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    Math.atanh()

    This is an experimental technology, part of the ECMAScript 6 (Harmony) proposal.
    Because this technology's specification has not stabilized, check the compatibility table for usage in various browsers. Also note that the syntax and behavior of an experimental technology is subject to change in future version of browsers as the spec changes.

    Summary

    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

    Example: 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

    Specification Status Comment
    ECMAScript 6 (ECMA-262)
    The definition of 'Math.atanh' in that specification.
    Draft Initial definition.

    Browser compatibility

    Feature Chrome Firefox (Gecko) Internet Explorer Opera Safari
    Basic support 38 25 (25) Not supported 25 7.1
    Feature Android Chrome for Android Firefox Mobile (Gecko) IE Mobile Opera Mobile Safari Mobile
    Basic support Not supported Not supported 25.0 (25) Not supported Not supported iOS 8

    See also

    Document Tags and Contributors

    Contributors to this page: fred.wang, realityking, fscholz, Mingun
    Last updated by: Mingun,