diff --git a/docs/src/functions/images/hyperbolicarctangent-curve.png b/docs/src/functions/images/hyperbolicarctangent-curve.png new file mode 100644 index 0000000..d4cdb0e Binary files /dev/null and b/docs/src/functions/images/hyperbolicarctangent-curve.png differ diff --git a/docs/src/functions/math_and_trigonometry/atanh.md b/docs/src/functions/math_and_trigonometry/atanh.md index 59b2a9f..eb1a2d1 100644 --- a/docs/src/functions/math_and_trigonometry/atanh.md +++ b/docs/src/functions/math_and_trigonometry/atanh.md @@ -4,8 +4,38 @@ outline: deep lang: en-US --- -# ATANH +# ATANH function +## Overview +ATANH is a function of the Math and Trigonometry category that calculates the inverse hyperbolic tangent (hyperbolic arctangent) of a number, returning the hyperbolic angle expressed in radians. +## Usage +### Syntax +**ATANH(number) => atanh** +### Argument descriptions +* *number* ([number](/features/value-types#numbers), required). The value whose inverse hyperbolic tangent is to be calculated, in the range (-1,+1). +### Additional guidance +The hyperbolic arctangent function is defined as: +$$ +\operatorname{atanh}(x) = \tfrac{1}{2}\,\ln\!\left(\dfrac{1+x}{1-x}\right),\quad |x| < 1 +$$ +### Returned value +ATANH returns a real [number](/features/value-types#numbers) that is the hyperbolic arctangent of the specified value, expressed in radians. +### Error conditions +* In common with many other IronCalc functions, ATANH propagates errors that are found in its argument. +* If no argument, or more than one argument, is supplied, then ATANH returns the [`#ERROR!`](/features/error-types.md#error) error. +* If the value of the *number* argument is not (or cannot be converted to) a [number](/features/value-types#numbers), then ATANH returns the [`#VALUE!`](/features/error-types.md#value) error. +* If the value of the *number* argument lies outside the domain (-1, +1), then ATANH returns the [`#NUM!`](/features/error-types.md#num) error. +* For some argument values, ATANH may return a [`#DIV/0!`](/features/error-types.md#div-0) error. + +## Details +* The ATANH function utilizes the *atanh()* method provided by the [Rust Standard Library](https://doc.rust-lang.org/std/). +* The figure below illustrates the output of the ATANH function. +
