On Euler–Maclaurin formula

摘要

We use a simple approach to show that an Euler–Maclaurin like formula can be associated to any interpolatory quadrature rule. This result is obtained by successively adding correcting terms that are exact for polynomials of increasing degree. A decomposition of the coefficients of the Euler–Maclaurin formula in terms of the integral to compute and representations of powers of the nodes is pointed out. Optimal truncation error bounds are also obtained.