Hankel Function of the First Kind

Author

Eric W. Weisstein
March 23, 2008

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

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

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

Notation

V5.2

HoldForm[HankelH1[0,z]]//TraditionalForm

V6

HankelH1[0,z]//TraditionalForm

Plots

<<Utilities`Plot`

Complex Plane

V5.2

ComplexPlot3D[HankelH1[0,z],{z,-5,5},
PlotPoints->100,
ComplexPlotLabel->HoldForm[HankelH1[0,z]]]//Timing

ComplexContourPlot[HankelH1[0,z],{z,-5,5},ComplexPlotLabel->HoldForm[HankelH1[0,z]]]//Timing

V6

ComplexPlot3D[HankelH1[0, z],{z,-5,5}]

ComplexContourPlot[HankelH1[0, z],{z,-5,5}]

Derivative

V5.2

D[HankelH1[n,z],z]//FullSimplify//TraditionalForm

V6

D[HankelH1[n,z],z]//FullSimplify//TraditionalForm

Integral

V5.2

Integrate[HankelH1[n,z],z]//FullSimplify//TraditionalForm

V6

(expr=Integrate[HankelH1[n,z],z])//TraditionalForm

D[expr,z]//FullSimplify

Table[expr,{n,0,3}]//FullSimplify

Table[Integrate[HankelH1[n,z],z],{n,0,2}]//FullSimplify//ColumnForm//TraditionalForm