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Identity for stable Lévy subordinator
I want a proof or a reference for the identity
$$
\int_0^\infty \frac{s^{n-1}}{\Gamma(n)} p_\beta(s,x)\,ds =\frac{x^{n\beta-1}}{\Gamma(\beta n)},\quad x>0, \,n\in\mathbb N,
$$
where $x\mapsto p_\beta …