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  26 <div class="titlepage"><div><div><h3 class="title">
  27 <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
  28       Sinus Cardinal Functions Overview</a>
  29 </h3></div></div></div>
  30 <p>
  31         The <a href="http://mathworld.wolfram.com/SincFunction.html" target="_top">Sinus Cardinal
  32         family of functions</a> (indexed by the family of indices <code class="literal">a
  33         &gt; 0</code>) is defined by
  34       </p>
  35 <p>
  36         <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb20.svg"></span>
  37       </p>
  38 <p>
  39         it sees heavy use in signal processing tasks.
  40       </p>
  41 <p>
  42         By analogy, the <a href="http://mathworld.wolfram.com/SinhcFunction.htm" target="_top">Hyperbolic
  43         Sinus Cardinal</a> family of functions (also indexed by the family of
  44         indices <code class="literal">a &gt; 0</code>) is defined by
  45       </p>
  46 <p>
  47         <span class="inlinemediaobject"><img src="../../../equations/special_functions_blurb22.svg"></span>
  48       </p>
  49 <p>
  50         These two families of functions are composed of entire functions.
  51       </p>
  52 <p>
  53         These functions (<a class="link" href="sinc_pi.html" title="sinc_pi">sinc_pi</a>
  54         and <a class="link" href="sinhc_pi.html" title="sinhc_pi">sinhc_pi</a>) are needed
  55         by <a href="http://www.boost.org/libs/math/quaternion/quaternion.html" target="_top">our
  56         implementation</a> of <a href="http://mathworld.wolfram.com/Quaternion.html" target="_top">quaternions</a>
  57         and <a href="http://mathworld.wolfram.com/Octonion.html" target="_top">octonions</a>.
  58       </p>
  59 <div class="blockquote"><blockquote class="blockquote"><p>
  60           <span class="emphasis"><em><span class="bold"><strong>Sinus Cardinal of index pi (purple) and
  61           Hyperbolic Sinus Cardinal of index pi (red) on R</strong></span></em></span>
  62         </p></blockquote></div>
  63 <div class="blockquote"><blockquote class="blockquote"><p>
  64           <span class="inlinemediaobject"><img src="../../../graphs/sinc_pi_and_sinhc_pi_on_r.png"></span>
  65         </p></blockquote></div>
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  69 <td align="right"><div class="copyright-footer">Copyright &#169; 2006-2010, 2012-2014 Nikhar Agrawal,
  70       Anton Bikineev, Paul A. Bristow, Marco Guazzone, Christopher Kormanyos, Hubert
  71       Holin, Bruno Lalande, John Maddock, Jeremy Murphy, Johan R&#229;de, Gautam Sewani,
  72       Benjamin Sobotta, Thijs van den Berg, Daryle Walker and Xiaogang Zhang<p>
  73         Distributed under the Boost Software License, Version 1.0. (See accompanying
  74         file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
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