Spence's Function

Author

Eric W. Weisstein
December 27, 2008

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

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

©2008 Wolfram Research, Inc. except for portions noted otherwise

Code

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

Integral

V6

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

Integrate[Log[1+t]/t,{t,0,x},Assumptions->Re[x]≥-1]

V7

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

Integrate[Log[1+t]/t,{t,0,x},Assumptions->Re[x]≥-1]

Plots

<<Utilities`Plot`

Real Axis

Plot[F[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