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We revisit the product convolution semigroup of probability densitiese_c(t),c>0 on the positive half-line with moments (n!)^c and determine theasymptotic behaviour of e_c(t) for large and small t>0. This shows that (n!)^cis indeterminate as Stieltjes moment sequence if and only if c>2

Asymptotic behaviour of the Urbanik semigroup