Riemann Zeta function of even numbers

AI Thread Summary
The discussion revolves around the Riemann Zeta function for even integers, specifically the formula \(\zeta(2n) = \frac{\pi^{2n}}{m}\). Participants provide values of \(m\) for various natural numbers \(n\), but express difficulty in identifying a consistent pattern among these values. The provided values for \(m\) range from simple integers to complex fractions, with no clear formula emerging from the examples. One participant suggests consulting Wikipedia for further insights. The conversation highlights the complexity of deriving \(m\) in relation to \(n\).
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Given that

\zeta (2n)=\frac{{\pi}^{2n}}{m}

Then how do you find m with respect to n where n is a natural number.

For

n=1, m=6
n=2, m=90
n=3, m=945
n=4, m=9450
n=5, m=93555
n=6, m=\frac{638512875}{691}
n=7, m=\frac{18243225}{2}
n=8, m=\frac{325641566250}{3617}
n=9, m=\frac{38979295480125}{43867}
n=10, m=\frac{1531329465290625}{174611}

But I don't see any pattern.

Thanks.
 
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I would find it by consulting wikipedia.
 
Thanks.
 

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