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A circular interpretation of the Euler–Maclaurin formula

Berrut, Jean-Paul

In: Journal of Computational and Applied Mathematics, 2006, vol. 189(1-2), p. 375-386

The present work makes the case for viewing the Euler–Maclaurin formula as an expression for the effect of a jump on the accuracy of Riemann sums on circles and draws some consequences thereof, e.g., when the integrand has several jumps. On the way we give a construction of the Bernoulli polynomials tailored to the proof of the formula and we show how extra jumps may lead to a smaller...