I'm trying to find an online derivation of why the mean of the Chi-Distribution with $n$ degrees of freedom is $$E(\chi_n)= \sqrt2 \frac{ \Gamma(\frac{n+1}{2})}{\Gamma(\frac{n}{2})}$$
Is it too involved to find online? Does anyone have any idea how I could derive it using something much more well-known (and available) online like the chi-squared distribution?
I've looked everywhere online, and even looked through some of the books referenced on Wikipedia and WolframAlpha's pages on the Chi Distribution. None of them list how to derive it, they just have the final answer.