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Zbl 1207.65003
Xu, Aimin; Cen, Zhongdi
Asymptotic behaviors of intermediate points in the remainder of the Euler-Maclaurin formula. (English)
[J] Abstr. Appl. Anal. 2010, Article ID 134392, 8 p. (2010). ISSN 1085-3375; ISSN 1687-0409/e

Summary: 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.

MSC 2000:: *65B15 Euler-Maclaurin formula
41A60 Asymptotic problems in approximation
41A55 Approximate quadratures
41A80 Remainders in approximation formulas

Keywords: Euler-Maclaurin formula; asymptotic expansion; remainder; composite trapezoidal rule

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