Nielsen's beta function and some infinitely divisible distributions

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Nielsen's beta function and some infinitely divisible distributions. / Berg, Christian; Koumandos, Stamatis; Pedersen, Henrik L.

In: Mathematische Nachrichten, Vol. 294, No. 3, 2021, p. 426-449.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Berg, C, Koumandos, S & Pedersen, HL 2021, 'Nielsen's beta function and some infinitely divisible distributions', Mathematische Nachrichten, vol. 294, no. 3, pp. 426-449. https://doi.org/10.1002/mana.v294.3

APA

Berg, C., Koumandos, S., & Pedersen, H. L. (2021). Nielsen's beta function and some infinitely divisible distributions. Mathematische Nachrichten, 294(3), 426-449. https://doi.org/10.1002/mana.v294.3

Vancouver

Berg C, Koumandos S, Pedersen HL. Nielsen's beta function and some infinitely divisible distributions. Mathematische Nachrichten. 2021;294(3):426-449. https://doi.org/10.1002/mana.v294.3

Author

Berg, Christian ; Koumandos, Stamatis ; Pedersen, Henrik L. / Nielsen's beta function and some infinitely divisible distributions. In: Mathematische Nachrichten. 2021 ; Vol. 294, No. 3. pp. 426-449.

Bibtex

@article{62b580f6974b4691b94be60013882708,
title = "Nielsen's beta function and some infinitely divisible distributions",
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.",
author = "Christian Berg and Stamatis Koumandos and Pedersen, {Henrik L.}",
year = "2021",
doi = "10.1002/mana.v294.3",
language = "English",
volume = "294",
pages = "426--449",
journal = "Mathematische Nachrichten",
issn = "0025-584X",
publisher = "Wiley - V C H Verlag GmbH & Co. KGaA",
number = "3",

}

RIS

TY - JOUR

T1 - Nielsen's beta function and some infinitely divisible distributions

AU - Berg, Christian

AU - Koumandos, Stamatis

AU - Pedersen, Henrik L.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

U2 - 10.1002/mana.v294.3

DO - 10.1002/mana.v294.3

M3 - Journal article

VL - 294

SP - 426

EP - 449

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

SN - 0025-584X

IS - 3

ER -

ID: 258841147