[Maxima-bugs] Incorrect derivative of the Jacobi elliptic function
Subject: [Maxima-bugs] Incorrect derivative of the Jacobi elliptic function
From: Raymond Toy
Date: Tue, 06 Jul 2010 18:39:42 -0400
On 7/6/10 4:08 PM, Ovidius Publius Naso wrote:
> Hi,
>
> I think the derivative of the Jacobi dn(x,k) elliptic function is
> incorrect. Typing
>
> diff(jacobi_dn(x,k),x);
>
> returns with
>
> -k * jacobi_cn(x,k) * jacobi_sn(x,k)
>
> but the pre-factor should be k^2 instead of simply k.
>
>
>
Maxima's elliptic functions use the parameter m, not the modulus k (m =
k^2). The derivative matches A&S 16.16.3. (I see the DLMF now defines
the functions in terms of k, but functions.wolfram.com still uses m.)
Ray
BTW, is the maxima-bugs list supposed to be for bugs? I thought it was
generated from the bug tracker, and not for general use.