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ATANH function

Inverse hyperbolic tangent function. ATANH(x) returns the inverse hyperbolic tangent of x. x must be in the open interval (−1, 1).

The inverse hyperbolic tangent can be expressed as a natural logarithm:

$$ \operatorname{atanh}(x) = \frac{1}{2}\ln\!\left(\frac{1+x}{1-x}\right) $$

The argument x can be a real number, a complex number, or a matrix. When it is a matrix, the function returns a matrix with the same dimensions and with the ATANH function applied to all elements.

Examples

ATANH(0) equals 0

ATANH(0.5) equals 0.5493061

Calculator

ATANH 0.69314718056

Graph

ATANH function

Relation with ASINH and ACOSH functions

Inverse hyperbolic functions ASINH, ACOSH, ATANH

Related functions

External links