From: "David Rusin" <drusin@starman.physics.upenn.edu>
Subject: c code for complex hypergeometric series?
Date: Mon, 22 Nov 1999 01:16:46 -0500
Newsgroups: sci.math

Does there exist some C code for the computation of the complex
hypergeometric series 2F1 (a, b; c, z) -- including the analytic
continuation for |z| > 1? I need to calculate many such series as part of
some new gravitational lens modeling software I'm writing -- and I've hit a
bit of a wall in my calculations of the analytic continuation.

If anybody would like to help out a tired grad student, you can write me at
drusin@starman.physics.upenn.edu. Your code contribution will be gratefully
acknowledged in future papers.

David Rusin
==============================================================================

From: rusin@vesuvius.math.niu.edu (Dave Rusin)
Subject: Re: c code for complex hypergeometric series?
Date: 22 Nov 1999 07:51:55 GMT
Newsgroups: sci.math

I don't have a really good answer, just a really good reason for
following up...

In article <81am7a$gve$1@netnews.upenn.edu>,
David Rusin <drusin@starman.physics.upenn.edu> wrote:
>Does there exist some C code for the computation of the complex
>hypergeometric series 2F1 (a, b; c, z) -- including the analytic
>continuation for |z| > 1? I need to calculate many such series as part of
>some new gravitational lens modeling software I'm writing -- and I've hit a
>bit of a wall in my calculations of the analytic continuation.

Well, there is code at Netlib ( http://www.netlib.org/ ) including e.g.
TOMS algorithm 191 and algorithm 707 (for the confluent hypergeometric 
function). You could also look at Maple code, for example, since
Maple seems to be able to compute these.

You would likely get a good response from the newsgroup sci.math.num-analysis

There is a SIAM interest group on Special Functions (which includes
the hypergeometric functions); see
    http://www.math.yorku.ca/Who/Faculty/Muldoon/siamopsf/

For more information about resources in numerical analysis, see
    http://tonic.physics.sunysb.edu/docs/num_meth.html

dave (the _other_ David Rusin!)

(I would write, "David _J._ Rusin", but I know from previous correspondence
that even that is still insufficient in this case!)