Over the last few days, I have been studying equation (20) in the following (http://mathworld.wolfram.com/InfiniteProduct.html)
A special case of this formula is given as follows
$$ \prod_{n=2}^{\infty} \left(1-\frac{1}{n^3}\right)= \frac{\cosh(\frac{\pi}{2} \sqrt3)}{3\pi} $$
where the RHS is $$ \frac{1}{3\cdot \Gamma(\sqrt[3]{-1})\cdot \Gamma(-\sqrt[3]{-1}^2)}$$
As I proceed to plug these gamma functions into WolframAlpha, it gives me approximations and integrals as if these did not have an exact value or it was not known.
So my question is how can I go about solving these?
I tried looking at the gamma reflection formula but no cigar.
Thank you very much for your help and time.