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Why do you need to change the interval? f-odd-extention (fox) fox[x_] := Piecewise[{ {-3 - x, x < -1}, {-x^2 - 1, -1 <= x < 0}, {x^2 + 1, 0 <= x <= 1}, {3 - x, 1 < x} }] which looks this Plot[fox[x], {x, -3, 3}] The Fourier series approximation to fox can be computed for 20 terns with fs[x_] = FourierSeries[f[x], ...



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