Copyright © 2010 Aimin Xu and Zhongdi Cen. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The Euler-Maclaurin formula is a very useful tool in calculus and numerical analysis. This
paper is devoted to asymptotic expansion of the intermediate points in the remainder of the
generalized 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 remainder
of the composite trapezoidal rule.