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Re: Elliptic integral and function
- From: Brian Gough <bjg at network-theory dot co dot uk>
- To: Liam Healy <Liam dot Healy at nrl dot navy dot mil>
- Cc: gsl-discuss at sources dot redhat dot com
- Date: Tue, 18 Dec 2001 21:32:44 +0000 (GMT)
- Subject: Re: Elliptic integral and function
- References: <15390.8891.712402.651008@shadow.nrl.navy.mil>
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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