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MathGroup Archive 2005

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Re: Simplifying Jacobian elliptic functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55637] Re: Simplifying Jacobian elliptic functions
  • From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
  • Date: Fri, 1 Apr 2005 05:36:09 -0500 (EST)
  • Organization: Uni Leipzig
  • References: <d2g5qo$f3h$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

Unprotect[Plus]
JacobiDN[p_, k_]^2 + k_ JacobiSN[p_, k_]^2 := 1
Protect[Plus]


Regards

  Jens

"John Billingham" 
<John.Billingham at Nottingham.ac.uk> schrieb im 
Newsbeitrag news:d2g5qo$f3h$1 at smc.vnet.net...
>I am doing a problem involving Jacobian elliptic 
>functions, and am trying to use Mathematica to 
>help. However, I find that I am unable to 
>persuade Mathematica to simplify the expression
>
> JacobiDN[p, k^2]^2 + k^2 JacobiSN[p, k^2]^2
>
> which is equal to 1. It is also unable to 
> integrate powers of Jacobian elliptic functions 
> higher than 2, which are given by Byrd and 
> Friedman in terms of elliptic functions and 
> integrals.
>
> Can anyone help with this?
>
> Thanks,
>
> John
> 



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