# Elliptic_integral_rc

Elliptic-integral-rc-func

## Definition:

calculates an approximate value for the integral

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