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MathGroup Archive 2005

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Re: Simplifying Jacobian elliptic functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg55649] Re: [mg55612] Simplifying Jacobian elliptic functions
  • From: Pratik Desai <pdesai1 at umbc.edu>
  • Date: Fri, 1 Apr 2005 05:36:21 -0500 (EST)
  • References: <200503310624.BAA15143@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

John Billingham wrote:

>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
>
>  
>
I think you need to pass arguments to your variables than it will work

 >>JacobiCN[2*Ï?,1]^2+JacobiSN[2*Ï?,1]^2//TrigReduce
 >>1

Also there is a lot of information you may seek in the note books 
available for elliptic functions on the following website
http://functions.wolfram.com/EllipticFunctions/JacobiSN/

Hope this helps

Praik Desai


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