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Show that $\frac{1}{2 \pi i} \oint_{\mathbb{S}^1} \frac{1-\hat{f}(\xi)}{1-\xi}\cdot \frac{\mathrm{d} \xi}{\xi^{n+1}} \to 0$ as $n \to \infty$
Let $f = (f_0,f_1,\ldots,f_n,\ldots) \in \mathcal{P}(\mathbb N)$ be a probability distribution on $\mathbb N$ and denote by $$\hat{f}(z) = \sum_{n\geq 0} z^n f_n$$ for its probability generating ...
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Density of Geometric Stable distribution
If we define
$$
\psi(t|\alpha, \beta, \gamma, \mu) = -it\mu+|\gamma t|^\alpha(1-i\beta \mathrm{sgn}(t) \Phi)
$$
with
$$\Phi = \tan \frac{\pi \alpha}{2} \mathbf{1}_{\{ \alpha \neq 1 \} } - \frac{2}{\pi}...