functions - FourierSeries command , for arbitrary period T?

ExptoTrig[FourierSeries[Piecewise[{{-Pi,-2Pi

You can see, the function goes from $(-2\pi,2\pi]$

But Wolfram Alpha gives a wrong answer to this, because she computes it as if the function would go from $-\pi$ to $\pi$ .

(The right answer should be $4\sin(\frac{x}{2}) + ..$ .)

So, how can I use this command when the function's period T is not 2 $\pi$ exactly?

Answer

f[x_] = Piecewise[{{-Pi, -2 Pi < x <= 0}, {Pi, 0 < x <= 2 Pi}}];
T = 4 \[Pi];
fr = FourierTrigSeries[f[x], x, 3, FourierParameters -> {1, 2 \[Pi]/T}]
(* 4 Sin[x/2] + 4/3 Sin[(3 x)/2] *)

Comments

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