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

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  • Aimin Xu
  • Zhongdi Cen

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.

Suggested Citation

  • Aimin Xu & Zhongdi Cen, 2010. "Asymptotic Behaviors of Intermediate Points in the Remainder of the Euler-Maclaurin Formula," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-8, December.
    • Handle: RePEc:hin:jnlaaa:134392
    DOI: 10.1155/2010/134392
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