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The Euler-MacLaurin summation formula, the sampling theorem, and approximate integration over the real axis. (English) Zbl 0534.65004

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.
Reviewer: R.Kreß

MSC:

65B15 Euler-Maclaurin formula in numerical analysis
41A55 Approximate quadratures
65D32 Numerical quadrature and cubature formulas
40A25 Approximation to limiting values (summation of series, etc.)
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