Hello, I am trying to show the following: \lim_{x\rightarrow\infty}\frac{\Gamma (x+c)}{x^c \Gamma (x)}=1, where c\in\mathbb{R}. Recall Stirling's formula: \lim_{x\rightarrow\infty}\frac{\Gamma (x+1)}{(x/e)^x \sqrt{2\pi x}}=1. Any suggestions on how to prove the former limit using this formula? I have tried the change of variables t=x(c+u), but got stuck. Any help would be greatly appreciated.

Thanks in advance,
Arlington