Find Infinite Product: Solve 1/2n² Puzzle

[end3r7]

Essentially I need to find (if possible) the following infinite product

$$1 - \frac{1}{2*n^{2}}$$

So, not quite Wallis number. I must say that I'm at a complete loss, not even sure where to begin.

 

[end3r7]

0.358486649396841... is approximately what the number is (thanks to Matlab).

Looks like anything to you guys?

 

[Hurkyl]

That looks awfully similar to the infinite product for sin z.

 

[Rainbow Child]

That looks awfully similar to the infinite product for sin z.

Which is

$$\sin(\pi\,z)=\pi\,z \prod_{n=1}^\infty\left(1-\frac{z^2}{n^2}\right)$$

 

[end3r7]

I'm not familiar, what does it look like?

 

[end3r7]

Thanks guys =)