Monotonicity of the error term in Gauss-Turan quadratures for analytic functions

Abstract

For Gauss-Turan quadrature formulae with an even weight function on the interval [—1, 1] and functions analytic in regions of the complex plane which contain in their interiors a circle of radius greater than 1, the error term is investigated. In some particular cases we prove that the error decreases monotonically to zero. Also, for certain more general cases, we illustrate how to check numerically if this property holds. Some l^2-error estimates are considered.