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
-
- English
- Classification
- Mathematics
- License
- License undefined
- Identifiers
-
- RERO DOC 5753
- DOI 10.1016/j.cam.2005.02.015
- Persistent URL
- https://folia.unifr.ch/unifr/documents/300205
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