Reading one article I came across this product:
$$ \prod_{\mu, n} \left( - E_\mu + \frac{(2n+1) \pi } {T} \right) = \prod_{n \ge 0} \left (- \frac{(2n+1)^2 \pi ^2 } {T^2} \right) \prod_{\mu, n \ge 0} \left( 1 - \frac{E_\mu T^2}{(2n+1)^2 \pi^2} \right) $$
I can not understand how one obtains this result. It looks like they put some multiplier out of the brackets, but still I do not understand.
I tried to write something like
$$ \prod_{\mu, n} \left( - E_\mu + \frac{(2n+1) \pi } {T} \right) = \prod_{\mu, n} \frac{(2n+1) \pi}{T} \left(1 - \frac{E_\mu T}{(2n+1) \pi} \right)$$
but it doesn't seem that it is what they do.
P.S. $E_\mu$ is some unknown eingenvalue of some (Dirac) operator. But I think it is not important here.