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Unlike computation of arbitrary integrals, however, Fourier-series integrations for periodic functions (like , by construction), up to the Nyquist frequency , are accurately computed by the equally spaced and equally weighted points for (except the endpoints are weighted by 1/2, to avoid double-counting, equivalent to the trapezoidal rule or the Euler–Maclaurin formula).
The notion of quasi-periodic functions was generalised still further by Harald Bohr when he introduced almost-periodic functions.