Loadable Function: z = gsl_sf_ellint_Ecomp (arg1, mode)

Loadable Function: [z, err] = gsl_sf_ellint_Ecomp (…)

Computes the complete elliptic integral E(k) to the accuracy specified by the mode variable mode.

                              pi
                             ---
                              2
                            /
                            |             2    2
        ellint_Ecomp(k)  =  |   sqrt(1 - k sin (t)) dt
                            |
                            /
                             0

See also: ellipj, ellipke.

The notation used here is based on Carlson, Numerische Mathematik 33 (1979) and differs slightly from that used by Abramowitz & Stegun, where the functions are given in terms of the parameter m = k^2.

err contains an estimate of the absolute error in the value z.

The argument mode must be an integer corresponding to

0 = GSL_PREC_DOUBLE

Double-precision, a relative accuracy of approximately 2e-16.

1 = GSL_PREC_SINGLE

Single-precision, a relative accuracy of approximately 1e-7.

2 = GSL_PREC_APPROX

Approximate values, a relative accuracy of approximately 5e-4.

This function is from the GNU Scientific Library, see http://www.gnu.org/software/gsl/ for documentation.

Package: gsl