# 3.5.1.3.28 Elliptic_integral_rj

## Definition:

$Rj = elliptic\_integral\_rj(x,y,z,r)$ calculates an approximation to the integral

$R_J(x,y,z,\rho )=\frac 32\int_0^\infty \frac{dt}{(t+\rho )\sqrt{(t+x)(t+y)(t+z)}}$

Where x,y,z ≥ 0 , $\rho$ ≠0 and at most one of x, y and z is zero.

If $\rho$ <0, the result computed is the Cauchy principal value of the integral.

## 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.
r (input, double)
The argument r of the function.
Constraint: x, y, z ≥ 0.0, r ≠ 0.0 and at most one of x, y and z may be zero.
Rj (output, double)
Approximate value of the integral
$R_J(x,y,z,\rho )=\frac 32\int_0^\infty \frac{dt}{(t+\rho )\sqrt{(t+x)(t+y)(t+z)}}$