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 ____________________________________________________________________