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Incoming links: Periodic N-point rectangle-rule error
Past exam of the mathematics course of the University of Cambridge 2019 ii Paper 4 39C b Solution Created 2026-09-24 Updated 2026-10-03
Insert the Fourier seriesinto the rectangle rule. The finite geometric sum obeysConsequently the quadrature value iswhereasThus the exact Periodic N-point rectangle-rule error is
By the Fourier coefficient decay of an analytic periodic function, there are constants and such thatIt follows thatThereforewhich is exponential, and hence spectral, convergence.