1
$\begingroup$

This is what I needed. Practically, a link were also okay.

$$\sum_{n=1}^{\infty}\frac{1}{n^2}=\frac{\pi^2}{6}$$

$\endgroup$

marked as duplicate by user91500, Jean-Sébastien, Did, M Turgeon, Claude Leibovici May 8 '14 at 12:37

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • 1
    $\begingroup$ You can use Fourier_transformation $\endgroup$ – Jlamprong May 8 '14 at 12:10
  • $\begingroup$ @Jlamprong Fourier-transformation without complexes??? $\endgroup$ – peterh May 8 '14 at 12:11
  • $\begingroup$ Yes. see here $\endgroup$ – Jlamprong May 8 '14 at 12:14
  • $\begingroup$ @Jlamprong Is it me, or complex numbers are clearly mentioned on pages 3, 5, 6, 7 and 8 of the slides you link to? $\endgroup$ – Did May 8 '14 at 12:41
3
$\begingroup$

Evaluating ζ(2) by Robin Chapman contains several proofs (~14 altogether). You can have a look through and find a nice one.

$\endgroup$
  • 2
    $\begingroup$ They are really good proofs. Thanks! $\endgroup$ – peterh May 8 '14 at 12:42
3
$\begingroup$

I think you have to compute the Fourier series of either $\sin$ or $x$ on $(0,2\pi)$ extended to $\mathbb R$ periodically to get the left hand side and then use Parseval's theorem to prove equivalence to the right hand side.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.