Rudy Toody
Diamond Member
I was playing around with pronic numbers and got a plus and minus reversed. The number I got was not what I expected, but I looked it up on OEIS.org and found:
[;\zeta(6)/\zeta(2)/\zeta(3);]
Reducing and inserting my series we get:
[;\zeta(3)=\frac{2 \pi ^4}{315} \prod _{n}^{\infty } \left(1- \frac{1}{p_{n}-p_{n}^{2}}\right);]
Is this a known identity? Yes.
Note: the product appears to converge very slowly.
[;\zeta(6)/\zeta(2)/\zeta(3);]
Reducing and inserting my series we get:
[;\zeta(3)=\frac{2 \pi ^4}{315} \prod _{n}^{\infty } \left(1- \frac{1}{p_{n}-p_{n}^{2}}\right);]
Is this a known identity? Yes.
Note: the product appears to converge very slowly.
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