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asinh

Inverse hyperbolic sine

Y = asinh(X)

Description

Y = asinh(X) returns the inverse hyperbolic sine for each element of X.

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

Examples

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Graph the inverse hyperbolic sine over the domain .

x = -5:.01:5;
plot(x,asinh(x))
grid on
xlabel('x')
ylabel('y')

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Inverse Hyperbolic Sine

For real values $x$ in the domain of all real numbers, the inverse hyperbolic sine satisfies

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

For complex numbers $z=x+iy$, the call asinh(z) returns complex results.