# atanh

Inverse hyperbolic tangent

## Description

example

Y = atanh(X) returns the inverse hyperbolic tangent of the elements of X. The function accepts both real and complex inputs. All angles are in radians.

## Examples

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Find the inverse hyperbolic tangent of the elements of vector X. The atanh function acts on X element-wise.

X = [2 -3 1+2i];
Y = atanh(X)
Y = 1×3 complex

0.5493 + 1.5708i  -0.3466 - 1.5708i   0.1733 + 1.1781i

Plot the inverse hyperbolic tangent function over the interval $-1.

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

## Input Arguments

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Hyperbolic tangent of angle, specified as a scalar, vector, matrix, or multidimensional array. The atanh operation is element-wise when X is nonscalar.

Data Types: single | double
Complex Number Support: Yes

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### Inverse Hyperbolic Tangent

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

${\mathrm{tanh}}^{-1}\left(x\right)=\frac{1}{2}\mathrm{log}\left(\frac{1+x}{1-x}\right).$

For complex numbers $z=x+iy$ as well as real values in the regions $-\text{\hspace{0.17em}}\infty and $1, the call atanh(z) returns complex results.