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