Abstract and Applied Analysis
Volume 2010 (2010), Article ID 134392, 8 pages
doi:10.1155/2010/134392
Research Article

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

Aimin Xu and Zhongdi Cen

Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, China

Received 23 June 2010; Revised 22 October 2010; Accepted 5 December 2010

Academic Editor: Dumitru Baleanu

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.

Abstract

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.