FW: Numerical Hypergeometric Functions

["Daniel Lozier" <lozier@nist.gov>]

Editor's Note:  The Web address in the editor's note below is incorrect.
The correct Web address is
http://math.nist.gov/mcsd/Reports/2001/nesf/ -- (just remove -i).  Sorry
for any inconvenience.

Dan Lozier

-----Original Message-----
From: opsftalk@nist.gov [mailto:opsftalk@nist.gov]On Behalf Of Daniel
Lozier
Sent: Tuesday, March 06, 2001 8:52 AM
To: Multiple recipients of list
Subject: FW: Numerical Hypergeometric Functions



Editor's Note:  A recently updated report by Frank Olver and me,
"Numerical Evaluation of Special Functions," contains an extensive
listing of available software.  It is available on the Web at
http://math-i.nist.gov/mcsd/Reports/2001/nesf/.

Dan Lozier

Sender: David Strozzi <dstrozzi@MIT.EDU>
Subject: Numerical Hypergeometric Functions


I am looking for a way to numerically compute the hypergeometric
function (the famous 2F1).  I need it for complex parameters (namely the
a and b in F(a,b;c;z) Abramowitz and Stegun notation) and analytically
continued outside the unit disk (along the negative real axis).

Any ideas?  Is there code for this on the web?  Is there a good article
or book that can be followed in a somewhat cookbook manner?

The function I need happens to be of the form F(a , b; a+b; -real^2),
and this can be "simplified" (A+S 15.3.10) to an infinite sum of Psi
functions.

Thanks a lot.

--
David Strozzi                             dstrozzi@mit.edu
home: 472 Putnam Ave., Apt. 2B     office: Bldg. NW 16-223
617-876-4929                                  617-452-2343
Cambridge, MA 02139           http://www.mit.edu/~dstrozzi