Algebraic means
(Italian - medie di potenze)
were an interest of Bonferroni's.
He wrote extensively on them
in his textbook
and also published a short article
on a generalisation of them.
The usual algebraic mean of order or degree p
of x_{1} ... x_{n} (positive), defined as

M_{p} =

æ ç
è

S_{p}n

ö ÷
ø

[1/p]

, S_{p} = x_{1}^{p}+ ... +
x_{n}^{p}

Many well known means are special cases

p

Name

-infinity

Minimum

-1

Harmonic

0

Geometric

1

Arithmetic

2

Quadratic

infinity

Maximum

I have prepared a translation
of his article
on a generalisation
of algebraic means.

Available as PDF version
I am investigating producing an HTML one. E-mail
me for details.

This page was last modified
no earlier than October 2003