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<a name="Inverse-Complex-Hyperbolic-Functions"></a>
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Next: <a href="Complex-Number-References-and-Further-Reading.html#Complex-Number-References-and-Further-Reading" accesskey="n" rel="next">Complex Number References and Further Reading</a>, Previous: <a href="Complex-Hyperbolic-Functions.html#Complex-Hyperbolic-Functions" accesskey="p" rel="previous">Complex Hyperbolic 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="Inverse-Complex-Hyperbolic-Functions-1"></a>
<h3 class="section">5.8 Inverse Complex Hyperbolic Functions</h3>
<a name="index-inverse-hyperbolic-functions_002c-complex-numbers"></a>
<dl>
<dt><a name="index-gsl_005fcomplex_005farcsinh"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arcsinh</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic arcsine of the
complex number <var>z</var>, <em>\arcsinh(z)</em>. The branch cuts are on the
imaginary axis, below <em>-i</em> and above <em>i</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005farccosh"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arccosh</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic arccosine of the complex
number <var>z</var>, <em>\arccosh(z)</em>. The branch cut is on the real
axis, less than <em>1</em>. Note that in this case we use the negative
square root in formula 4.6.21 of Abramowitz & Stegun giving
<em>\arccosh(z)=\log(z-\sqrt{z^2-1})</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005farccosh_005freal"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arccosh_real</strong> <em>(double <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic arccosine of
the real number <var>z</var>, <em>\arccosh(z)</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005farctanh"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arctanh</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic arctangent of the complex
number <var>z</var>, <em>\arctanh(z)</em>. The branch cuts are on the real
axis, less than <em>-1</em> and greater than <em>1</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005farctanh_005freal"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arctanh_real</strong> <em>(double <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic arctangent of the real
number <var>z</var>, <em>\arctanh(z)</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005farcsech"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arcsech</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic arcsecant of the complex
number <var>z</var>, <em>\arcsech(z) = \arccosh(1/z)</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005farccsch"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arccsch</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic arccosecant of the complex
number <var>z</var>, <em>\arccsch(z) = \arcsin(1/z)</em>.
</p></dd></dl>
<dl>
<dt><a name="index-gsl_005fcomplex_005farccoth"></a>Function: <em>gsl_complex</em> <strong>gsl_complex_arccoth</strong> <em>(gsl_complex <var>z</var>)</em></dt>
<dd><p>This function returns the complex hyperbolic arccotangent of the complex
number <var>z</var>, <em>\arccoth(z) = \arctanh(1/z)</em>.
</p></dd></dl>
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