I would like to find a (closed nice) expression for the non-centered Gaussian moments with mean $\mu$ and variance $\sigma$. In found something in wikipedia:
http://en.wikipedia.org/wiki/Normal_distribution#Moments
$$E|X|^p = \sigma^p 2^{p/2} \frac{\Gamma \left(\frac{p+1}{2}\right)}{\sqrt{\pi}} {}_1 F_1 \left(-\frac{1}{2}p, \frac{1}{2}, -\frac{1}{2}(\mu/\sigma)^2\right)$$
but I don't understand this "confluent hypergeometric function" ${}_1F_1$ because it doesn't seem to be well-defined for negative integers according to this article in wikipedia.. (it seems to be only valid for positive integers)
http://en.wikipedia.org/wiki/Confluent_hypergeometric_function
Does anyone know about this? Thank you very much for the help!
