A circular interpretation of the Euler–Maclaurin formula

Berrut, Jean-Paul

doi:10.1016/j.cam.2005.02.015

Back

Journal article

A circular interpretation of the Euler–Maclaurin formula

Berrut, Jean-Paul Department of Mathematics, University of Fribourg

2006

Published in:

Journal of Computational and Applied Mathematics. - 2006, vol. 189, no. 1-2, p. 375-386

English 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 quadrature error.

Faculty

Faculté des sciences et de médecine

Department

Département de Mathématiques

Language