I'm trying to prove $| \Gamma (x_{n})| \to 0 $ as $n \to \infty$ where $x_{n} \in [-n+\delta,1-n-\delta] $ for some $\delta > 0 $.
What possible method can I use?
As a special case, I've proved the above result for $x_{n} = 1/2 - n$. Can I use this result for the proof of the above?