Berg, ChristianLópez García, José Luis2020-10-282020-10-2820150021-904510.1016/j.jat.2014.05.006https://academica-e.unavarra.es/handle/2454/38549We revisit the product convolution semigroup of probability densities ec(t); c > 0 on the positive half-line with moments (n!)c and determine the asymptotic behaviour of ec for large and small t > 0. This shows that (n!)c is indeterminate as Stieltjes moment sequence if and only if c > 2. When c is a natural number ec is a Meijer-G function. From the results about ec we obtain the asymptotic behaviour at 1 of the convolution roots of the Gumbel distribution.16 p.application/pdfeng© 2014 Elsevier Inc. This manuscript version is made available under the CC-BY-NC-ND 4.0Product convolution semigroupAsymptotic approximation of integralsLaplace and saddle point methodsMoment problemsGumbel distributioninfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess