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The Euler-Maclaurin sum formula for a closed derivation

Part of: Approximations and expansions Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

John Boris Miller
John Boris Miller
Affiliation:
Department of Mathematics Monash UniversityClayton, Victoria 3168, Australia
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Abstract

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An operator form of the Euler-Maclaurin sum formula is obtained, expressing the sum of the Euler-Maclaurin infinite series in a closed derivation, whose spectrum is compact, not equal to {0}, and does not have 0 as a clusterpoint, as the difference between a summation operator and an antiderivation which is the local inverse of the derivation.

Keywords

Euler-Maclaurin formuladerivationantiderivationsummation operatorBaxter operator.

MSC classification

Secondary: 47B47: Commutators, derivations, elementary operators, etc. 41A58: Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 1 , August 1984 , pp. 128 - 138
Copyright
Copyright © Australian Mathematical Society 1984

References

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