Is there a "closed form" (with which I mean an expression not involving an indexed sum or product) for any of these four products?
$$\prod_{k=1}^{n} \Gamma(\frac{x}{k*2+1})$$ $$\prod_{k=1}^{n} \Gamma(1-\frac{x}{k*2+1})$$
$$\prod_{k=2}^{n} \Gamma(\frac{x}{k})$$ $$\prod_{k=2}^{n} \Gamma(1-\frac{x}{k})$$
Its not part of a homework or anything, just out of curiosity. I've tried a bit myself, but since I barely understand half the Wikipedia page about the Gamma function, I did not make much progress.