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<title>Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview</title>
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<div class="titlepage"><div><div><h3 class="title">
<a name="math_toolkit.sinc.sinc_overview"></a><a class="link" href="sinc_overview.html" title="Sinus Cardinal and Hyperbolic Sinus Cardinal Functions Overview">Sinus Cardinal and Hyperbolic
Sinus Cardinal Functions Overview</a>
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<p>
The <a href="http://mathworld.wolfram.com/SincFunction.html" target="_top">Sinus Cardinal
family of functions</a> (indexed by the family of indices <code class="literal">a
> 0</code>) is defined by
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb20.png"></span>
</p>
<p>
it sees heavy use in signal processing tasks.
</p>
<p>
By analogy, the <a href="http://mathworld.wolfram.com/SinhcFunction.htm" target="_top">Hyperbolic
Sinus Cardinal</a> family of functions (also indexed by the family of
indices <code class="literal">a > 0</code>) is defined by
</p>
<p>
<span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb22.png"></span>
</p>
<p>
These two families of functions are composed of entire functions.
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<p>
These functions (<a class="link" href="sinc_pi.html" title="sinc_pi">sinc_pi</a>
and <a class="link" href="sinhc_pi.html" title="sinhc_pi">sinhc_pi</a>) are needed
by <a href="http://www.boost.org/libs/math/quaternion/quaternion.html" target="_top">our
implementation</a> of <a href="http://mathworld.wolfram.com/Quaternion.html" target="_top">quaternions</a>
and <a href="http://mathworld.wolfram.com/Octonion.html" target="_top">octonions</a>.
</p>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="emphasis"><em><span class="bold"><strong>Sinus Cardinal of index pi (purple) and
Hyperbolic Sinus Cardinal of index pi (red) on R</strong></span></em></span>
</p></blockquote></div>
<div class="blockquote"><blockquote class="blockquote"><p>
<span class="inlinemediaobject"><img src="../../../graphs/sinc_pi_and_sinhc_pi_on_r.png"></span>
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<td align="right"><div class="copyright-footer">Copyright © 2006-2010, 2012-2014 Nikhar Agrawal,
Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
Holin, Bruno Lalande, John Maddock, Johan Råde, Gautam Sewani, Benjamin Sobotta,
Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
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