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how we can rely on Fourier's assertion that any periodic function can be represented as a sum of periodic functions such as trigonometric functions.

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2023/05/07 00:51

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A proof that a Fourier series is a valid representation of any periodic function (that satisfies the Dirichlet conditions) is overviewed in § Fourier theorem proving convergence of Fourier series.

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In engineering applications, the Fourier series is generally assumed to converge except at jump discontinuities since the functions encountered in engineering are better-behaved than functions encountered in other disciplines. 

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