Chi

Author

Eric W. Weisstein
September 22, 2007

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

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

©2007 Wolfram Research, Inc. except for portions noted otherwise

Plots

<<Utilities`Plot`

Real Axis

Plot[CoshIntegral[x],{x,0,5},
PlotRange->{Automatic,{-6,20}},AxesLabel->{x,CoshIntegral[x]}]

Complex Plane

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

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

Frowny :(

ContourPlot[Abs[CoshIntegral[I x-y]],{x,-5,5},{y,-5,5},ColorFunction->Hue,ContourLines->False,PlotPoints->50]

Real Root

Reduce[CoshIntegral[x]==0&&0<x<1,x]

Reduce[CoshIntegral[x]==0&&0<x<10,x]

Reduce[CoshIntegral[x]==0&&0<x<100,x]

FullSimplify[CoshIntegral[Root[{CoshIntegral[#1]&,0.5238225713898644064509582943832556696492516321326263192512`30.102999566398122}]]]

Derivative

D[CoshIntegral[z],z]

Integral

FullSimplify[Integrate[CoshIntegral[z],z]]