From mboxrd@z Thu Jan  1 00:00:00 1970
From: Liam Healy <Liam.Healy@nrl.navy.mil>
To: gsl-discuss@sources.redhat.com
Subject: Elliptic integral and function
Date: Mon, 17 Dec 2001 08:52:00 -0000
Message-ID: <15390.8891.712402.651008@shadow.nrl.navy.mil>
X-SW-Source: 2001-q4/msg00158.html
Message-ID: <20011217085200.vWVAPyRNH3thLIduYKj9f68g6zFntAzKbWxUbqssLss@z>

My understanding is that the Jacobi elliptic function is the inverse
of the elliptic function.  That is, 
  sn(K(k),k) = 1
  cn(K(k),k) = 0
  dn(K(k),k) = sqrt(1-k^2)
see http://mathworld.wolfram.com/JacobiEllipticFunctions.html

but when I try this I get e.g.
gsltest 0.5
k=  0.50000000000000 K(k)=  1.68575035481260
sn=  0.99289175131682 cn=  0.11902088122262 dn=  0.71209759519570
all three of these seem wrong.  My driver program is attached.

What is wrong here?  Thank you for any light you can shed on this. 

Liam