Hi
I've made a small script to play around with Bessel functions of the
first kind... but this is very basic and I'm wondering if there's a
smarter way.
Below is the script I made (the function + a small test which plots the
result).
Best regards,
Claus
// bessel_test.sce
function z=Jn(n,x)
// The following power series approximates the nth Bessel
// function of the first kind for each input x
// In acoustics x = 2ka, defines the iput frequency k = omega / c and size
// of the piston radiator
powerseries = 0;
for m=0:19 // actually it should be infinity, but 10 approximates OK ...
powerseries_m = ((-1)^m / (factorial(m) * factorial(m + n))) *
(x/2)^(2*m);
powerseries = powerseries + powerseries_m; // sum the powerseries
end
z = ((x/2)^n) .* powerseries;
endfunction
x_array = 0:0.1:9.9; // define 100 points on the x-axis
// with 2ka (x) from 0 to 10, and with m = 0-19,
// this approximation is reasonably good for 2ka< 10
z_0_array = Jn(0,x_array); // Calculate J0
z_1_array = Jn(1,x_array); // Calculate J1
scf();
a = gca();
plot(x_array,z_0_array,'-b');
plot(x_array,z_1_array,'-r');
xtitle("Bessel functions","x (2ka)","output (z)");
legend("J0","J1");
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