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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. +
Graph showing atanh(x).
-::: warning -🚧 This function is implemented but currently lacks detailed documentation. For guidance, you may refer to the equivalent functionality in [Microsoft Excel documentation](https://support.microsoft.com/en-us/office/excel-functions-by-category-5f91f4e9-7b42-46d2-9bd1-63f26a86c0eb). -::: \ No newline at end of file +## Examples +[See some examples in IronCalc](https://app.ironcalc.com/?example=atanh). + +## Links +* For more information about inverse hyperbolic functions, visit Wikipedia's [Inverse hyperbolic functions](https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions) page. +* See also IronCalc's [ASINH](/functions/math_and_trigonometry/asinh), [ACOSH](/functions/math_and_trigonometry/acosh) and [TANH](/functions/math_and_trigonometry/tanh) functions. +* Visit Microsoft Excel's [ATANH function](https://support.microsoft.com/de-de/office/atanh-function-453534d1-76a5-4f17-8c04-c3f2feee0dd5) page. +* Both [Google Sheets](https://support.google.com/docs/answer/3093397) and [LibreOffice Calc](https://wiki.documentfoundation.org/Documentation/Calc_Functions/ATANH) provide versions of the ATANH function. \ No newline at end of file