a proof for the following Gamma function inequality Could you please provide or point me to a proof of inequality 5.6.8 found at this site? That is, 
$\left|\frac{\Gamma(z+a)}{\Gamma(z+b)}\right| \leq \frac{1}{|z|^{b-a}}$
for $z\in \mathbb{C}$, $a,b\in\mathbb{R}$, and $a≥0, b≥a+1, Re(z)>0$.

Thanks to joriki's link to Google Books, here is the passage in question.


R. B. Paris and D. Kaminski, Asymptotics and Mellin-Barnes Integrals, pp. 33-34.
