How can I use Wolfram|Alpha to compute the Fourier series (with real coefficients $a_0, a_n$ and $b_n$)? (The 'Fourier series' command seems to summon the complex series)

I.e. $f(x) = x + \pi$ for $-\pi < x < 0$ and $f(x) = \pi - x$ for $0 \leq x < \pi$

$\Rightarrow f(x) \approx \pi/2 + 4/\pi(cos x + \dfrac 1 3 cos 3x + \dfrac 1 5 cos 5x + \cdot \cdot \cdot)$

I know I can use indefinite or definite integrals to check the integration itself, but I'd be interesting to see a complete solution aid.


You could use the FourierCosSeries command. Here is the documentation of it.

  • 1
    $\begingroup$ Thanks! Looking at the 'see also' I see that the FourierTrigSeries command was what I was actually looking for. $\endgroup$ – Cecil Dishwasher Aug 1 '11 at 11:14
  • $\begingroup$ Ok, no problem :-) $\endgroup$ – Listing Aug 1 '11 at 11:19
  • $\begingroup$ But how do I get it to show the steps? The Steps-button is missing! :O $\endgroup$ – Cecil Dishwasher Aug 1 '11 at 11:26
  • $\begingroup$ Sadly that is not implemented for every command yet, it is still to be added. $\endgroup$ – Listing Aug 1 '11 at 11:36

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