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
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