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Eric Kvaalen (talk | contribs) Corrected a condition. Added some more special cases (closed form solutions). |
Jackie Young (talk | contribs) |
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::<math>M_{\kappa,\mu}(z) = e^{-\tfrac{z}{2}} z^{\mu+\tfrac{1}{2}}M\left(\mu-\kappa+\tfrac{1}{2}, 1+2\mu; z\right)</math>
::<math>W_{\kappa,\mu}(z) = e^{-\tfrac{z}{2}} z^{\mu+\tfrac{1}{2}}U\left(\mu-\kappa+\tfrac{1}{2}, 1+2\mu; z\right)</math>
* The general {{mvar|p}}-th raw moment ({{mvar|p}} not necessarily an integer) can be expressed as{{Citation needed|date=March 2017}}
:: <math>\begin{align}
\operatorname{E} \left[\left|N\left(\mu, \sigma^2 \right)\right|^p \right] &= \frac{\left(2 \sigma^2\right)^{\frac{p}{2}} \Gamma\left(\tfrac{1+p}{2}\right)}{\sqrt \pi} \ {}_1F_1\left(-\tfrac p 2, \tfrac 1 2, -\tfrac{\mu^2}{2 \sigma^2}\right)\\
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