Mighty efficient there, RV (as always)!

Not my turn, mind, but just out of interest... Have you tried proving the equivalent canonical product for the Barnes' G-Function (Double Gamma Function)? I'm sure you'd find it a doddle...

\(\displaystyle G(z+1)=G(z)\,\Gamma(z)\)

\(\displaystyle G(z+1)=(2\pi)^{z/2}\text{exp}\left(-\frac{z+z^2(1+\gamma)}{2}\right)\, \prod_{k=1}^{\infty}\left(1+\frac{z}{k}\right)\text{exp}\left(\frac{z^2}{2k}-z\right)\)

More on the Barnes' G-Function here... http://arxiv.org/pdf/math/0308086v1.pdf