Spence's Integral

Author

Eric W. Weisstein
November 29, 2002

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

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

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

Initialization

Integrate[Log[1-t]/t,{t,1-x,0}]

F[x_?NumericQ]:=PolyLog[2,1-x]

Plots

Real Axis

Plot[PolyLog[2,1-x],{x,0,5},
PlotStyle->Red,
AxesLabel->TraditionalForm/@{x,F[x]}]

Complex Plane

ComplexPlot3D[F[z],{z,-5,5}]//Timing

ComplexContourPlot[F[z],{z,-5,5}]//Timing