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

INTEGRAL ERROR REPRESENTATION OF HERMITE INTERPOLATING POLYNOMIAL AND RELATED INEQUALITIES FOR QUADRATURE FORMULAE