\[\prod_{k=0}^{\infty}\frac{(a_{1}+k)(a_{2}+k)\cdots(a_{m}+k)}{(b_{1}+k)(b_{2}+k%
)\cdots(b_{m}+k)}=\frac{\Gamma\left(b_{1}\right)\Gamma\left(b_{2}\right)\cdots%
\Gamma\left(b_{m}\right)}{\Gamma\left(a_{1}\right)\Gamma\left(a_{2}\right)%
\cdots\Gamma\left(a_{m}\right)},\]