Math.atanh()

The Math.atanh() function returns the inverse hyperbolic tangent of a number. That is,

∀ x ∊ ( − 1 , 1 ) , 𝙼𝚊𝚝𝚑.𝚊𝚝𝚊𝚗𝚑 ( 𝚡 ) = artanh ( x ) = the unique  y  such that  tanh ( y ) = x = 1 2 ln ( 1 + x 1 − x ) \begin{aligned}\forall x \in ({-1}, 1),;\mathtt{\operatorname{Math.atanh}(x)} &= \operatorname{artanh}(x) = \text{the unique } y \text{ such that } \tanh(y) = x \&= \frac{1}{2},\ln\left(\frac{1+x}{1-x}\right)\end{aligned}

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Syntax

Math.atanh(x)

Parameters

x

A number between -1 and 1, inclusive.

Return value

The inverse hyperbolic tangent of x. If x is 1, returns Infinity. If x is -1, returns -Infinity. If x is less than -1 or greater than 1, returns NaN.

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

Specifications

Specification
ECMAScript Language Specification
# sec-math.atanh

Browser compatibility

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See also