Documentation/Calc Functions/ATANH

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Function name:

ATANH

Category:

Mathematical

Summary:

Calculates the inverse hyperbolic tangent (artanh) of a real number, in radians.

Syntax:

ATANH(Number)

Returns:

Returns a real number that is the inverse hyperbolic tangent of Number in radians.

Arguments:

Number is a real number in the range (-1, 1), or a reference to a cell containing that number, whose inverse hyperbolic tangent is to be calculated.

  • If Number is non-numeric, then ATANH reports a #VALUE! error.
  • If Number lies outside the range (-1, 1), the ATANH reports an invalid argument error (Err:502).

Additional details:

The formula for the inverse hyperbolic tangent of x is:

[math]\displaystyle{ \operatorname{artanh}(x) = \frac{1}{2}~ \ln\left (\dfrac{1+x}{1-x}\right ) }[/math]

The figure below illustrates the function ATANH.

ATANH function

Examples:

Formula Description Returns
=ATANH(0) Inverse hyperbolic tangent of 0. 0
=ATANH(TANH(4)) Inverse hyperbolic tangent of hyperbolic tangent of 4. 3.99999999999999
=ATANH(D1) where cell D1 contains the number 0.5. Inverse hyperbolic tangent of 0.5. 0.549306144334055

Related LibreOffice functions:

ACOSH

ACOTH

ASINH

FISHER

TANH

ODF standard:

Section 6.16.11, Part 2

Equivalent Excel functions:

ATANH