[math] \newcommand{\mathds}{\mathbb}[/math]

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Learn and use the Stieltjes inversion formula, namely

[[math]] d\mu (x)=\lim_{t\searrow 0}-\frac{1}{\pi}\,Im\left(G(x+it)\right)\cdot dx [[/math]]

in order to find the centered laws having as [math]2k[/math]-th moments the numbers [math](2k)!![/math] and [math]C_k[/math].