### 5.7 Complex Hyperbolic Functions

Function: gsl_complex gsl_complex_sinh (gsl_complex z)

  This function returns the complex hyperbolic sine of the complex number z, \sinh(z) = (\exp(z) - \exp(-z))/2.

Function: gsl_complex gsl_complex_cosh (gsl_complex z)

  This function returns the complex hyperbolic cosine of the complex number z, \cosh(z) = (\exp(z) + \exp(-z))/2.

Function: gsl_complex gsl_complex_tanh (gsl_complex z)

  This function returns the complex hyperbolic tangent of the complex number z, \tanh(z) = \sinh(z)/\cosh(z).

Function: gsl_complex gsl_complex_sech (gsl_complex z)

  This function returns the complex hyperbolic secant of the complex number z, \sech(z) = 1/\cosh(z).

Function: gsl_complex gsl_complex_csch (gsl_complex z)

  This function returns the complex hyperbolic cosecant of the complex number z, \csch(z) = 1/\sinh(z).

Function: gsl_complex gsl_complex_coth (gsl_complex z)

  This function returns the complex hyperbolic cotangent of the complex number z, \coth(z) = 1/\tanh(z).