Euler-Maclaurin formula


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Euler-Maclaurin formula

[¦ȯi·lər mə′klȯr·ən ‚fȯr·myə·lə]
(mathematics)
A formula used in the numerical evaluation of integrals, which states that the value of an integral is equal to the sum of the value given by the trapezoidal rule and a series of terms involving the odd-numbered derivatives of the function at the end points of the interval over which the integral is evaluated.
References in periodicals archive ?
With the Euler-Maclaurin formula, Moak [6] obtained the following q-analogue of Stirling formula
In this paper, the Euler-Maclaurin formula is exploited to provide an expression for the q-factorial function as an infinite integral.
The Euler-Maclaurin formula provides a powerful connection between integrals and sums.
In mathematics, the Euler-Maclaurin formula provides a powerful connection between integrals and sums.
In the context of computing asymptotic expansions of sums and series, usually the most useful form of the Euler-Maclaurin formula is
15), however, the Euler-Maclaurin formula may be used to obtain a more easily evaluated, asymptotic expression for Q(A):