Nielsen's beta function and some infinitely divisible distributions
- 28 December 2020
- journal article
- research article
- Published by Wiley in Mathematische Nachrichten
- Vol. 294 (3) , 426-449
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 , 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.Keywords
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