atanh

Inverse hyperbolic tangent

Syntax

Y = atanh(X)

Description

The atanh function operates element-wise on arrays. The function's domains and ranges include complex values. All angles are in radians.

Y = atanh(X) returns the inverse hyperbolic tangent for each element of X.

Examples

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Graph the inverse hyperbolic tangent over the domain -1<x<1.

x = -0.99:0.01:0.99; 
plot(x,atanh(x))
grid on
xlabel('x')
ylabel('y')

More About

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Inverse Hyperbolic Tangent

For real values x in the domain 1<x<1, the inverse hyperbolic tangent satisfies

tanh1(x)=12log(1+x1x).

For complex numbers z=x+iy as well as real values in the regions <z<1 and 1<z<, the call atanh(z) returns complex results.

Extended Capabilities

See Also

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Introduced before R2006a