Is there a closed form solution for
$$ \mathbb{E}(|X^p|) $$
where $X$ is a Gaussian random variable?
Remarks:
- I know that $\mathbb{E}(X^p)$ is just given by the moments of the Gaussian distribution (https://en.wikipedia.org/wiki/Normal_distribution#Moments)
- I know that $\mathbb{E}(|X|^p)$ is the $p$-th moment of the folded normal distribution