From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 20724 invoked by alias); 19 Dec 2001 14:18:40 -0000 Mailing-List: contact gsl-discuss-help@sources.redhat.com; run by ezmlm Precedence: bulk List-Subscribe: List-Archive: List-Post: List-Help: , Sender: gsl-discuss-owner@sources.redhat.com Received: (qmail 20702 invoked from network); 19 Dec 2001 14:18:39 -0000 Received: from unknown (HELO mail12.svr.pol.co.uk) (195.92.193.215) by sources.redhat.com with SMTP; 19 Dec 2001 14:18:39 -0000 Received: from modem-126.eledhwen.dialup.pol.co.uk ([62.136.182.126] helo=debian) by mail12.svr.pol.co.uk with esmtp (Exim 3.13 #0) id 16GhYH-000122-00; Wed, 19 Dec 2001 14:18:34 +0000 Received: from bjg by debian with local (Exim 2.05 #1 (Debian)) id 16GRqv-0000AS-00; Tue, 18 Dec 2001 21:32:45 +0000 From: Brian Gough MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <15391.46588.180743.817113@debian> Date: Wed, 12 Dec 2001 16:16:00 -0000 To: Liam Healy Cc: gsl-discuss@sources.redhat.com Subject: Re: Elliptic integral and function In-Reply-To: <15390.8891.712402.651008@shadow.nrl.navy.mil> References: <15390.8891.712402.651008@shadow.nrl.navy.mil> X-Mailer: VM 6.62 under Emacs 19.34.1 X-SW-Source: 2001-q4/txt/msg00152.txt.bz2 Message-ID: <20011212161600.r_CKHGL_UfAROYV9fBUTq-7yjugsW20cMQNnSmLQPK4@z> 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 ---------------------------------------------------------------------- Network Theory Ltd Phone: +44 (0)117 3179309 15 Royal Park WWW: http://www.network-theory.co.uk/ Clifton Email: bjg@network-theory.co.uk Bristol BS8 3AL ----------------------------------------------------------------------