Factorial of infinity So, I've read in this article that:
$$\zeta'(0) = \log\sqrt\frac 1 {2\pi}$$
And that:
$$e^{-\zeta'(0)} = 1\cdot2\cdot3\cdots \infty = \infty! = \sqrt{2\pi}$$
I found this result very strange and tried to simplify if but i couldn't. Can somebody help me?
Thanks!

I am riemannium, author of the above quoted entry and the blog The Spectrum Of Riemannium (TSOR). 
I have just corrected the typos in my article quoted above. I mean, I wrote $\eta (1)=\log 2$. It was a typo while I was writing the article. I think there are no additional mistakes but if you find more "errors", let me know. I am taking my blog as a serious specialized "job", so I don't like to input errors. I am also a perfectionist.
I also thank you for the links so some pretty references about regularized infinite products I did not know till now! :).
