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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