Abstract and Applied Analysis

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

Aimin Xu and Zhongdi Cen

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 134392, 8 pages.

Dates
First available in Project Euclid: 12 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1313170932

Digital Object Identifier
doi:10.1155/2010/134392

Mathematical Reviews number (MathSciNet)
MR2746010

Zentralblatt MATH identifier
1207.65003

Citation

Xu, Aimin; Cen, Zhongdi. Asymptotic Behaviors of Intermediate Points in the Remainder of the Euler-Maclaurin Formula. Abstr. Appl. Anal. 2010 (2010), Article ID 134392, 8 pages. doi:10.1155/2010/134392. https://projecteuclid.org/euclid.aaa/1313170932


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