These are the hyperbolic functions defined for ComplexBox objects. Apart from sinhcosh, which returns an expression sequence of two ComplexBox objects, each of these computes a ComplexBox representing the value of the named function on the values in the ComplexBox input.

Use the 'precision' = n option to control the precision used in these methods. For more details on precision, see BoxPrecision.

$a≔\mathrm{ComplexBox}\left(0.34+1.1\mathrm{I}\right)$

$a≔⟨\text{ComplexBox:}\text{[0.34 +/- 2.91038e-11]}+\text{[1.1 +/- 1.16415e-10]}\cdot \mathrm{I}⟩$

$b≔\mathrm{ComplexBox}\left(2.3-4.4\mathrm{I}\right)$

$b≔⟨\text{ComplexBox:}\text{[2.3 +/- 2.32831e-10]}+\text{[-4.4 +/- 4.65661e-10]}\cdot \mathrm{I}⟩$

$\sinh \left(b\right)$

$⟨\text{ComplexBox:}\text{[-1.51729 +/- 2.9924e-09]}+\text{[4.79343 +/- 3.07814e-09]}\cdot \mathrm{I}⟩$

$\cosh \left(b\right)$

$⟨\text{ComplexBox:}\text{[-1.5481 +/- 3.04039e-09]}+\text{[4.69802 +/- 3.05774e-09]}\cdot \mathrm{I}⟩$

$\tanh \left(b\right)$

$⟨\text{ComplexBox:}\text{[1.01637 +/- 1.36325e-10]}+\text{[-0.0119527 +/- 2.29125e-11]}\cdot \mathrm{I}⟩$

$\mathrm{sech}\left(b\right)$

$⟨\text{ComplexBox:}\text{[-0.0632704 +/- 1.31738e-10]}+\text{[-0.192006 +/- 1.39835e-10]}\cdot \mathrm{I}⟩$

$\mathrm{csch}\left(b\right)$

$⟨\text{ComplexBox:}\text{[-0.0600215 +/- 1.19315e-10]}+\text{[-0.18962 +/- 1.16933e-10]}\cdot \mathrm{I}⟩$

$\coth \left(b\right)$

$⟨\text{ComplexBox:}\text{[0.983758 +/- 7.77339e-11]}+\text{[0.0115692 +/- 2.25103e-11]}\cdot \mathrm{I}⟩$

$\mathrm{arcsinh}\left(b\right)$

$⟨\text{ComplexBox:}\text{[2.2898 +/- 2.36325e-08]}+\text{[-1.08066 +/- 2.28804e-08]}\cdot \mathrm{I}⟩$

$\mathrm{arccosh}\left(b\right)$

$⟨\text{ComplexBox:}\text{[2.30138 +/- 5.87225e-10]}+\text{[-1.09732 +/- 4.70888e-10]}\cdot \mathrm{I}⟩$

$\mathrm{arctanh}\left(a\right)$

$⟨\text{ComplexBox:}\text{[0.150593 +/- 2.42726e-10]}+\text{[0.858865 +/- 3.60329e-10]}\cdot \mathrm{I}⟩$

$\mathrm{sinhcosh}\left(b\right)$

$⟨\text{ComplexBox:}\text{[-1.51729 +/- 2.9924e-09]}+\text{[4.79343 +/- 3.07814e-09]}\cdot \mathrm{I}⟩,⟨\text{ComplexBox:}\text{[-1.5481 +/- 3.04039e-09]}+\text{[4.69802 +/- 3.05774e-09]}\cdot \mathrm{I}⟩$

The ComplexBox[Hyperbolic], ComplexBox:-sinh, ComplexBox:-cosh, ComplexBox:-tanh, ComplexBox:-sech, ComplexBox:-csch, ComplexBox:-coth, ComplexBox:-arcsinh, ComplexBox:-arccosh, ComplexBox:-arctanh and ComplexBox:-sinhcosh commands were introduced in Maple 2022.

For more information on Maple 2022 changes, see Updates in Maple 2022.