Trigamma Function

Author

Eric W. Weisstein
February 25, 2005

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

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

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

Plots

<<Utilities`Plot`

Real Axis

PlotDiscontinuous[PolyGamma[1,z],{z,Sequence@@Range[-5,0],5},PlotRange->{Automatic,{-1,15}},
VerticalAsymptotes->Range[-5,0],
AxesLabel->TraditionalForm/@{x,PolyGamma[1,z]}]

Complex Plane

ComplexPlot3D[PolyGamma[1,z],{z,-5,5},PlotPoints->100]//Timing

ComplexContourPlot[PolyGamma[1,z],{z,-5,5}]//Timing

Definition

D[Log[Gamma[z]],{z,2}]

Special Values

v=Union[Flatten[Outer[#1/#2&,Range[5],Range[5]]]]

{#,FunctionExpand[PolyGamma[1,#]]}&/@v//ColumnForm

<<Utilities`Simplify`

TranscendentalRecognize[N[PolyGamma[1,1/4],200],{Pi^2,Catalan}]