Re: Hypergeometric function

• To: mathgroup at smc.vnet.net
• Subject: [mg50209] Re: Hypergeometric function
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Fri, 20 Aug 2004 04:58:06 -0400 (EDT)
• Organization: The University of Western Australia
• References: <cg20ms\$p0q\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <cg20ms\$p0q\$1 at smc.vnet.net>, jujio77 at yahoo.com (Scott)
wrote:

> I have a finite alternating series of hypergeometric (2F1) functions.

Why not give the series?

> These functions have complex parameters.  When I sum the series I get
> larger and larger values.

THen perhaps it is divergent?

> My question is this,  does anyone know how
> precise Mathematica is when calculating a hypergeometric fn
> numerically ie, how many sig figs are correct?

Are you working with machine precision or arbitrary precision? For
example, compare

machine = Hypergeometric2F1[1 + 2 I, 2 - I, 3 - I, 0.95]

with

arbitrary = Hypergeometric2F1[1 + 2 I, 2 - I, 3 - I, 0.95`30]

In the second case the argument is given with Precision 30. If you
compute the difference between these expressions

machine - arbitrary

you will see that the machine precision result is correct to
MachinePrecision.

> I have done various transformations on the hypergeometric fn and then
> summed the series.  Each time I arrive at the same result.

Which is good to hear, at least from a consistency viewpoint.

Cheers,
Paul

--
Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)
35 Stirling Highway
Crawley WA 6009                      mailto:paul at physics.uwa.edu.au
AUSTRALIA                            http://physics.uwa.edu.au/~paul

```

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