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Harmonic-Geometric Mean

Let

alpha_(n+1)=(2alpha_nbeta_n)/(alpha_n+beta_n)
(1)
beta_(n+1)=sqrt(alpha_nbeta_n),
(2)

then

H(alpha_0,beta_0)=lim_(n->infty)a_n=1/(M(alpha_0^(-1),beta_0^(-1))),
(3)

where M is the arithmetic-geometric mean.

See also

Arithmetic Mean, Arithmetic-Geometric Mean, Geometric Mean, Harmonic Mean

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Cite this as:

Weisstein, Eric W. "Harmonic-Geometric Mean." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Harmonic-GeometricMean.html

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