Asymptotic Behaviors of Intermediate Points in the Remainder ofthe Euler-Maclaurin Formula

摘要

The Euler-Maclaurin formula is a very useful tool in calculus and numerical analysis. Thispaper is devoted to asymptotic expansion of the intermediate points in the remainder of thegeneralized Euler-Maclaurin formula when the length of the integral interval tends to be zero. In the special case we also obtain asymptotic behavior of the intermediate point in the remainderof the composite trapezoidal rule.