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MathGroup Archive 2005

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Re: Simplifying Jacobian elliptic functions

  • To: mathgroup at smc.vnet.net
  • Subject: [mg56313] Re: Simplifying Jacobian elliptic functions
  • From: John Billingham <John.Billingham at Nottingham.ac.uk>
  • Date: Fri, 22 Apr 2005 06:22:36 -0400 (EDT)
  • References: <d2j94b$oi$1@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*Ã?Â?,1]^2+JacobiSN[2*Ã?Â?,1]^2//TrigReduce
>  >>1
> 

I'm not sure what the symbols mean here, but I do know that JacobiCN[x,1] = cos(x) and JacobiSN[x,1] = sin(x). Does this idea work for general JacobiSN[x,k]?

John


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