The hyperbolic arc-tangent is the inverse of the hyperbolic tangent function. Calcute implements it with the atanh function. The inverse hyperbolic tangent of a value x is the value y for which the hyperbolic tangent of y is x. In other words if y = atanh(x) then x = tanh(y).
The hyperbolic arc-tangent function is only defined in the open range
In some mathematical texts and hand-held calculators, the notation tanh-1 is sometimes used to represent the hyperbolic arc-tangent function. This is an unfortunate notational choice since it could also stand for the multiplicative inverse 1/tanh which is a different function.
Yet another term also used to represent the inverse hyperbolic tangent function is "arctanh".