# Upper bound for a gamma function

Let $n \in N$. How to find a non-asymptotic upper bound for $\Gamma(n)$ and $\Gamma(\frac n2+1)$?

Thank you

Equation 6.5.1 here gives a reasonably tight bound except for very small n. I suppose section 5.11 here also could be unpacked to yield some upper bounds, depending on exactly what you're looking for. (I assume you know that for integer n, $\Gamma(n) = (n-1)!$.)