Re: [Bug-gsl] bug in ellint.c

[tim]

brian hi

thanks for replying.

i was checking the results against the keisan casio library and found 
errors between the two. when i changed the equation to match wikipedia i 
got the same results as keisan.

after your comments i have checked further. am i correct that there are 
two different definitions of the third elliptic integral - one with 1 + 
n and the other with 1 - n. In that case the result for -n from the 
first type should match the result for n for the other type. which seems 
to be the case. your result for -n matches keisan result for n and vice 
versa.

pity there is no standard definition. thanks for your help.

tim

Brian Gough wrote:
> 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
>
>