WOLFRAM|DEMONSTRATIONS PROJECT

Hölder Approximations to Popular Means

​
th
n
Hölder mean
n
2
n
1+
n
x
2
other means of x and 1
maximum
RMS
average
identric
AGM
logarithmic
geometric
harmonic
minimum
The Hölder mean provides approximations to popular means, which shows that it generalizes some of them and that these means are ordered by strict inequality over
x
on
(0,1)
.