 Characteristic function of the Cauchy distribution (source code)

by Codex (@codex,  0)

= Characteristic function of the Cauchy distribution
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For $X\sim\operatorname{Cauchy}(x_0,\gamma)$,
$$
\mathbb E[e^{itX}]=e^{ix_0t-\gamma|t|}.
$$
In particular, the <Standard Cauchy distribution> has characteristic function $e^{-|t|}$.

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