[Scilab-users] Bessel functions

[Claus Futtrup]

Hi Nikolay, et al.

You're right, I should have checked Scilab help for Bessel functions 
before trying to do my own.

I executed besselj(0,x_array) as well as besselj(1,x_array) ... it seems 
that this function works exactly like what I made myself. And the output 
is indistinguishable (for the range I'm interested in).

Trying to find the Scilab code for besselj, I see that it's an 
uneditable and hard coded. Is there anywhere I can study in detail how 
besselj was coded?

Best regards,
Claus

On 24-01-2015 18:01, Nikolay Strelkov wrote:
> 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 ofMathieu 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 
> <mailto: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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