[Date Index] [Thread Index] [Author Index]

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
>