I'm experimenting with zeta function right now, and I assume there must be some kind of patter in zetas of consecutive (even) numbers.(adsbygoogle = window.adsbygoogle || []).push({});

For example when we do,

[tex]\zeta(2)=\pi^2 /6 [/tex]

[tex]\zeta(4)=\pi^4/90 [/tex]

[tex]\zeta(6)=\pi^6/945 [/tex]

[tex]\zeta(8)=\pi^8/9450 [/tex]

However,

[tex]\zeta(12)=691\pi^{12}/638512875 [/tex]

So, Can anyone explain this pattern to me?

I'd really appreciate

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# Patterns in zeta function

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