3.5.1.3.32 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.

For more information please review the s21bdc 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.

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

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