= Pointwise convergence of a piecewise smooth Fourier series
For a periodic <function> that is piecewise continuously differentiable with finitely many pieces, its <Fourier series> converges at each point to the average of the two one-sided limits. At a point of continuity this is the function value. This includes the identified interval endpoints, whose two limits belong to the periodic extension. Absolute summability of the <Fourier coefficients> additionally gives uniform convergence.
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