Integral representations of the weighted geometric mean and the logarithmic mean

Abstract

In the paper, the authors show that the weighted geometric mean and the logarithmic mean are Bernstein functions and establish integral representations of these means by Cauchy's integral theorem in the theory of complex functions.

12 pages. arXiv admin note: text overlap with arXiv:1301.6848

Cited by in corpus (4)

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• Completely monotonic degree of a function involving the tri- and tetra-gamma functions
• Some Bernstein functions and integral representations concerning harmonic and geometric means
• A ratio of many gamma functions and its properties with applications