[Bug-gsl] [bug #53876] gsl_sf_hyperg_2F1_renorm missing factor

[Charles Hussong]

URL:
  <http://savannah.gnu.org/bugs/?53876>

                 Summary: gsl_sf_hyperg_2F1_renorm missing factor
                 Project: GNU Scientific Library
            Submitted by: chussong
            Submitted on: Fri 11 May 2018 02:08:22 AM UTC
                Category: Accuracy problem
                Severity: 3 - Normal
        Operating System: 
                  Status: None
             Assigned to: None
             Open/Closed: Open
                 Release: 
         Discussion Lock: Any

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Details:

Hello,

I apologize for the poor formatting; I hope this report is simple enough that
it isn't too offensive.

I was surprised today to see gsl putting out a wrong answer for the
renormalized hypergeometric function. The behavior is easily observed with the
following call from one of my unit tests: gsl_sf_hyperg_2F1_renorm(1, 2, -3,
0.4). This returns 2572.02, but the correct answer is 65.8436.

Upon further inspection, the cause is pretty clear: the case in question
begins on line 843 of specfunc/hyperg_2F1.c, where an appeal is made to
Abramowitz and Stegun (15.1.2) [see
http://people.math.sfu.ca/~cbm/aands/page_556.htm]; this is perfectly valid,
but the subsequent code omits the z^(m+1).

I would offer a patch for this directly, but I'm certain I'd do the error
handling incorrectly; if not for this concern, simply changing the first
argument on line 863 from "sg * F.val" to "sg * pow(x, -c+1) * F.val" would
give the right answer.

Please let me know if there is any further assistance I can provide.

Best regards,
Charles




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