Re: [Bug-gsl] hyperg_U(a,b,x) Questions about x<0 and values

[Raymond Rogers]

Brian Gough <address@hidden>
Subject: Re: [Bug-gsl] hyperg_U(a,b,x) Questions about x<0 and values
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At Wed, 07 Jul 2010 10:14:34 -0500,
Raymond Rogers wrote:

> > 
> > 1) I was unable to find the valid domain of  the argument a when x<0. 
> > Experimenting yields what seem to be erratic results.  Apparently
> > correct answers occur when {x<0&a<0& a  integer}.  References would be
> > sufficient.   Unfortunately {x<0,a<0} is exactly the wrong range for my
> > problem; but the recursion relations can be used to stretch to a>0.  If
> > I can find a range of correct operation for the domain of "a" of width >1.
>   

| Brian Gough
| Thanks for the email.  There are some comments about the domain for
| the hyperg_U_negx function in specfunc/hyperg_U.c -- do they help?

They explain some things, but I believe the section

  if (b_int && b >= 2 && !(a_int && a <= (b - 2))){}
  else {}

is implemented incorrectly; and probably the preceding section as well.  Some 
restructuring of the code would make things clearer; but things like that 
should probably done in a different forum: email, blog, etc...
I think the switches might be wrong.  In any case it seems that b=1 has a hole. 
 Is there a source for this code?

Note: the new NIST Mathematical handbook might have better algorithms.  I am 
certainly no expert on implementing mathematical functions (except for finding 
ways to make them fail).

Ray