atanh

Inverse hyperbolic tangent

collapse all in page

Syntax

Y = atanh(X)

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

collapse all

Open Live Script

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
Open Live Script

Plot the inverse hyperbolic tangent function over the interval -1<x<1.

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

Input Arguments

collapse all

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

More About

collapse all

Inverse Hyperbolic Tangent

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

tanh−1(x)=12log(1+x1−x).

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

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

See Also

| | | |

Introduced before R2006a

MATLAB Documentation

Support