| Pré. | Proc. |
ellpk
Complete elliptic integral of the first kind.SYNOPSIS:
double m1, y, ellpk();
y = ellpk(m1);
DESCRIPTION:
Approximates the integral:
pi/2
-
| |
| dt
K(m) = | ------------------
| 2
| | sqrt(1 - m sin t)
-
0
where m = 1 - m1, using the approximation:
P(x) - log x Q(x).
The argument m1 is used rather than m, so that the logarithmic singularity at m = 1 will be shifted to the origin; this preserves maximum accuracy.
K(0) = pi/2.
ACCURACY:
Relative error:
arithmetic domain # trials peak rms
DEC 0,1 16000 3.5e-17 1.1e-17
IEEE 0,1 30000 2.5e-16 6.8e-17
ERROR MESSAGES:
message condition value returned
domain x<0, x>1 0.0