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- W3101475236 abstract "It is general knowledge that the harmonic mean $H(x,y)=frac2{frac1x+frac1y}$ and that the geometric mean $G(x,y)=sqrt{xy},$, where $x$ and $y$ are two positive numbers. In the paper, the authors show by several approaches that the harmonic mean $H_{x,y}(t)=H(x+t,y+t)$ and the geometric mean $G_{x,y}(t)=G(x+t,y+t)$ are all Bernstein functions of $tin(-min{x,y},infty)$ and establish integral representations of the means $H_{x,y}(t)$ and $G_{x,y}(t)$." @default.
- W3101475236 created "2020-11-23" @default.
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- W3101475236 date "2016-02-13" @default.
- W3101475236 modified "2023-10-16" @default.
- W3101475236 title "The harmonic and geometric means are Bernstein functions" @default.
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- W3101475236 doi "https://doi.org/10.1007/s40590-016-0085-y" @default.
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