A two-parameter extension of the Urbanik semigroup

Christian Berg

We prove that s_n(a,b)=Γ(an+b)/Γ(b), n=0,1,\ldots is an infinitely divisible Stieltjes moment sequence for arbitrary a,b>0. Its powers s_n(a,b)^c, c>0 are Stieltjes determinate if…