Elliptic integral and function

[Brian Gough]

Liam Healy writes:
 > 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
 > 

Hi,
Using the conventions in the GSL manual the relation is,

 sn(K(k),k^2) = 1
 cn(K(k),k^2) = 0
 dn(K(k),k^2) = sqrt(1-k^2)

which should work correctly. I think there is a note about the
different notations used by Carlson and Abramowitz&Stegun somewhere in
the chapter there.

regards

-- 
Brian Gough

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