Does GSL or IMSL or GMP or MPFR have high precision hypergeometric function 2F1?

[Linas Vepstas]

On Wed, Jul 04, 2007 at 07:52:21PM -0400, Michael wrote:
> Does GSL or IMSL or GMP or MPFR have high precision hypergeometric function 2F1?
> 
> Hi all,
> 
> I am looking for a high/multiple precision hypergeometric function
> 2F1(a, b, c, z) implementation. My application needs b and c to be
> very large, and it is beyond the range of double precision.

? 
GSL only goes as far as double precision.

If b and c are "beyond the range of double precision", then one can get
a good approximation by computing 1F0 instead. This isn't what you need?

> More specifically, I hope I will be able to looking into the multiple
> precision implementation of the hypergeometric function 2F1(a, b, c,
> z) and change the power series
> 
> a0+a1*z+a2*z^2+a3*z^3+...
> 
> into
> 
> a0+a1*z1+a2*z2+a3*z3+...

!? It is not hard to write code for this.  Its maybe 50 lines 
of code or so. I spent a (very) short afternoon writing 2F1 for GMP, 
and then tweaking and tesing it. Its not "rocket science".

> The whole evaluation of the hypergeometric function has to be
> extremely fast for my application.

Heh. And how fast must that be?

--linas