Nielsen's beta function and some infinitely divisible distributions

Berg Christian; Koumandos Stamatis; Pedersen Henrik L.

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Nielsen's beta function and some infinitely divisible distributions

机译：Nielsen的Beta函数和一些无限可分的分布

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摘要

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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来源
《Mathematische Nachrichten》 |2021年第3期|共24页
作者
Berg Christian; Koumandos Stamatis; Pedersen Henrik L.;
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作者单位

Univ Copenhagen Dept Math Sci Univ Pk 5 DK-2100 Copenhagen Denmark;

Univ Cyprus Dept Math &

Stat POB 20537 CY-1678 Nicosia Cyprus;

Univ Copenhagen Dept Math Sci Univ Pk 5 DK-2100 Copenhagen Denmark;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
completely monotonic function; generalized Stieltjes function; Laplace transform; Nielsenamp; apos; s beta function;

机译：完全单调函数;广义stieltjes功能;拉普拉斯变换;尼尔森＆amp;aps的beta函数;

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Nielsen's beta function and some infinitely divisible distributions

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