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MathGroup Archive 1997

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Re: Errors in Jacobian Elliptic Functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg7729] Re: Errors in Jacobian Elliptic Functions
  • From: Paul Abbott <paul at physics.uwa.edu.au>
  • Date: Wed, 2 Jul 1997 14:21:53 -0400 (EDT)
  • Organization: University of Western Australia
  • Sender: owner-wri-mathgroup at wolfram.com

seanross at worldnet.att.net wrote:
> 
> I have an application which requires extensive use of Jacobian Elliptic
> Functions like JacobiSN, EllipticPi and EllipticF.  I have found that
> these functions have some very small errors near the ends of their
> ranges.  For example, JacobiSN is supposed to be bounded by +1 and -1,
> just like Sine and Cosine.  However, for JacobiSN[x,p], with p very
> close to zero, JacobiSN can occasionally come out slightly greater than
> +1.  

I have not been able to reproduce this behaviour.  However I think I
know what you are encountering -- and the general solution: you probably
need to use arbitrary precision arithmetic.  There is an example in the
Mathematica Journal about computing Legendre functions of large order. 
One gets garbage there unless high precision is used.

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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