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Illustration Taylor and Fourier Approximations for a Function

Taylor and Fourier Approximations for a Function
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A periodic function \(f\) or a function in an interval, can be approximated (locally) at a point by a Taylor series. The approximation is \(f_{\text{taylor}}\). However, we can also approximate the function \(f\) by a Fourier series in the entire interval. A Fourier series contains periodic basis functions ("building blocks") from which \(f\) is assembled.