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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/




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