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<title>GNU Scientific Library – Reference Manual: Complex Hyperbolic Functions</title>
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<a name="Complex-Hyperbolic-Functions"></a>
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Next: <a href="Inverse-Complex-Hyperbolic-Functions.html#Inverse-Complex-Hyperbolic-Functions" accesskey="n" rel="next">Inverse Complex Hyperbolic Functions</a>, Previous: <a href="Inverse-Complex-Trigonometric-Functions.html#Inverse-Complex-Trigonometric-Functions" accesskey="p" rel="previous">Inverse Complex Trigonometric Functions</a>, Up: <a href="Complex-Numbers.html#Complex-Numbers" accesskey="u" rel="up">Complex Numbers</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<a name="Complex-Hyperbolic-Functions-1"></a>
<h3 class="section">5.7 Complex Hyperbolic Functions</h3>
<a name="index-hyperbolic-functions_002c-complex-numbers"></a>
<dl>
<dt><a name="index-gsl_005fcomplex_005fsinh"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_sinh</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic sine of the complex number
<var>z</var>, <em>\sinh(z) = (\exp(z) - \exp(-z))/2</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005fcosh"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_cosh</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic cosine of the complex number
<var>z</var>, <em>\cosh(z) = (\exp(z) + \exp(-z))/2</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005ftanh"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_tanh</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic tangent of the complex number
<var>z</var>, <em>\tanh(z) = \sinh(z)/\cosh(z)</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005fsech"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_sech</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic secant of the complex
number <var>z</var>, <em>\sech(z) = 1/\cosh(z)</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005fcsch"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_csch</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic cosecant of the complex
number <var>z</var>, <em>\csch(z) = 1/\sinh(z)</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005fcoth"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_coth</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic cotangent of the complex
number <var>z</var>, <em>\coth(z) = 1/\tanh(z)</em>.
</p></dd></dl>
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