File:Kelvin Bessel function.png

Plot of zeroth order Kelvin-Bessel functions ber(x) and bei(x).

 

This plot was created with Gnuplot.

Made with the following Gnuplot 3.7 script :

# Define zeroth order Kelvin-Bessel functions
ber(x) = 1. -1*(x/2.)**4 / (1.*2.)**2 +1*(x/2.)**8 / (1.*2.*3.*4.)**2 -1*(x/2.)**12 / (1.*2.*3.*4.*5.*6.)**2 
+1*(x/2.)**16 / (1.*2.*3.*4.*5.*6.*7.*8.)**2 -1*(x/2.)**20 / (1.*2.*3.*4.*5.*6.*7.*8.*9.*10.)**2 +1*(x/2.)**24 /  
(1.*2.*3.*4.*5.*6.*7.*8.*9.*10.*11.*12.)**2 -1*(x/2.)**28 / (1.*2.*3.*4.*5.*6.*7.*8.*9.*10.*11.*12.*13.*14.)**2
+1*(x/2.)**32 / (1.*2.*3.*4.*5.*6.*7.*8.*9.*10.*11.*12.*13.*14.*15.*16.)**2 -1*(x/2.)**36 /
(1.*2.*3.*4.*5.*6.*7.*8.*9.*10.*11.*12.*13.*14.*15.*16.*17.*18.)**2 
bei(x) =     +1*(x/2.0)**2/(1.)**2-1*(x/2.0)**6/(1.*2.*3.)**2 +1*(x/2.0)**10/(1.*2.*3.*4.*5.)**2 
-1*(x/2.0)**14/(1.*2.*3.*4.*5.*6.*7.)**2 +1*(x/2.0)**18/(1.*2.*3.*4.*5.*6.*7.*8.*9.)**2
-1*(x/2.0)**22/(1.*2.*3.*4.*5.*6.*7.*8.*9.*10.*11.)**2
+1*(x/2.0)**26/(1.*2.*3.*4.*5.*6.*7.*8.*9.*10.*11.*12.*13.)**2
-1*(x/2.0)**30/(1.*2.*3.*4.*5.*6.*7.*8.*9.*10.*11.*12.*13.*14.*15.)**2
+1*(x/2.0)**34/(1.*2.*3.*4.*5.*6.*7.*8.*9.*10.*11.*12.*13.*14.*15.*16.*17.)**2
# Open bitmap terminal and plot functions
set term pbm medium color
set output "kb01.pnm"
set samples 1000
set grid
set key top left
set mxtics
set mytics
plot [-8:8] [-30:30] ber(x) with lines lt 1 lw 2, bei(x) with lines lt 7 lw 2

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