Main Content

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

collapse all

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<1.

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

Figure contains an axes object. The axes object with xlabel x, ylabel atanh(x) contains an object of type line.

Input Arguments

collapse all

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

Data Types: single | double | table | timetable
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

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

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

Version History

Introduced before R2006a

expand all

See Also

| | | |