Re: Elliptic and Theta functions
- To: mathgroup at smc.vnet.net
- Subject: [mg9158] Re: Elliptic and Theta functions
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Thu, 16 Oct 1997 03:37:59 -0400
- Organization: University of Western Australia
- Sender: owner-wri-mathgroup at wolfram.com
Mr. Kashif Rasul wrote:
> I want to rewrite EllipticPi[-n,phi,m] where n>0, in terms of elliptic
> theta functions but when I try this, I seem to get the wrong answer. Can
> any one help me?
Can you give an example?
> Also if any one can tell me how Mathematica calculates EllipticPi, it
> might help because I suspect the algorithm for doing EllipticPi might
> use theta functions.
Section A.9.4 of the Mathematica book says that
o Elliptic integrals are evaluated using the descending Gauss
o Elliptic theta functions use series summation with recursive
evaluation of series terms.
o Other elliptic functions mostly use arithmetic-geometric mean methods.
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia Nedlands WA 6907
mailto:paul at physics.uwa.edu.au AUSTRALIA
God IS a weakly left-handed dice player
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