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Mathematical Analysis Volume II
According to Dirichlet's convergence condition, for the continuous points of f(x) on (-∞, +∞), the Fourier series converges to f(x), and the equal sign holds. But for the first kind of discontinuous points where f(x) is on (-∞, +∞), the Fourier series converges to [f(x+)+f(x-)]/2≠f(x). Therefore, considering the situation of continuous points and discontinuous points, the sign less than or equal to should be taken.