Gamma functions and limits How can someone calculate the limit $\lim_{n\rightarrow \infty}\frac{\Gamma(n+p)}{n^p\Gamma(n)}$ ? Is there an article about it? Is $\frac{\Gamma(n+p)}{n^p\Gamma(n)}$ greater than unity?

Stirling's approximation
$$\Gamma(z) \sim \sqrt{\frac{2 \pi}{z}} \left( \frac{z}{\mathrm{e}} \right)^z $$
does the trick:
$$\frac{\Gamma(n+p)}{n^p \Gamma(n)} \sim \frac{ \sqrt{\frac{2 \pi}{n+p}} \left( \frac{n+p}{\mathrm{e}} \right)^{n+p}}{n^p \sqrt{\frac{2 \pi}{n}} \left( \frac{n}{\mathrm{e}} \right)^n}= \frac{1}{e^p} \sqrt{\frac{n}{n+p}} \left(\frac{n+p}{n} \right)^{n+p} \to 1, \quad \text{ as } n \to \infty. $$
I don't know about such an article.
