Mu Function

Author

Eric W. Weisstein
May 20, 2002

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

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

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

Initialization

<<Graphics`Colors`

μ(x,β)

μ[x_,β_]:=Integrate[(((x^t)(t^β))/(Gamma[β+1]Gamma[t+1])),{t,0,∞}]

μ[x,β]

Plot[Evaluate[Table[μ[x,n],{n,0,4}]],{x,0,2},
PlotStyle->{Black,Red,Yellow,Green,Blue},
AxesLabel->TraditionalForm/@{x,HoldForm[μ[x,β]]}]//Timing

μ(x,β, α)

Integrate[(((x^(α+t))(t^β))/(Gamma[β+1]Gamma[α+t+1])),{t,0,∞}]