The hyperbolic arctangent of a number is the angle whose hyperbolic tangent is that number. The angle is returned in radians, regardless of the current trigonometric mode. ATNH accepts either a COMPLEX or REAL argument and returns a value of the same type. For REAL arguments the domain is between -1 and 1. For complex arguments, ATNH returns the principal value, defined (in terms of complex arithmetic) as
ATNH(Z) = 1/2*LOG((1+Z)/(1-Z))
which returns an imaginary part in the range -PI/2 to PI/2. The domain for COMPLEX arguments includes all points in the complex plane except CMPLX(±1,0). Notice that intermediate values generated during the calculation of the function can cause over or underflow errors for very large or small values of Z.