ellpe

Complete elliptic integral of the second kind.

SYNOPSIS:

double m1, y, ellpe();
y = ellpe(m1);

DESCRIPTION:

Approximates the integral

            pi/2
             -
            | |                 2
E(m) =    |    sqrt( 1 - m sin t ) dt
          | |
           -
            0

Where m = 1 - m1, using the approximation:

      P(x) - x log x Q(x).

Though there are no singularities, the argument m1 is used rather than m, for compatibility with ellpk().

E(1) = 1; E(0) = pi/2.

ACCURACY:
                      Relative error:
arithmetic   domain     # trials      peak         rms
    DEC        0, 1       13000       3.1e-17     9.4e-18
    IEEE       0, 1       10000       2.1e-16     7.3e-17

ERROR MESSAGES:

   message       condition      value returned
   domain        x<0, x>1            0.0