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.

Return value

The hyperbolic arctangent of the given 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).

Polyfill

For |x|<1\left|x\right| < 1, we have artanh(x)=12ln(1+x1-x)\operatorname {artanh} (x) = \frac{1}{2}\ln \left( \frac{1 + x}{1 - x} \right) so this can be emulated by the following function:

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

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.

Specifications

Specification
ECMAScript (ECMA-262)
The definition of 'Math.atanh' in that specification.

Browser compatibility

Update compatibility data on GitHub
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ChromeEdgeFirefoxInternet ExplorerOperaSafariAndroid webviewChrome for AndroidFirefox for AndroidOpera for AndroidSafari on iOSSamsung InternetNode.js
atanhChrome Full support 38Edge Full support 12Firefox Full support 25IE No support NoOpera Full support 25Safari Full support 8WebView Android Full support 38Chrome Android Full support 38Firefox Android Full support 25Opera Android Full support 25Safari iOS Full support 8Samsung Internet Android Full support 3.0nodejs Full support 0.12

Legend

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See also