[Scilab-users] Bessel functions

[Dang, Christophe]

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
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