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MathGroup Archive 1997

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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
transformation.  
o Elliptic theta functions use series summation with recursive
evaluation of series terms. 
o Other elliptic functions mostly use arithmetic-geometric mean methods.


Cheers,
	Paul 

____________________________________________________________________ 
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                            
http://www.pd.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________


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