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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).

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 |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;
};

Specifications

Browser compatibilityUpdate compatibility data on GitHub

Desktop
Chrome Edge Firefox Internet Explorer Opera Safari
atanh 38 12 25 No 25 8
Mobile
Android webview Chrome for Android Firefox for Android Opera for Android Safari on iOS Samsung Internet
atanh 38 38 25 25 8 3.0
Server
Node.js
atanh 0.12

See also

© 2005–2018 Mozilla Developer Network and individual contributors.
Licensed under the Creative Commons Attribution-ShareAlike License v2.5 or later.
https://wiki.developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Math/atanh