Euler Polynomials and the Related Quadrature Rule

Abstract

The use of Euler polynomials and Euler numbers allows us to construct a quadrature rule similar to the well-known Euler–MacLaurin quadrature formula, using Euler (instead of Bernoulli) numbers, and even (instead of odd) order derivatives of a given function evaluated at the extrema of the considered interval. An expression of the remainder term and numerical examples are also given.