From: Liam Healy <Liam.Healy@nrl.navy.mil>
To: Brian Gough <bjg@network-theory.co.uk>
Cc: Liam Healy <Liam.Healy@nrl.navy.mil>, gsl-discuss@sources.redhat.com
Subject: Re: Elliptic integral and function
Date: Wed, 19 Dec 2001 13:20:00 -0000 [thread overview]
Message-ID: <15392.62637.529777.544027@shadow.nrl.navy.mil> (raw)
In-Reply-To: <15391.46588.180743.817113@debian>
>>>>> "Brian" == Brian Gough <bjg@network-theory.co.uk> 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
WARNING: multiple messages have this Message-ID
From: Liam Healy <Liam.Healy@nrl.navy.mil>
To: Brian Gough <bjg@network-theory.co.uk>
Cc: Liam Healy <Liam.Healy@nrl.navy.mil>, gsl-discuss@sources.redhat.com
Subject: Re: Elliptic integral and function
Date: Thu, 13 Dec 2001 01:01:00 -0000 [thread overview]
Message-ID: <15392.62637.529777.544027@shadow.nrl.navy.mil> (raw)
Message-ID: <20011213010100.y3L1oROFd1Yvlxtr-VcgIdrsdnNQX0_GZzB7FIDJIbs@z> (raw)
In-Reply-To: <15391.46588.180743.817113@debian>
>>>>> "Brian" == Brian Gough <bjg@network-theory.co.uk> 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
WARNING: multiple messages have this Message-ID
From: Liam Healy <Liam.Healy@nrl.navy.mil>
To: Brian Gough <bjg@network-theory.co.uk>
Cc: Liam Healy <Liam.Healy@nrl.navy.mil>, gsl-discuss@sources.redhat.com
Subject: Re: Elliptic integral and function
Date: Wed, 19 Dec 2001 12:12:00 -0000 [thread overview]
Message-ID: <15392.62637.529777.544027@shadow.nrl.navy.mil> (raw)
Message-ID: <20011219121200.d2Y9wYg1gS8BIotrjhlpXcGCvX7euMHXKkgx7hhY-Wk@z> (raw)
In-Reply-To: <15391.46588.180743.817113@debian>
>>>>> "Brian" == Brian Gough <bjg@network-theory.co.uk> 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
next prev parent reply other threads:[~2001-12-19 20:12 UTC|newest]
Thread overview: 10+ messages / expand[flat|nested] mbox.gz Atom feed top
2001-12-19 13:20 Liam Healy
2001-12-08 10:51 ` Liam Healy
2001-12-17 8:52 ` Liam Healy
2001-12-19 13:20 ` Brian Gough
2001-12-12 16:16 ` Brian Gough
2001-12-19 6:18 ` Brian Gough
2001-12-19 13:20 ` Liam Healy [this message]
2001-12-13 1:01 ` Liam Healy
2001-12-19 12:12 ` Liam Healy
2001-12-19 13:20 ` Liam Healy
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