Power Mean

Author

Eric W. Weisstein
December 12, 2003

This notebook downloaded from http://mathworld.wolfram.com/notebooks/SpecialFunctions/PowerMean.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/PowerMean.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Special Cases

((x^p+1)/2)^(1/p)

Limit[((x^p+1)/2)^(1/p),p->#,Assumptions->0<x<1]&/@{-∞,0,∞}

Function[p,((x^p+1)/2)^(1/p)]/@{-1,1,2}//FullSimplify

Plot

<<Graphics`Colors`

Plot[{x,((2 x)/(1+x)),Sqrt[x],((1+x)/2),((Sqrt[1+(x^2)])/(Sqrt[2])),1},
{x,0,1},AxesLabel->TraditionalForm/@{x,(Subscript[M, p])[x,1]},
PlotStyle->{Red,Orange,Black,Green,Blue,Violet}]