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Re: [Bug-gsl] bug in gsl_sf_coulomb_wave_FG_e (gsl 1.14 compiled with gc
Re: [Bug-gsl] bug in gsl_sf_coulomb_wave_FG_e (gsl 1.14 compiled with gcc 4.5.0)
Sun, 29 Aug 2010 14:12:28 +0100
Wanderlust/2.15.6 (Almost Unreal) Emacs/23.2 Mule/6.0 (HANACHIRUSATO)
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
> 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.