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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