7.4 Convergence and Sum of Fourier Series

If a periodic function \(f(x)\) with period \(2\pi \) is piecewise continuous in the interval \(-\pi < x < \pi \) and has a left and right -hand derivative at each point of that interval , then Fourier series of \(f(x)\) is convergent. Its sum is \(f(x)\), except at a point \(x_0\) at which \(f(x)\) is discontinuous and the sum of the series is the average the left - and right - hand limits of \(f(x)\) at \(x_0\).

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