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# Math.atanh

## Math.atanh

The Math.atanh() function returns the hyperbolic arctangent of a number, that is

$∀x∊(-1,1),Math.atanh(x)=arctanh(x)= the unique ysuch thattanh(y)=x\forall x \in \left( -1, 1 \right), \mathtt{\operatorname{Math.atanh}(x)} = \operatorname{arctanh}(x) = \text{ the unique } \; y \; \text{such that} \; \tanh(y) = x$

## Syntax

Math.atanh(x)

### Parameters

x
A number.

## Description

Because atanh() is a static method of Math, you always use it as Math.atanh(), rather than as a method of a Math object you created (Math is not a constructor).

## Examples

### Using Math.atanh()

Math.atanh(-2);  // NaN
Math.atanh(-1);  // -Infinity
Math.atanh(0);   // 0
Math.atanh(0.5); // 0.5493061443340548
Math.atanh(1);   // Infinity
Math.atanh(2);   // NaN


For values greater than 1 or less than -1, NaN is returned.

## Polyfill

For $\left|x\right| < 1$, we have $\operatorname \left\{artanh\right\} \left(x\right) = \frac\left\{1\right\}\left\{2\right\}\ln \left\left( \frac\left\{1 + x\right\}\left\{1 - x\right\} \right\right)$ so this can be emulated by the following function:

Math.atanh = Math.atanh || function(x) {
return Math.log((1+x)/(1-x)) / 2;
};