Modified Bessel Function of the Second Kind

Author

Eric W. Weisstein
July 9, 2004

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

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

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

Plots

Real Axis

Plot[Evaluate[Table[BesselK[n,x],{n,0,5}]],{x,0,5},PlotRange->{0,10},AxesLabel->TraditionalForm/@{x,BesselK[n,x]},PlotStyle->{Black,Red,Yellow,Green,Blue,Violet}]

Complex Plane

ComplexPlot3D[BesselK[0,z],{z,-5,5},PlotPoints->100]//Timing

ComplexContourPlot[BesselK[0,z],{z,-5,5}]//Timing

Integrals

Integrate[Cos[x Sinh[t]],{t,0,∞}]

Integrate[Cos[x t]/Sqrt[t^2+1],{t,0,∞},Assumptions->Im[x]==0]