[Scilab-users] Bessel functions

[Nikolay Strelkov]

Dear Claus!

For me it seems that using standard functions is always better, than
writing them from scratch.

So I recommend to use built-in Scilab functions besseli, besselj, besselk,
bessely, besselh <http://help.scilab.org/docs/5.5.1/en_US/bessel.html>.

With best regards,
maintainer of Mathieu functions toolbox for Scilab
<http://atoms.scilab.org/toolboxes/Mathieu>,
IEEE member, Ph.D.,
Nikolay Strelkov.


2015-01-24 19:53 GMT+03:00 Claus Futtrup <cfuttrup at gmail.com>:

>  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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