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The summation formulae of Euler-Maclaurin, Abel-Plana, Poisson, and their interconnections with the approximate sampling formula of signal analysis. (English) Zbl 1225.65007

The paper is concerned with the two summation formulae of Euler-Maclaurin and Abel-Plana of numerical analysis, that of Poisson of Fourier analysis, and the approximate sampling formula of signal analysis. The results are brought into connection with four propositions of mathematical analysis for band limited functions, including the Whittaker-Kostelnikov-Shannon sampling theorem.

MSC:

65B15 Euler-Maclaurin formula in numerical analysis
65D32 Numerical quadrature and cubature formulas
94A20 Sampling theory in information and communication theory
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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