# 3.5.1.3.26 Elliptic_integral_rd

## Definition:

$Rd = elliptic\_integral\_rd(x,y,z)$ calculates an approximate value for the integral

$R_D(x,y,z)=\frac 32\int_0^\infty \frac{dt}{\sqrt{(t+z)(t+y)(t+z)^3}}$

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

## 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 ≥ 0.0, z>0.0 and only one of x, y and z may be zero.
Rd (output, double)
Approximate value of the integral
$R_D(x,y,z)=\frac 32\int_0^\infty \frac{dt}{\sqrt{(t+z)(t+y)(t+z)^3}}$