point wise convergence of fourier series
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Theorem 5.5 (Pointwise convergence). (i) The Fourier series converges to f(x) pointwise in (a, b), if f(x) is continuous, and f (x) is piecewise continuous on [a, b]. ... Thus, if a function has a jump discontinuity, then its Fourier series converges to the average of the one-sided limits.
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