ellik

Incomplete elliptic integral of the first kind.

SYNOPSIS:

double phi, m, y, ellik();
y = ellik(phi, m);

DESCRIPTION:

Approximates the integral:

                phi
                 -
                | |
                |           dt
F(phi_\m) =    |    ------------------
                |                  2
              | |    sqrt(1 - m sin t)
               -
                0

of amplitude phi and modulus m, using the arithmetic - geometric mean algorithm.

ACCURACY:

Tested at random points with m in [0, 1] and phi as indicated.

                    Relative error:
arithmetic   domain     # trials      peak         rms