I wish to prove the following inequality. I have done a plot and it looks ok. $\mu \geq 1$ is an integer and so is $h$, where $0 \leq h \leq \mu-1$.
I started like this:
$\frac{e^{-\mu}\mu^{(\mu+h)}}{(\mu+h)!} \geq \frac{e^{-\mu}\mu^{(\mu-h-1)}}{(\mu-h-1)!}$.
I have rewritten this to
$(\mu-h-1)!\mu^{(\mu+h)} \geq (\mu+h)!\mu^{(\mu-h-1)}$,
however I am not able to go further from there. Can you help me out?