Hankel Function of the Second Kind

Author

Eric W. Weisstein
March 23, 2008

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

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

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

Enumeration

V5.2

Table[HankelH[2,n,z],{n,0,4}]//ColumnForm//TraditionalForm

V6

Table[HankelH2[n,z],{n,0,4}]//FunctionExpand//ColumnForm//TraditionalForm

Plots

<<Utilities`Plot`

Complex Plane

V5.2

ComplexPlot3D[HankelH2[0, z],{z,-5,5},
PlotPoints->100,
ComplexPlotLabel->HoldForm[HankelH2[0, z]]]//Timing

ComplexContourPlot[HankelH2[0, z],{z,-5,5},ComplexPlotLabel->HoldForm[HankelH2[0, z]]]//Timing

V6

ComplexPlot3D[HankelH2[0, z],{z,-5,5}]

ComplexContourPlot[HankelH2[0, z],{z,-5,5}]

Derivative

D[HankelH2[n,z],z]//TraditionalForm

Integral

(expr=Integrate[HankelH2[n,z],z])//TraditionalForm

D[expr,z]//FullSimplify

FullSimplify[Integrate[HankelH2[n,z],z],n∈Integers]

Integrate[HankelH2[n,z],z]/.n->0