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Re: [Bug-gsl] bug in ellint.c
From: |
Brian Gough |
Subject: |
Re: [Bug-gsl] bug in ellint.c |
Date: |
Mon, 21 Sep 2009 12:59:08 +0100 |
User-agent: |
Wanderlust/2.14.0 (Africa) Emacs/22.2 Mule/5.0 (SAKAKI) |
At Fri, 11 Sep 2009 19:28:59 +1200,
tim wrote:
> should be
>
> const int rjstatus = gsl_sf_ellint_RJ_e(0.0, y, 1.0, 1.0 - n, mode, &rj);
> result->val = rf.val + (n/3.0) * rj.val;
>
> From Wikipedia
>
> K(k)=R_F\left(0,1-k^2,1\right)
>
> E(k)=R_F\left(0,1-k^2,1\right)-\frac{1}{3}k^2 R_D\left(0,1-k^2,1\right)
>
> \Pi(n,k)=R_F\left(0,1-k^2,1\right)+\frac{1}{3}n R_J
> \left(0,1-k^2,1,1-n\right)
Thanks for your email. Wikipedia is using a different sign convention
for n -- we use the sign in the original Carlson paper, equation 4.3.
For reference, the paper is available at
http://resolver.sub.uni-goettingen.de/purl?GDZPPN001175246
--
Brian Gough
GNU Scientific Library -
http://www.gnu.org/software/gsl/