4.9 Complex hyperbolic trigonometric functions
The standard hyperbolic trigonometric functions are supported for complex numbers.
complex cosh(complex z)
Return the complex hyperbolic cosine of z,
\[
\textrm{cosh}(z)
= \frac{\exp(z) + \exp(-z)}
{2}.
\]
Available since 2.28
complex sinh(complex z)
Return the complex hyperbolic sine of z,
\[
\textrm{sinh}(z)
= \frac{\displaystyle \exp(z) - \exp(-z)}
{\displaystyle 2}.
\]
Available since 2.28
complex tanh(complex z)
Return the complex hyperbolic tangent of z,
\[
\textrm{tanh}(z)
\ = \ \frac{\textrm{sinh}(z)}
{\textrm{cosh}(z)}
\ = \ \frac{\displaystyle \exp(z) - \exp(-z)}
{\displaystyle \exp(z) + \exp(-z)}.
\]
Available since 2.28
complex acosh(complex z)
Return the complex hyperbolic arc (inverse) cosine of z,
\[
\textrm{acosh}(z)
= \log(z + \sqrt{(z + 1)(z - 1)}).
\]
Available since 2.28
complex asinh(complex z)
Return the complex hyperbolic arc (inverse) sine of z,
\[
\textrm{asinh}(z)
= \log(z + \sqrt{1 + z^2}).
\]
Available since 2.28
complex atanh(complex z)
Return the complex hyperbolic arc (inverse) tangent of z,
\[
\textrm{atanh}(z)
= \frac{\log(1 + z) - \log(1 - z)}
{2}.
\]
Available since 2.28