Error bounds for Gauss-Jacobi quadrature rules

Gaussian quadrature has been extensively studied in literature and several error estimates have been proved under dierent smoothness assumptions of the integrand function. In this talk we are going to state a general error estimate for Gauss-Jacobi quadrature, based on the weighted moduli of smoothness introduced by Z. Ditzian and V. Totik in [1]. Such estimate improves a previous result in [1, Theorem 7.4.1] and it includes several error bounds from literature as particular cases. Its proof has been achieved by using certain delayed means of the Fourier projections (de la Vallee Poussin means), which approximation properties will be also discussed. References [1] Z.Ditzian, V.Totik, Moduli of smoothness, SCMG Springer{Verlag, New York, 1987.