The $\Gamma$ function is the analytic continuation of the factorial function. Is there a similar analog for multifactorials?
I am particularly interested in the double factorial. All Google has given me is the following formula relating the $\Gamma$ function to the double factorial for half integer values: $$\Gamma\left(n+\frac{1}{2}\right)=\frac{(2n-1)!!}{2^n}\sqrt{\pi}$$ But I want to double factorial nonintegers, so this is not really helpful.
Why is this not helpful? If you write the identity as $$(2n-1)!! = \frac{\Gamma(n + \frac{1}{2}) 2^n}{\sqrt{\pi}}$$ and then let $n = (x+1)/2$ you get $$x!! = \frac{\Gamma(\frac{x+2}{2}) 2^{(x+1)/2}}{\sqrt{\pi}}$$ The right side is now defined for any complex $x$ as long as the argument for the Gamma function is defined.