Generalized Mean

A generalized version of the Mean

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

with parameter $t$ which gives the Geometric Mean, Arithmetic Mean, and Harmonic Mean as special cases:

$$\lim_{t\to 0} m(t)=G$$ (2)

$$m(1)=A$$ (3)

$$m(-1)=H.$$ (4)

See also Mean