Lévy-Khintchine representation of the geometric mean of many positive numbers and applications

DOI10.7153/mia-17-53zbMath1296.26114arXiv1301.6432OpenAlexW2328674226MaRDI QIDQ4980067

Wen-Hui Li, Feng Qi, Xiao-Jing Zhang

Publication date: 20 June 2014

Published in: Mathematical Inequalities & Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.6432

zbMATH Keywords

integral representationgeometric meanarithmetic-geometric mean inequalitycompletely monotonic functionBernstein functionlogarithmically completely monotonic functionCauchy integral formulacomplete Bernstein functionLévy-Khintchine representation

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Laplace transform (44A10) Integral transforms of special functions (44A20) Means (26E60) Monotonic functions, generalizations (26A48)

Related Items (15)

Some properties of the Schröder numbers ⋮ Unnamed Item ⋮ Integral representations of bivariate complex geometric mean and their applications ⋮ On the degree of the weighted geometric mean as a complete Bernstein function ⋮ The harmonic and geometric means are Bernstein functions ⋮ A LOGARITHMICALLY COMPLETELY MONOTONIC FUNCTION INVOLVING THE RATIO OF GAMMA FUNCTIONS ⋮ The reciprocal of the weighted geometric mean of many positive numbers is a Stieltjes function ⋮ Lévy-Khintchine representation of Toader-Qi mean ⋮ The reciprocal of the weighted geometric mean is a Stieltjes function ⋮ Several identities involving the falling and rising factorials and the Cauchy, Lah, and Stirling numbers ⋮ A ratio of finitely many gamma functions and its properties with applications ⋮ The reciprocal of the geometric mean of many positive numbers is a Stieltjes transform ⋮ Integral representations of the large and little Schröder numbers ⋮ Logarithmically complete monotonicity of a function related to the Catalan-Qi function ⋮ Logarithmically complete monotonicity of Catalan-Qi function related to Catalan numbers

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