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Riemann zeta function at odd positive integers

We know that $\zeta(2)=\frac{\pi^2}{6}$ and also for every even number it's known, but it's still unknown what the exact value of $\zeta(3)$ is. How is it possible that $\zeta(2)$ has been calculated circa 250 years ago, but $\zeta(3)$ is stil not calculated exactly? Why is the difference in difficulty so big?


marked as duplicate by user17762, froggie, Old John, Hans Lundmark, robjohn Dec 19 '12 at 15:31

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    $\begingroup$ Actually it can be calculated fairly easily using fourier series techniques. The problem is expressing it with known mathematical constants like e and $\pi$. Thats where the difficulty is. $\endgroup$ – Gautam Shenoy Dec 19 '12 at 15:10