[Scilab-users] Bessel functions

[Nikolay Strelkov]

I can add two resources to the list:

   - N. W. McLachlan, Bessel Functions for Engineers
   - Chapter about Bessel Functions at NIST - http://dlmf.nist.gov/10



2015-01-26 17:28 GMT+03:00 grivet <grivet at cnrs-orleans.fr>:

> Le 26/01/2015 10:57, Dang, Christophe a écrit :
>
>  Hello,
>>
>>  De  Claus Futtrup
>>> Envoyé : samedi 24 janvier 2015 17:53
>>>
>>> I've made a small script to play around with Bessel functions of the
>>> first kind
>>> [...]
>>> for m=0:19 // ...
>>> powerseries_m = ((-1)^m / (factorial(m) * factorial(m + n))) *
>>> (x/2)^(2*m);
>>> powerseries = powerseries + powerseries_m; // sum the powerseries
>>> end
>>>
>> Generally speaking, I think you'd better use the possibilities of vector
>> calculation as much as possible, to have a faster calculation.
>>
>> The lines above could look like the following, assuming x is a column
>> vector:
>>
>> m = 0:19;
>>
>> [x_mat, m_mat] = ndgrid(x, m); // rectangular matrices for group
>> evaluation
>>
>> f = 1 ./(factorial(m) .* factorial(m + n));
>>
>> f_mat = ndgrid(f, x)';
>>
>> powerseries = sum((-1).^m_mat.*f_mat.*(x_mat/2).^(2*m_mat), "c");
>>
>> However, this quite naive implementation is probably not accurate when x
>> and m are high,
>> for f would have some zeros (if m or m+n > 170) leading to zeros in
>> powerseries,
>> whereas f*(x/2)^(2m) might not be negligible.
>>
>> The reason why you should follow Nikolay's advice and use built-in
>> functions, which usually use strong algorithms.
>>
>> --
>> Christophe Dang Ngoc Chan
>> Mechanical calculation engineer
>> This e-mail may contain confidential and/or privileged information. If
>> you are not the intended recipient (or have received this e-mail in error),
>> please notify the sender immediately and destroy this e-mail. Any
>> unauthorized copying, disclosure or distribution of the material in this
>> e-mail is strictly forbidden.
>> _______________________________________________
>> users mailing list
>> users at lists.scilab.org
>> http://lists.scilab.org/mailman/listinfo/users
>>
> Almost every numerical analysis textbook comprises a chapter on the
> evaluation of Bessel functions, as for instance
>     Abramowitz ans Stegun, Handbook of mathematical functions, chapters
> 9,10 (elegant use of recurrence relation)
>     Press et al., Numerical recipes, chapter 6 (rational approximations)
> Enjoy!
>
> _______________________________________________
> users mailing list
> users at lists.scilab.org
> http://lists.scilab.org/mailman/listinfo/users
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.scilab.org/pipermail/users/attachments/20150126/c13cfd00/attachment.htm>