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Asymptotic behaviors of intermediate points in the remainder of the Euler-Maclaurin formula. (English) Zbl 1207.65003
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.

65B15Euler-Maclaurin formula (numerical analysis)
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
41A55Approximate quadratures
41A80Remainders in approximation formulas
Full Text: DOI EuDML
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