From mboxrd@z Thu Jan 1 00:00:00 1970 Return-Path: Received: (qmail 22692 invoked by alias); 19 Dec 2001 20:12:19 -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 22680 invoked from network); 19 Dec 2001 20:12:19 -0000 Received: from unknown (HELO shadow.nrl.navy.mil) (132.250.121.160) by sources.redhat.com with SMTP; 19 Dec 2001 20:12:19 -0000 Received: by shadow.nrl.navy.mil (Postfix, from userid 1114) id BF9A63F8B; Wed, 19 Dec 2001 15:12:29 -0500 (EST) From: Liam Healy MIME-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit Message-ID: <15392.62637.529777.544027@shadow.nrl.navy.mil> Date: Thu, 13 Dec 2001 01:01:00 -0000 To: Brian Gough Cc: Liam Healy , gsl-discuss@sources.redhat.com Subject: Re: Elliptic integral and function In-Reply-To: <15391.46588.180743.817113@debian> References: <15390.8891.712402.651008@shadow.nrl.navy.mil> <15391.46588.180743.817113@debian> X-Mailer: VM 6.72 under 21.1 (patch 8) "Bryce Canyon" XEmacs Lucid Reply-To: Liam Healy X-SW-Source: 2001-q4/txt/msg00153.txt.bz2 Message-ID: <20011213010100.y3L1oROFd1Yvlxtr-VcgIdrsdnNQX0_GZzB7FIDJIbs@z> >>>>> "Brian" == Brian Gough writes: Brian> 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 >> Brian> Hi, Brian> Using the conventions in the GSL manual the relation is, Brian> sn(K(k),k^2) = 1 Brian> cn(K(k),k^2) = 0 Brian> dn(K(k),k^2) = sqrt(1-k^2) Brian> which should work correctly. I think there is a note about the Brian> different notations used by Carlson and Abramowitz&Stegun somewhere in Brian> the chapter there. You're absolutely right, I had overlooked the m (where m=k^2). And it is documented, if a bit obscurely, "The Jacobian Elliptic functions are defined in Abramowitz & Stegun, Chapter 16." so one has to hunt down A&S for the definition and see how they've defined the arguments. Thank you for solving this mystery. Liam