I have crafted an infinite product for zeta(2) shown here. Euler's prime product is the only one I'm aware of. In checking Math World, I don't see any products. Is that because they are trivial?
2026-03-25 10:57:16.1774436236
Is this infinite product for zeta(2) trivial?
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Your product can be easily rewritten as $\dfrac B{A^2}$, where $A=\displaystyle\prod_{n=1}^\infty\bigg(1-\dfrac{x^2}{n^2}\bigg)$ with $x=\dfrac16$, and
$B=\displaystyle\prod_{n=2}^\infty\frac{n^3+1}{n^3-1}$, which, believe it or not, is telescopic, and yields a rational number as result.
$(B$ has been evaluated on this site several times$)$. So the answer to your question is yes.