ON A QUADRATURE FORMULA WITH FIRST DERIVATIVE AND ITS DEGREE OF ACCURACY

摘要

This paper develops a clase of quadrature formula with first derivativesIt is demonstrated that its degree of accuracy is not less than 2k+1 for a set of distinct nodes {x0,x1,...,xn} over interval [a,b],and just only 2k+1 for equally spaced nodes.Far overcoming the shortcoming of involving a great number of manual computations for the integration rules of the Hermitian interpolation formula,some simple formulas for computing automatically βi,γi and E [f] by computer are given,especially for equally spaced nodes.