
From:  tim 
Subject:  Re: [Buggsl] bug in ellint.c 
Date:  Tue, 22 Sep 2009 15:12:33 +1200 
Useragent:  Thunderbird 1.5.0.12 (X11/20080430) 
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 WikipediaK(k)=R_F\left(0,1k^2,1\right)E(k)=R_F\left(0,1k^2,1\right)\frac{1}{3}k^2 R_D\left(0,1k^2,1\right) \Pi(n,k)=R_F\left(0,1k^2,1\right)+\frac{1}{3}n R_J\left(0,1k^2,1,1n\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.unigoettingen.de/purl?GDZPPN001175246
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