Nielsen's beta function and some infinitely divisible distributions

2019/05/10 by Christian Berg, Berg, Christian, Stamatis Koumandos +3 · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA

paper · pdf · doi:10.48550/arxiv.1905.04131

32 pages

arxiv created 2019/09/20 · arxiv updated 2019/09/23

Abstract

We show that a large collection of special functions, in particular Nielsen's beta function, are generalized Stieltjes functions of order 2, and therefore logarithmically completely monotonic. This includes the Laplace transform of functions of the form xf(x), where f is itself the Laplace transform of a sum of dilations and translations of periodic functions. Our methods are also applied to ratios of Gamma functions, and to the remainders in asymptotic expansions of the double Gamma function of Barnes.

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