Cauchy distribution
= Cauchy distribution
{c}
{title2=$\operatorname{Cauchy}(x_0,\gamma)$}
{wiki}
The Cauchy distribution with location $x_0$ and scale $\gamma>0$ has <probability density function>
$$
f(x)=\frac{1}{\pi\gamma\left(1+((x-x_0)/\gamma)^2\right)}.
$$
The standard Cauchy distribution has $x_0=0$, $\gamma=1$, <characteristic function> $e^{-|t|}$, and infinite first absolute moment.