Densities of the Raney distributions
Densities of the Raney distributions
We prove that if p\ge1 and 0< r\le p then the sequence \binom{mp+r}m\frac{r}{mp+r} is positive definite. More precisely, it is the moment sequence of a probability measure \mu(p,r) with compact support contained in [0,+\infty) . This family of measures encompasses the multiplicative free powers of the Marchenko-Pastur distribution as well …