I have problem with see the relation between the transform of $x^2$ in $[-\pi,\pi]$ and the function $\zeta$ de Riemann in the point 2, this say that using the transform fourier of $x^2$ prove that $\zeta (2)$ is equal to $\sum_{n=1}^{\infty}\dfrac{1}{n^2}=\dfrac{\pi^2}{6}$, but here is not my trouble because I did this part but the answer me which is the relation between $\zeta(2)$ the fourier tranform of $x^2$?
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1You could start by actually evaluating the fourier $series$ of $x^2$ on $[-\pi,\pi]$. – Alex R. Jun 17 '15 at 01:58
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Do you mean the Fourier series (rather than transform)? – Ben Grossmann Jun 17 '15 at 02:02
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1See the answer given here – Ben Grossmann Jun 17 '15 at 02:24
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I see, thanks. ! – sti9111 Jun 17 '15 at 02:26
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Here is the fourier transform of $x^2$.
If you put $x=0$ you get the solution to Basel problem.
Daniele Tampieri
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Jose Perez
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As it’s currently written, your answer is unclear. Please [edit] to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. – Community Oct 23 '23 at 11:11
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After you get the Fourier series for $x^2$ in $[−\pi,\pi]$, put $x=\pi$, and there you go!
mrtaurho
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