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Nielsen's beta function and some infinitely divisible distributions

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  • Christian Berg
  • Stamatis Koumandos
  • Henrik L. Pedersen

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.

Suggested Citation

  • Christian Berg & Stamatis Koumandos & Henrik L. Pedersen, 2021. "Nielsen's beta function and some infinitely divisible distributions," Mathematische Nachrichten, Wiley Blackwell, vol. 294(3), pages 426-449, March.
    • Handle: RePEc:bla:mathna:v:294:y:2021:i:3:p:426-449
    DOI: 10.1002/mana.201900217
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    Cited by:

    1. Mansour Mahmoud & Hanan Almuashi, 2022. "An Approximation Formula for Nielsen’s Beta Function Involving the Trigamma Function," Mathematics, MDPI, vol. 10(24), pages 1-8, December.

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