss formulas are of particular interest. In this paper, using the modified anti-Gauss formulas introduced by Ehrich, we determine the degree optimal stratified extensions of Gauss–Gegenbauer formulas, and we investigate their properties.