Asymptotic behaviour of the Urbanik semigroup
arXiv:1310.0252 · doi:10.1016/j.jat.2014.05.006
Abstract
We revisit the product convolution semigroup of probability densities e_c(t),c>0 on the positive half-line with moments (n!)^c and determine the asymptotic behaviour of e_c(t) for large and small t>0. This shows that (n!)^c is indeterminate as Stieltjes moment sequence if and only if c>2
13 pages