The inverse hyperbolic tangent function.
xis a real or complex number
arctanh is the inverse of the hyperbolic tangent function. For real numbers, the domain is (−1, 1). It is defined by
arctanh(z) = [ln(1 + z) − ln(1 − z)] / 2
for all complex
z. This formula is also used for real numbers outside [−1, 1].
This function is also called
artanh (area hyperbolic cotangent) in the literature. Some authors claim that the name
arctanh is a misnomer, but this depends crucially on how you view the connections between the trigonometric and the hyperbolic functions and their (restriction) inverses. One can argue that the name
arctanh makes perfect sense.
0.549306144334 − 1.57079632679⋅i