Riemann Zeta Function of 4/Proof 3
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Theorem
The Riemann zeta function of $4$ is given by:
| \(\ds \map \zeta 4\) | \(=\) | \(\ds \dfrac 1 {1^4} + \dfrac 1 {2^4} + \dfrac 1 {3^4} + \dfrac 1 {4^4} + \cdots\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \dfrac {\pi^4} {90}\) | ||||||||||||
| \(\ds \) | \(\approx\) | \(\ds 1 \cdotp 08232 \, 3 \ldots\) |
Proof
 | This theorem requires a proof. In particular: $\ds \int_0^1\int_0^1\int_0^1\int_0^1 \frac 1 {1 - x_1x_2x_3x_4} \rd x_1 \rd x_2 \rd x_3 \rd x_4$. Use Beukers-Calabi-Kolk sub. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code.If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page. |