Re: [Bug-gsl] bug in gsl_sf_coulomb_wave_FG_e (gsl 1.14 compiled with gcc 4.5.0)

[Brian Gough]

At Fri, 27 Aug 2010 13:36:08 -0400,
Alexey A. Illarionov wrote:
> It looks like that these values are incorrect since both F and Fp should 
> be very small (correct me if I'm wrong since I'm not familiar with Pari 
> and gsl test system). If you need verify the values than its better to 
> use bessel function series.
> 
> For eta == 0. and integer lambda coulomb function are just 
> bessel-ricatti functions, i.e. spherical_bessel functions times argument
> F_l(x) = j_l (x) * x
> G_l(x) = n_l (x) * x
> Thus
> F_l(x) = 1/(2l+1)!! x^(l+1) [1 - x^2/(2l+3)/2 + ...]
> G_l(x) = (2l+1)!!/(2l+1) x^(-l) [1 + x^2/(2l-1)/2 + ...]
> I think Abramowitz, Stegun should have the complete expressions.

Thanks that is much better, the calculation of the integral was not
reliable.  I've committed the new test values.