[Scilab-users] Bessel functions

[Nikolay Strelkov]

In modern Scilab these functions are called from Fortran library.
Here is its source
<http://gitweb.scilab.org/?p=scilab.git;a=blob;f=scilab/modules/special_functions/src/fortran/dbesjg.f>
.



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 20:21 GMT+03:00 Claus Futtrup <cfuttrup at gmail.com>:

>  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 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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>
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