[Bug-gsl] bug in ellint.c

[tim]

hi

i have come across a bug in ellint.c (special functions)

function  gsl_sf_ellint_Pcomp_e(double k, double n, gsl_mode_t mode, 
gsl_sf_result * result)

the signs are interchanged on the following lines:

the lines:

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;

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) 

great library.

cheers

tim