Densities of the Raney distributions

Wojciech Mlotkowski, Karol A. Penson, Karol Zyczkowski

We prove that if $p\ge 1$ and $0<r\le p$ then the sequence $\left(\genfrac{}{}{0ex}{}{mp+r}{m}\right)\frac{r}{mp+r}$, $m=0,1,2,...$, is positive definite, more precisely, is the moment sequence of a probab…