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Generalized Mean

A generalized version of the Mean

\begin{displaymath}
m(t)\equiv \left({{1\over n} \sum_{k=1}^n {a_k}^t}\right)^{1/t}
\end{displaymath} (1)

with parameter $t$ which gives the Geometric Mean, Arithmetic Mean, and Harmonic Mean as special cases:
\begin{displaymath}
\lim_{t\to 0} m(t)=G
\end{displaymath} (2)


\begin{displaymath}
m(1)=A
\end{displaymath} (3)


\begin{displaymath}
m(-1)=H.
\end{displaymath} (4)

See also Mean




© 1996-9 Eric W. Weisstein
1999-05-25