# 3.5.1.3.27 Elliptic_integral_rf

## Definition:

$Rf=elliptic\_integral\_rf(x,y,z)$ calculates an approximation to the integral

$R_F(x,y,z)=\frac 12\int_0^\infty \frac{dt}{\sqrt{(t+x)(t+y)(t+z)}}$

where x, y, z ≥ 0 and at most one is zero.

For more information please review the s21bbc function in the NAG document.

## Parameters:

x (input, double)
The argument x of the function.
y (input, double)
The argument y of the function.
z (input, double)
The argument z of the function.
Constraint: x, y, z ≥ 0.0 and only one of x, y and z may be zero.
Rf (output, double)
Approximation of the integral
$R_F(x,y,z)=\frac 12\int_0^\infty \frac{dt}{\sqrt{(t+x)(t+y)(t+z)}}$