Nielsen's beta function and some infinitely divisible distributions

Christian Berg, Stamatis Koumandos, Henrik L. Pedersen

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

8 Citationer (Scopus)
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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 x f ( 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.
OriginalsprogEngelsk
TidsskriftMathematische Nachrichten
Vol/bind294
Udgave nummer3
Sider (fra-til)426-449
ISSN0025-584X
DOI
StatusUdgivet - 2021

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