# 3.5.1.3.25 Elliptic_integral_rc

## Definition:

$rc = elliptic\_integral\_rc(x,y)$ calculates an approximate value for the integral

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

where x ≥ 0 and y ≠ 0.

This function, which is related to the logarithm or inverse hyperbolic functions for y < x and to inverse circular functions if x < y, arises as a degenerate form of the elliptic integral of the first kind. If y < 0, the result computed is the Cauchy principal value of the integral.

For more information please review the s21bac function in the NAG document

## Parameters:

x (input, double)
The argument x of the function.
i1 (output, double)
The argument y of the function
Constraint: x ≥ 0 and y ≠ 0.
rc (output, double)
An approximate value of the integral $R_c(x,y)=\frac 12\int_0^\infty \frac{dt}{\sqrt{t+x}(t+y)}$