Complete elliptic integral of the first kind
Approximates the integral
K(m) = $(INTEGRATE 0, π/2) dt/ (sqrt( 1- m sin2 t))
where m = 1 - x, using the approximation
P(x) - log x Q(x).
The argument x is used rather than m so that the logarithmic singularity at x = 1 will be shifted to the origin; this preserves maximum accuracy.
x must be in the range 0 <= x <= 1
This is equivalent to ellipticF(PI_2, 1-x).
K(0) = π/2.
See Implementation
Complete elliptic integral of the first kind
Approximates the integral
K(m) = $(INTEGRATE 0, π/2) dt/ (sqrt( 1- m sin2 t))
where m = 1 - x, using the approximation
P(x) - log x Q(x).
The argument x is used rather than m so that the logarithmic singularity at x = 1 will be shifted to the origin; this preserves maximum accuracy.
x must be in the range 0 <= x <= 1
This is equivalent to ellipticF(PI_2, 1-x).
K(0) = π/2.