The Euler-MacLaurin summation formula, the sampling theorem, and approximate integration over the real axis (Q790579)
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scientific article; zbMATH DE number 3848483
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Euler-MacLaurin summation formula, the sampling theorem, and approximate integration over the real axis |
scientific article; zbMATH DE number 3848483 |
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The Euler-MacLaurin summation formula, the sampling theorem, and approximate integration over the real axis (English)
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1983
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The Euler-MacLaurin summation formula is used to deduce the Shannon sampling series expansion, that is the Whittaker cardinal series for not necessarily band-limited functions, and to obtain error estimates for the numerical integration over the real axis by the trapezoidal rule for smooth functions which are not necessarily analytic.
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Euler-MacLaurin summation formula
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Whittaker-Shannon sampling theorem
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band-limited functions
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error estimates
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Whittaker cardinal series
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trapezoidal rule
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