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<h3 class="section">5.7 Complex Hyperbolic Functions</h3>
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<p><a name="index-hyperbolic-functions_002c-complex-numbers-198"></a>
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— Function: gsl_complex <b>gsl_complex_sinh</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005fsinh-199"></a></var><br>
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<blockquote><p>This function returns the complex hyperbolic sine of the complex number
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<var>z</var>, \sinh(z) = (\exp(z) - \exp(-z))/2.
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</p></blockquote></div>
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— Function: gsl_complex <b>gsl_complex_cosh</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005fcosh-200"></a></var><br>
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<blockquote><p>This function returns the complex hyperbolic cosine of the complex number
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<var>z</var>, \cosh(z) = (\exp(z) + \exp(-z))/2.
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</p></blockquote></div>
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— Function: gsl_complex <b>gsl_complex_tanh</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005ftanh-201"></a></var><br>
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<blockquote><p>This function returns the complex hyperbolic tangent of the complex number
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<var>z</var>, \tanh(z) = \sinh(z)/\cosh(z).
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</p></blockquote></div>
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— Function: gsl_complex <b>gsl_complex_sech</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005fsech-202"></a></var><br>
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<blockquote><p>This function returns the complex hyperbolic secant of the complex
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number <var>z</var>, \sech(z) = 1/\cosh(z).
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</p></blockquote></div>
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— Function: gsl_complex <b>gsl_complex_csch</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005fcsch-203"></a></var><br>
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<blockquote><p>This function returns the complex hyperbolic cosecant of the complex
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number <var>z</var>, \csch(z) = 1/\sinh(z).
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</p></blockquote></div>
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— Function: gsl_complex <b>gsl_complex_coth</b> (<var>gsl_complex z</var>)<var><a name="index-gsl_005fcomplex_005fcoth-204"></a></var><br>
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<blockquote><p>This function returns the complex hyperbolic cotangent of the complex
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number <var>z</var>, \coth(z) = 1/\tanh(z).
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</p></blockquote></div>
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