Integral Error Representation of Hermite Interpolating Polynomial and Related Inequalities for Quadrature Formulae

We consider integral error representation related to the Hermite interpolating polynomial and derive some new estimations of the remainder in quadrature formulae of Hermite type, using Holder’s inequality and some inequalities for the Čebyšev functional. As a special case, generalizations for the zeros of orthogonal polynomials are considered

Estimates for the Gauss four-point formula for functions with low degree of smoothness

AbstractThe aim of this work is to derive the Gauss four-point quadrature formula using Euler-type identities. The advantage of this approach is that it enables us to obtain estimates of the error for functions with low degree of smoothness and also to produce quadrature formulae which contain values of derivatives at the end points of the interval