Re: [Bug-gsl] gsl_sf_hyperg_1F1

[Brian Gough]

At Mon, 30 Nov 2009 15:26:11 +0100,
Weibin Li wrote:
> The output of above code shows an extremely large error. by increasing
> Ri, the relative error decreases. Is there any idea to fix this?

I've looked at the problem.  Unfortunately I think it is just very
difficult to compute an accurate value in this region.  The large
error reflects that.  I have logged it at as bug at
https://savannah.gnu.org/bugs/index.php?28267

I could not find of any algorithm that gives an accurate value in this
region of parameters (a<<0, |a|>b>0, x>>0) , due to cancellation
errors in both the ordinary 1F1 series and Kummer transformed series.
If you know of one I would be glad to hear it.

-- 
Brian Gough

GNU Scientific Library -
http://www.gnu.org/software/gsl/