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The Arithmetic-Harmonic mean and Landen transformations

2019
An elementary transformation on the coefficients of a rational function of degree 2, preserving the value of its integral, is presented.
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A Harmonic Mean Inequality for the Gamma Function

SIAM Journal on Mathematical Analysis, 1974
We prove that the harmonic mean of $\Gamma (x)$ and $\Gamma (1/ x)$ is greater than or equal to $\Gamma (1) = 1$ for arbitrary $x > 0$.
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Modeling and numerical analysis of fractional order hepatitis B virus model with harmonic mean type incidence rate

Computer Methods in Biomechanics and Biomedical Engineering, 2023
Rahat Zarin
exaly  

The Harmonic Mean

National Mathematics Magazine, 1939
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Approximation in the mean by harmonic functions

Journal of Soviet Mathematics, 1975
Maz'ya, V. G., Khavin, V. P.
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Harmonic Expectation of Harmonic Mean of Random Variables

An interesting property of harmonic expectation, whose concept had been introduced on the basis of harmonic mean, and which was consequently defined mathematically, has been identified in the current attempt. The property describes an interesting result on harmonic expectation of harmonic mean of random variables.
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The harmonic mean

2004
Israel M. Gelfand, Alexander Shen
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