* Does GSL or IMSL or GMP or MPFR have high precision hypergeometric function 2F1?
@ 2007-07-04 23:52 Michael
2007-07-06 17:29 ` Linas Vepstas
0 siblings, 1 reply; 2+ messages in thread
From: Michael @ 2007-07-04 23:52 UTC (permalink / raw)
To: gsl-discuss, help-gsl, gmp-discuss, mpfr
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.
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+...
where z1, z2, z3, ... are user supplied high precision numbers.
The whole evaluation of the hypergeometric function has to be
extremely fast for my application.
Could anybody shed some lights?
Thanks a lot!
^ permalink raw reply [flat|nested] 2+ messages in thread
* Re: Does GSL or IMSL or GMP or MPFR have high precision hypergeometric function 2F1?
2007-07-04 23:52 Does GSL or IMSL or GMP or MPFR have high precision hypergeometric function 2F1? Michael
@ 2007-07-06 17:29 ` Linas Vepstas
0 siblings, 0 replies; 2+ messages in thread
From: Linas Vepstas @ 2007-07-06 17:29 UTC (permalink / raw)
To: Michael; +Cc: gsl-discuss, help-gsl, gmp-discuss, mpfr
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
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2007-07-04 23:52 Does GSL or IMSL or GMP or MPFR have high precision hypergeometric function 2F1? Michael
2007-07-06 17:29 ` Linas Vepstas
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